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Caking of amorphous powders — Material aspects, modelling and applications
Powder Technology 206 (2011) 112–121
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Powder Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p ow t e c
Caking of amorphous powders — Material aspects, modelling and applications Markus Hartmann a,⁎, Stefan Palzer b a b
Nestlé Product Technology Centre, Lange Straße 21, 78224 Singen, Germany Nestlé Research Center, Vers-Chez-Les-Blanc, 1000 Lausanne 26, Switzerland
a r t i c l e
i n f o
Available online 24 April 2010 Keywords: Caking Amorphous powders Sintering Time consolidation
a b s t r a c t Caking of powders and bulk granules and adhesion of powders on equipment surfaces is a serious problem in the food, chemical and pharmaceutical industries. While caking of crystalline particles is tackled only briefly, this publication deals mainly with caking of water-soluble amorphous particles. Caking of amorphous particles starts with stickiness of the powder surface and can result in a collapse of the powder structure. The powder bulk turns from a free flowable powder bulk composed of single particles into a massive block. The material aspects (hygrocapacity, hygrosensitivity and viscosity) of water-soluble amorphous materials and sintering are discussed. The increase of the sinter bridges during caking could be modelled through the known sinter equations and measured by carrying out experiments in a ring shear cell. The calculated sinter bridge diameter could be correlated with the strength of the caked powder bulk measured in a ring shear tester. © 2010 Elsevier B.V. All rights reserved.
1. Introduction
1.1. Powders affected by caking
A number of powders are agglomerated to provide superior dispersibility. They should rehydrate and/or dissolve quickly without forming lumps. In addition, agglomeration improves the flowability of powders significantly. Another aspect is that more and more consumers prefer agglomerated to powdery products because of their more intense colour, the different visual aspect and the reduced dustiness. Sometimes also undesired agglomeration effects can be observed while processing food powders. The following undesired agglomeration phenomena are observed during handling, processing and storing of powders:
Time consolidation during storage, often referred to as caking, is a major problem when handling powders. Caking requires grinding to transform the powder cake into single particles or agglomerates. But in some cases, however, a grinding procedure is not effective because the structure of the agglomerates will be destroyed. Sometimes even whole silos are blocked by caked powder and the content of the silos can only be removed manually by mining techniques. Furthermore, the quality of packed powder products is negatively affected by caking during storage or transport. To reduce processing costs for posttreatment and to increase the quality of the end products such caking has to be avoided. Mainly powders which contain a major amount of water-soluble amorphous substances are sensitive to caking. The following amorphous food powders tend to consolidate during storage: powdered vegetable, yeast and meat extracts, hydrolysed fish proteins, meat powders, hydrolysed plant proteins, flavour powders containing such hydrolysates, maltodextrins and sugar syrups, organic acids used as food additives, spray-dried dairy powders, brown sugar and all food powders containing a significant amount of the mentioned ingredients [1–4]. In the chemical and pharmaceutical industries, e.g. urea, dextrose, citric acid and other organic acid are prone to caking. The main mechanism responsible for caking of such powders is sintering. Occasionally, also caking of fine, water-soluble crystalline powders is observed. The reason for caking of such crystalline powders is a partial dissolution and re-crystallisation of the crystalline substance [5–7]. In some cases also a partial melting and re-crystallisation of triglycerides can be the reason for caking of fat-containing powders. The chemical composition, the supra-molecular structure and the micro-structure as well as external factors like stress, humidity and
⋅ Stickiness and lumping of amorphous powders at high humidity and/or high temperature ⋅ Collapse of a fluid bed at high air humidity ⋅ Lumping of carrier powders due to over-saturation with nondissolving liquids ⋅ Post-hardening of amorphous or crystalline tablets during storage ⋅ Caking of amorphous or crystalline powders during storage ⋅ Soiling of equipment. With the exception of lumping due to an over-saturation with non-dissolving liquids all these undesired agglomeration phenomena can be explained with accelerated sinter processes or dissolution of crystalline substances at high relative humidity. This study focuses mainly on the caking of amorphous powders during storage.
⁎ Corresponding author. E-mail address: [email protected] (M. Hartmann). 0032-5910/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2010.04.014
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temperature are decisive for the caking mechanism and the caking kinetics. Fig. 1 shows scanning electron microscopic pictures of different caked food powders containing major amounts of amorphous substances. Several sinter bridges (highlighted by white circles) are clearly visible. In the current article the mechanisms and kinetics of caking will be discussed, test methods will be introduced and an approach for predicting the intensity of caking is presented. 2. Basics 2.1. Caking mechanisms Several mechanisms can lead to a time consolidation of powders [9]. It will be demonstrated in the frame of the current study that mainly sintering is responsible for the observed caking of amorphous food powders. Macroscopically, several stages of caking can be distinguished (Fig. 2). In the initial phase of the process the powder starts to get sticky and particles adhere to each other which leads to a reduced flowability of the powder bulk (which is often described as “stickiness”). They form brittle lumps and with progressing sintering a mechanically stable powder cake is obtained. In a later phase of sintering, particles missing a stabilising inner structure, which are built of non-dissolving substances lose their structure and shape. The powder structure collapses, open pores in the particle package disappear and, finally, a highly viscous, foam-like, amorphous melt is obtained. The shape of some particles (e.g. dehydrated vegetable pieces) is preserved due to an insoluble matrix (e.g. composed of cellulose, silicate, fat or proteins) and, thus, no collapse of the powder structure is observed.
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When water-soluble amorphous substances are stored in an environment with a high humidity, they absorb water and, thus, their viscosity decreases. Although sintering is accelerated due to the decreasing viscosity, the tensile strength of the sinter material/ bridge decreases with increasing water content. Due to the progressing absorption of water the strength of the powder cake first increases and in a later phase of the progress decreases again. Explanation: At low moisture content or in the early phase of the sintering process the diameter of the sinter bridges limits the stability of the particle cake. The growing diameter of the sinter bridges leads to an increasing strength of the cake. With progressing moisture absorption the viscosity of the bridge decreases and, thus, the strength of the powder cake decreases again. Finally, the powder structure collapses and a pasty mass is obtained. The viscosity of amorphous substances is also reduced at higher temperatures leading to an accelerated sintering of the particles and a steadily increasing strength of the powder cake. Crystalline water-soluble powders behave differently while they are exposed to a high humidity or temperature. If their critical humidity is temporarily exceeded, they will partially dissolve. The formed low-viscosity liquid bridges are rather fragile. However, a stable powder cake can be formed if the absorbed water evaporates again enabling a re-crystallisation of the dissolved substance. Accordingly, caking of crystalline powders stored in closed containers can be induced by condensation and evaporation of moisture due to temperature variations. The condensate builds liquid bridges between the particles. After a short time span the liquid forming these bridges is saturated with the dissolving substance. If the water is evaporated out of this liquid later, stable bridges between the particles are formed.
Fig. 1. Scanning electron microscopic pictures of caked powders (sinter bridges highlighted by white circles) [8].
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Fig. 2. Different phases of the sintering process.
Finally, also melting and following re-crystallisation of fat (e.g. cocoa, palm fat, etc.) due to temperature variations can cause caking of fat-containing powder masses. 2.2. Adhesion principles relevant for caking Increasing adhesion forces between particles are prerequisite for agglomeration and caking. Adhesion can be linked to the development of material bridges or increasing Van der Waals forces between neighbouring particles. For caking of water-soluble amorphous particles the following adhesion mechanisms are relevant: ⋅ ⋅ ⋅ ⋅ ⋅
Increasing Van der Waals forces due to plastic deformation Increasing Van der Waals forces due to visco-elastic deformation Liquid bridges with low viscosity Amorphous bridges with high viscosity Crystalline solid bridges
In specific cases also inter-locking might contribute to the tensile strength of powder bulks. Electrostatic forces are not relevant for caking since the particles are in continuous contact. Only with nonconducting plastic particles electrostatic charges could cause caking problems, but no relevant experiments and results are known [10]. The above-mentioned mechanisms increase the adhesion force F holding two neighbouring particles together. The tensile strength of the powder cake depends on the strength of these adhesion forces between the primary particles. According to Rumpf [11] the tensile strength of a powder cake composed of spheres with a diameter a can be estimated through the following equation. σt =
1−ε F ⋅k⋅ a2 k⋅ε≈3:1≈π: π a
ð1Þ
Fa is the adhesion force between two particles (spheres), ε the porosity of the agglomerate and k represents the coordination number of the primary particles building the agglomerate. For spherical particles k is approximately equal to π/ε [11]. In the following, the different adhesion mechanisms and their relevance for the caking of particles are discussed/explained. 2.3. Increased Van der Waals forces by particle deformation Adhesion between particles can be linked to increasing Van der Waals forces. The Van der Waals forces between two deformed particles can be estimated according to Lifshitz [12] and Hamaker [13]. Except for plastically deformable particles most caking processes are not caused by increasing Van der Waals forces. However, plastic or visco-elastic deformation of particles leading to increasing contact points and decreasing distance between neighbouring particle surfaces might enhance caking caused by sintering or dissolution and following re-crystallisation. 2.4. Hygrocapacity of water-soluble substances The water activity at a given moisture content is a function of the chemical composition, the supra-molecular structure and the microstructure of the powder. The sorption isotherm describes the relation
between water content and water activity for a given temperature. The sorption isotherm of a product can be modelled according to Guggenheim, Anderson and deBoer (GAB) [14] or according to Brunauer, Emmett and Teller (BET) [15]. Establishing the sorption isotherm of a crystalline (e.g. crystalline lactose, NaCl) and water-soluble material it can clearly be seen that the water capacity of crystalline materials is rather low. Below a critical relative humidity leading to dissolution of the crystalline substance a significant quantity of water can only be stored in the crystal matrix in form of crystal water. Apart from crystal water nearly no water can be stored within the crystalline structures. Crystalline substances do not absorb water until they dissolve at a specific relative humidity (e.g. 73– 75% RH for NaCl or 83–85% RH for sucrose) [16]. Amorphous hydrophilic substances behave differently when they are exposed to an increasing relative humidity. They absorb increasing amounts of water with increasing relative humidity. The water molecules are stored within the free volume left within the amorphous matrix. In contrast to crystalline materials a critical humidity at which particles might dissolve cannot be defined. With increasing water content the viscosity of the amorphous melt decreases and, finally, a diluted solution of the substance is obtained. Due to differences in the hygrocapacity observed between watersoluble amorphous and crystalline solids, re-crystallisation of the metastable amorphous form liberates moisture. The liberated water affects the crystallisation velocity of the remaining amorphous fraction. This might also lead to caking of the powder. 2.5. Effects of water on water-soluble amorphous substances (hygrosensitivity) Changes in the physico-chemical properties of materials linked to changing water content are referred to as hygrosensitivity. Amorphous and crystalline substances demonstrate a significantly different hygrosensitivity. Crystalline substances preserve their mechanical properties with increasing humidity until they dissolve at a substance-specific critical relative humidity of the surrounding air. In most cases the resulting solution has a low or medium viscosity. Such crystalline watersoluble substances, amongst them various minerals, mono- and disaccharides, do not provide a high viscosity due to their low molecular weight. Amorphous water-soluble materials do not dissolve like crystalline substances as their water content increases. They already have a liquidlike supra-molecular structure although they are perceived as solids. Water does not dissolve amorphous particles, but it migrates into the amorphous molecular matrix. Water stored in the amorphous matrix has a plastifying effect on the amorphous structure. The viscosity and elasticity of the material decrease with increasing water content. In parallel the glass transition temperature decreases due to the absorption of water. The well-known Gordon and Taylor equation (Eq. 2) describes the dependency between the glass transition temperature Tg and the water content w (as a percentage on wet basis) of an amorphous watersoluble substance.
Tg =
ð1−wÞ⋅Tg;s + w⋅k⋅Tg;w : ð1−wÞ + w⋅k
ð2Þ
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Tg,s is the glass transition temperature of the dry solid, Tg,w represents the glass transition temperature of pure water commonly considered equal to −135 °C. Although the Gordon and Taylor constant k [17] can be calculated theoretically (equations not shown), k is mostly used as a fitting parameter after Tg measurement. The k values of different materials can also be found in literature. In a powder mix in equilibrium the water activity is the same for all components although they might have different individual water contents. Therefore, it is useful to measure the glass transition temperature of powders depending on their water activity in order to identify the most critical component in the blend. Obviously, the powder fraction with the lowest glass transition temperature of the mix is the most sensitive component within the blend. Combining the GAB equation and Eq. 2, the dependence of the glass transition temperature on the water activity can be modelled according to Eq. 3 [18,19].
contact with amorphous particles, crystalline substances exhibit a lower deliquescence point, i.e. they start earlier to dissolve, coinciding with the glass transition of the amorphous component in the mix [21]. Dissolution of KCl or NaCl attracts a great amount of water in the powder mix and, as a consequence, the amorphous substance absorbs more water. Consequently, the mix of an amorphous and a crystalline substance has a greater water sorption capacity and is plasticized faster than the pure amorphous substance. Its glass transition temperature decreases strongly according to the Gordon–Taylor equation. With increasing water content the function Tg = f(aw) for mixes of amorphous and crystalline particles is not linear anymore in the water activity range between 0.2 and 0.7. It presents an inflection point coinciding with the glass transition where the crystalline material starts to dissolve. At this point the Tg = f(aw) curve drops sharply [22].
ð1−K⋅aw Þ⋅ð1 + ðC−1Þ⋅K⋅aw Þ⋅Tg;s + k⋅wm ⋅C⋅K⋅aw ⋅Tg;w Tg aw;22 ∘C = : ð1−K⋅aw Þ⋅ð1 + ðC−1Þ⋅K⋅aw Þ + k⋅wm ⋅C⋅K⋅aw
2.6. Effects of the water content and the temperature on the viscosity
ð3Þ A similar approach was taken by Khalloufi et al. [20] to describe the dependency of the glass transition temperature on the water activity of different fruit powders. Plotting the function Tg = f(aw) a sigmoidal-shaped curve, which can be approximated in the water activity range from 0.2 to 0.7 by a straight line, is observed. Fig. 3 shows the glass transition temperature and the water content of dextrose syrup (DE 21) and a tomato powder depending on their water activity. However, in the case of binary powder mixtures of crystalline and water-soluble amorphous particles, it has been shown with maltodextrin/dextrose syrup (DE 6, 21, 47) together with KCl or NaCl that the behaviour of the mix follows not a sorption isotherm obtained by a linear combination of both single sorption isotherms. In fact, in
Most substances, amongst them various amorphous water-soluble materials, deform visco-elastically. The deformation and relaxation behaviour of food materials can be described through various viscoelastic models. Depending on the nature of the stress/strain applied either the storage and loss modulus or the elasticity and the viscosity are included as material parameters. All these material parameters depend on the temperature and the plasticiser content of the viscoelastic substance as well as on the applied strain rate. Because of the relatively long time required for caking only the viscosity is relevant and the elasticity can be neglected. To model the temperature dependence of visco-elastic material parameters the time–temperature superposition principle is applied [23]. According to this principal visco-elastic data (like viscosity, compliance or modulus) obtained for one temperature and time or frequency can be extrapolated to a different temperature by multiplying the logarithmic time or frequency values with a temperature-
Fig. 3. Glass transition temperature and water content of dextrose syrup (DE 21) depending on the water activity (DSC onset of the second scan at a heating rate of 5 °C/min; water content analysed according to Karl–Fischer) [19].
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dependent shift factor. Especially in the case of the viscosity η it can be shown that the following equation is valid: −C⋅ T−Tg η for 0 K≤ T−Tg ≤100 K: log = ηg B + T−Tg
ð4Þ
This is a frequently applied form of the Williams, Landel and Ferry (WLF) equation where Tg is the reference temperature and C and B (in K) are constant factors [24,25]. 2.7. Sinter bridges between amorphous particles In general, in literature sintering is not considered as an important adhesion mechanism. This study demonstrates that sintering is in fact a ubiquitous process of striking importance for various powder processing operations. In the authors' opinion sintering is the main adhesion mechanism for many desired and undesired agglomeration processes related to powders. Especially in agglomeration of amorphous powders at elevated humidity or temperature the adhesion forces between the particles are generated by growing sinter bridges. In the following paragraph the mechanism of sintering is explained. All materials have the tendency to reduce their free surface area which is associated with the specific energy of the system. Like lowviscosity liquid droplets, amorphous particles tend to adopt a spherical shape. By bringing two amorphous particles into contact with each other, they can be considered as one new single particle. To minimise the free surface area of this newly created particle, molecules are transported to the contact point between the two primary particles (Fig. 4). Such a process is called sintering. The driving force for the sinter process is the difference between the capillary pressure at the contact point between the particles and the laplace pressure in the volume of the two initial particles. Eq. 5 enables the calculation of this pressure difference for two spherical primary particles attached to each other. Δpc = pc1 −pc2 =
4⋅γ 2 1 −γ ⋅ − : a x s
ð5Þ
pc1 represents the capillary pressure in the volume of the primary particles, pc2 is the capillary pressure in the sinter bridge and a is the diameter of the primary particles. γ is the surface tension of the amorphous substance, x the diameter of the sinter bridge and s represents the radius of the curvature of the meniscus of the viscous bridge. Since the capillary pressure is directly linked to the vapour pressure in the continuous gas phase surrounding the particles, a gradient of the vapour pressure across the particles exists. Based on these local differences in capillary and vapour pressure different molecular transport mechanisms are observed. The relevant literature [26–28] distinguishes between a transport through the vapour phase, surface diffusion and volume diffusion (Fig. 4). Diffusion of molecules inside the particles, sometimes also referred to as viscous flow, seems to be the relevant mechanism for caking of most amorphous water-soluble substances caused by sintering.
The kinetics of such transport processes strongly depends on the diffusion coefficient which is a function of viscosity. As discussed, the viscosity of amorphous solids depends on the temperature as well as on the plasticiser content of the material. Thus, sintering of amorphous water-soluble particles can be controlled by adjusting the temperature and/or the water content of system. 2.8. Modelling sinter bridges between amorphous particles For modelling the sintering of organic particles by viscous flow, Frenkel [29] published the following equation. Assuming spherical particles of a diameter a, the diameter of the sinter bridge x can be calculated depending on the sinter time t, the surface tension γ and the viscosity η. x2 a
=
1 γ t : 6⋅ a⋅η
ð6Þ
Alternatively, the sinter kinetics can be predicted according to Rumpf et al. [30]. Assuming a punctual contact between the particles and neglecting changes in the particle geometry during sintering, Rumpf et al. modelled the viscous flow based on the Navier–Stokes equation. Ft represents the force with which particles are pressed together. x2 a
=
4 γ 2⋅Ft t ⋅ + ⋅η: 2 5 a 5⋅π⋅a
ð7Þ
Both equations are valid only for the initial phase of the sinter process. For non-spherical particles the relevant radius a has to be estimated based on the curvature radius at the contact point between the particles. A prerequisite for a sinter process is a molecular contact between the particles. A moderate force (e.g. caused by the weight of the particles) pressing the particles together ensures a continuous contact between the particles during sintering. In most systems variations in surface tension with increasing solvent content or presence of surface ingredients are limited. Hence, in most applications the viscosity which might vary by magnitudes governs the sinter kinetics [31,32]. As already elaborated the viscosity of water-soluble amorphous substances depend on the moisture (plasticiser) content w and the temperature T. Combining Eqs. 4 and 7 and considering the fact that due to sorption or desorption processes the humidity of the amorphous substance might change as a function of time, Eq. 8 is obtained. x2 a
tmax
= ∫ t =0
−C ⋅ðT−Tg ðt ÞÞ 4 γ 2⋅Ft 1 B+ T−T ðt Þ + ⋅ ⋅ ⋅10 ð g Þ ⋅dt 5 a 5⋅π⋅a2 ηg
where tmax is the time available for the sinter process.
Fig. 4. Sintering mechanisms.
ð8Þ
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By combining Eq. 8 with Eq. 1 the tensile strength of sintering agglomerates can be estimated. tmax −C ⋅ðT−Tg ðt ÞÞ ð1−εÞ⋅π 4 γ 2⋅Ft 1 σs ðT; w; ωÞ⋅ ∫ + 10 B+ ðT−Tg ðtÞÞ ⋅dt: σt = ⋅ ⋅ ⋅ ⋅ 2 ε 5 a ηg 5⋅π⋅a t=0 ð9Þ However, in practice it remains difficult to predict the tensile strength of sintered agglomerates because of the geometrical diversity of primary particles and the visco-elastic nature of the built sinter bridges. According to Downtown et al. [33] a significant adhesion force F between particles should be observed if the diameter ratio x/a exceeds a value of 0.01. Wallack and King [2] reported a value x/a of 0.1 required for adhesion. For practical applications these empirical value was found to be useful in order to estimate whether a stable powder cake can be expected. 2.9. Methods for measuring caking One possibility for measuring caking is to fill powder samples in a container and store this container under a certain temperature and relative humidity. After a defined time the evaluation is done visually by using a qualitative evaluation scale. These results are only meaningful for this special setup and hardly transferable to other situations and dimensions. More advanced caking test methods include time consolidation trials. The powder sample is stored under defined conditions and the mechanical strength of the obtained powder cake is measured. One of the more scientific time consolidation tests is the uniaxial tester which exists in different design variations. A sample is filled into a cylinder, consolidated without wall friction by applying normal consolidating stress σ1,c and stored under a defined temperature and relative humidity. After removing the cylinder the sample is loaded again with an increasing normal stress up to the point of failure, leading to the unconfined yield strength σc [10,34]. The disadvantage of a uniaxial tester is that there is no consolidation of the bulk solids sample up
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to steady state flow and that it is not possible to measure the yield loci (τ = f (σc)) of powders as it is the case in a ring shear cell (see below). A more accurate and reproducible way to quantify caking are time consolidation experiments performed in ring shear cells. After preconsolidation under steady flow conditions and storage under defined settings the strength of the powder cake within the ring cells is measured by shearing [35]. One of the major drawbacks of time consolidation experiments in the almost closed cells is the hampered exchange of moisture between the air and the sample during the consolidation phase. Contrary to such test conditions, moisture absorption and time consolidation are often parallel processes which are difficult to separate from each other in practice. To quantify the caking intensity the unconfined yield strength σc of the initial and the stored powder have to be compared with each other. The increase in unconfined yield strength σc or the decrease of the flow factor ffc [36] can both be used for quantifying the degree of caking. Empirically, it has been found that strong caking corresponds to an increase in unconfined yield strength of more than 1000 Pa [37]. Fig. 5 shows the shift of the yield locus and the increase in unconfined yield strength σc of yeast extract with a water activity of 0.17 stored for 4 days at 10 °C above its glass transition temperature. The yeast extract shown exhibits a strong caking corresponding to an increase of unconfined yield strength of roughly 1000 Pa. 3. Material and methods For the trials spray-dried dextrose syrup with a dextrose equivalent (DE) of 20–23 (DE 21, Roquette GmbH, Frankfurt, Germany) was used. The dextrose syrup powder has a water content of 4% (db) (water activity aw = 0.18) and a medium particle size x50,3 of 150 µm. Furthermore, spray-dried tomato powder (Transa/Badojoz/Spain and Conesa/Villafranco del Guadiana Badajoz/Spain) produced on a Filtermat® spray dryer was used for the time consolidation experiments. In addition, a series of time consolidation trials was performed with powdered yeast extract (Biospringer, Maison-Alsort, France).
Fig. 5. Initial shear locus of yeast extract and shear locus of yeast extract stored for 4 days at 10 °C above Tg (ring shear tester; T = 25 °C; aw = 0.17; t = 96; consolidation stress 1200 Pa).
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The glass transition temperature was measured by Differential Scanning Calorimetry (DSC) with a heating gradient of 5 °C/min (STARe SW 8.10 from Mettler-Toledo GmbH, Switzerland). The onset of the resulting thermogram was defined to be the glass transition temperature Tg. The water activity was measured using a capacitive sensor equipped with hygroscopic material (HygroPalm AW1 from Rotronic, Ettlingen, Germany) at a temperature of 20–25 °C. The water content of the samples was analysed by titration according to the method of Karl–Fischer. The time consolidation measurements were performed using a ring shear tester (RST-01.pc from Schulze-Schüttgutmesstechnik, Wolfenbüttel, Germany). Three samples were stored at different relative humidity for one week. The preconditioned samples were filled into a ring cell and the cover of the cell was loaded with a defined weight. After the consolidation time the flowability of the product was measured in the ring shear cell tester. The yield locus was established and the unconfined yield stress was determined. By definition a sample providing an unconfined yield strength of more than 1000 Pa is considered to be caked. For the scanning electronic microscopy (SEM) images of crystals about 10 g of NaCl crystals (X50,3 = 420 µm) were filled in a thin layer in small petri-dishes and stored for different periods (1, 2 and 5 days) at 25 °C and various relative humidity in desiccators containing saturated salt solutions from Fluka Chemie AG of known values (62% RH, NH4NO3; 75% RH, NaCl; KNO3, 88% RH). After the treatment the samples were dried in a chamber with 20 °C at 20% RH for several days and observed with a SEM.
4. Results and discussion 4.1. Sintering of pairs of single amorphous particles The sintering of two amorphous dextrose syrup particles (DE 21) which were exposed to a relative humidity of 70% was investigated.
Both particles were placed on a silanised hydrophobic glass plate and the relative humidity of the surrounding air was adjusted by a saturated salt solution. Fig. 6 shows the water content of the particles depending on the storage time and images of the sinter bridge developed between the two particles. The absorbed moisture leads to a decreasing viscosity of the amorphous matrix and, thus, sintering is accelerated. A stable sinter bridge is already obtained after 3 to 6 h of storage. Finally, the two particles coalesce and form a single viscous droplet. Fig. 7 shows a comparison of the calculated sinter bridge diameter with the measured sinter bridge diameter between two dextrose syrup (DE 21) particles stored at 30 °C and 70% RH values for bridge diameter corresponding to Fig. 6. The calculated kinetics of sintering is in good agreement with the measured increase of the diameter of the sinter bridge. Despite the various assumptions and simplifications made, Eq. 8 allows a satisfying prediction of the sinter kinetics of amorphous water-soluble particles. Possibly the accuracy of the prediction can be further improved by taking into account a moisture gradient along the particle diameter. Establishing the Navier–Stokes equation for a pair of sintering particles the viscosity gradient corresponding to the moisture distribution inside the particles has to be considered.
4.2. Caking of a bulk of amorphous particles As already mentioned, different mechanisms might be responsible for the observed caking of powders. In case of amorphous, water-soluble solids, sintering is supposed to be the main mechanism responsible for increasing adhesion forces between the particles. Assuming a constant viscosity of the amorphous substance forming the bridge, the unconfined yield strength should be a function of the average sinter bridge diameter (Eq. 7). In Fig. 8 the unconfined yield strength of spray-dried tomato powder, dextrose syrup and hydrolysed whey permeate is plotted against the calculated squared ratio between the diameter of the sinter bridge and the particle diameter (x/a)2. The ratio (x/a)2 is
Fig. 6. Moisture content and images of two dextrose syrup particles (DE 21) stored at 30 °C and 70% RH.
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Fig. 7. Comparison between calculated and measured sinter bridge/particle diameter ratio for pairs of spray-dried dextrose syrup particles (DE 21) stored at 30 °C and 75% RH (Tg = −4 °C; γl,g = 70 mNm, η = 106 Pa s) [31].
calculated through Eq. 7. According to the results obtained, the unconfined yield strength increases with increasing ratio (x/a)2 more or less linearly for (x/a)2 values exceeding 0.05. This result is in agreement with the studies of Downtown et al. [33], Wallack and King [2] and Aguilera et al. [3] who observed a caking if the ratio between the radius of the sinter bridge and the particle diameter x/a exceeds a value of 0.01 to 0.1. According to Eq. 9 the unconfined yield strength of the powder cake should theoretically increase linearly with (x/a)2. Such
correlation can be confirmed for values (x/a)2 exceeding 0.05 (Fig. 8). In the initial phase of the storage process the growth of the sinter bridge might be delayed because of the incomplete contact between the particles. The gap at the contact points between single particles has to be bridged before the development of the bridge is initiated. Such a delay of the sinter process might explain why a theoretical value of (x/a)2 of 0.05 has to be exceeded before a linear increase in tensile strength is observed. Another explanation is that the initial powder is
Fig. 8. Measured unconfined yield strength of tomato powder, dextrose syrup DE 21 and hydrolysed whey permeate plotted against ratio (x/a)2 (Eq. 9) [8,38].
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in disequilibrium with the surrounding air and in the early phase of the experiments moisture still migrates into the particles. On the one hand, the moisture content on the particle surface is used for calculating the diameter of the sinter bridge. On the other hand, also the viscosity of the particle inside is relevant for sintering by viscous flow. Hence, a calculation based on the initial moisture content of the particle surface yields for the beginning of the process a too large bridge diameter. Apparently, the risk of caking can be predicted through the calculated sinter bridge diameter. It is important to remember that Eq. 9 used for calculating the theoretical ratio (x/a)2 is valid only for the initial phase of the sintering process. Furthermore, dehydrated cell structures, which bind the strongly plastified amorphous substance through capillary forces or crystallisation processes, might limit the availability of amorphous material for building the sinter bridge. Thus, the real growth kinetics of the sinter bridge might deviate significantly from the predicted growth rate. Despite these effects, it has been demonstrated that the risk of caking of water-soluble amorphous powders can be predicted by calculating the theoretical sinter bridge diameter. When the calculated x/a value exceeds 0.01 caking of the powder can be expected. 4.3. Caking of a bulk of crystals Crystalline particles show no time consolidation at constant moisture content. However, if the relative humidity of the air temporarily or locally exceeds the critical humidity of the crystalline substance, a partial superficial dissolution is observed. For sodium chloride this critical relative humidity leading to dissolution is in the range of 73–76% RH. As it can be seen in Fig. 9 sodium chloride crystals
stored at 60–62% and 71–73% RH for 120 h are not dissolving. Contrarily, sodium chloride crystals exposed to a relative humidity of 80–83% RH for 120 h dissolve partially and a saturated sodium solution builds liquid bridges between the cubic crystals. When decreasing the relative humidity the generated liquid bridges dry out again. During the drying the sodium chloride dissolved within the liquid crystallizes in form of small cubic fractal structures. Some of these cubic crystals build bridges between the larger initial crystals. Finally, a porous cake built of larger crystals which are connected by re-crystallized sodium chloride remain. When exposing a thick layer of crystals to an elevated relative humidity the outer layer of crystals dissolves first. The generated saturated sodium chloride solution builds a liquid film limiting diffusion of moisture into the core of the particle bulk. Accordingly, a caked powder layer is obtained after decreasing the relative moisture again. Exposing crystalline sodium chloride for a longer time to a relative humidity above 75% leads to the entire dissolution of the material. Caking of crystalline material might be observed especially when storing the powder in closed storage containers excluding a convective moisture transfer to the environment. To estimate the risk of caking, it is sufficient to analyse the expected variations in temperature and to estimate the corresponding changes in relative humidity of the air through the Mollier diagram for humid air. If the predicted maximum relative humidity inside the powder bulk exceeds the critical humidity of the crystalline substance, the probability of caking is high. 5. Conclusion and outlook Generally, it seems to be highly feasible to predict the caking of crystalline and amorphous water-soluble particles. For amorphous
Fig. 9. Scanning electronic microscope images of NaCl crystals stored at different relative humidity and different times.
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substances the viscosity of the material is estimated by considering the temperature and the moisture content. Based on the viscosity the kinetics with which the diameter of the sinter bridge increases with time can be predicted. The calculated average sinter bridge diameter could be linked qualitatively to the strength of the powder cake. Further improvement of the precision of this estimation is possible by considering the moisture exchange between particles and the surrounding air. Furthermore, the tridimensional distribution of the bridge diameters between the particles of a caked powder bulk has to be considered for establishing a relation between sinter bridge diameter and the unconfined yield strength. Caking of crystalline powders is simply linked to a partial dissolution and re-crystallisation of the crystalline substance. Such caking is only observed while temporarily exceeding the substancespecific critical relative humidity. Nomenclature list a Diameter of a sphere/particle aw Water activity B Constant factor in the WLF equation C Constant factor in the WLF equation Flow factor ffc F Adhesion force Adhesion force between two particles Fa Ft Force with which particles are pressed together k Coordination number k Gordon and Taylor constant K Parameter (GAB equation) Capillary pressure in the volume of primary particles pc1 Capillary pressure in a sinter bridge pc2 Plastic yield pressure ppl s Radius of the curvature of a meniscus of a bridge t Sinter time Time available for a sinter process tmax T Temperature Glass transition temperature Tg Glass transition temperature of a dry solid Tg,s Glass transition temperature of pure water Tg,w w Water/plasticiser content x Diameter of a sinter bridge γ Surface tension ε Porosity η Viscosity Unconfined yield strength σc Consolidating stress (steady flow conditions) σ1 Consolidating stress (uniaxial tester) σ1,c
[m] [–] [K] [–] [–] [N] [N] [N] [–] [–] [–] [N/m2] [N/m2] [N/m2] [m] [s] [s] [T] [K] [K] [K] [–] [m] [N/m] [–] [Pa·s] [N/m2] [N/m2] [N/m2]
References [1] M. Peleg, C. Mannheim, The mechanism of caking of powdered onion, J. Food Proc. Preserv. 1 (1977) 3–11. [2] D. Wallack, C. King, Sticking and agglomeration of hygroscopic, amorphous carbohydrates and food powders, Biotechnol. Prog. 4 (1988) 31–35. [3] J. Aguilera, G. Levi, M. Karel, Effect of water content on the glass transition and caking of fish protein hydrolysates, Biotechnol. Prog. 9 (1993) 651–654. [4] J. Aguilera, J. Valle, M. Karel, Caking phenomena in amorphous food powders, Trends Food Sci. Technol. 6 (1995) 149–154. [5] U. Bröckel, M. Wahl, R. Kirsch, H.J. Feise, Formation and growth of crystal bridges in bulk solids, Chem. eng. Technol. 29 (6) (2006) 691–695. [6] M. Wahl, U. Bröckel, H.J. Feise, B. Weigl, M. Röck, J. Schwedes, Understanding powder caking: predicting caking strength from individual particle contacts, Powder Technol. 188 (2008) 147–152. [7] J.M. Mauer, L.S. Taylor, Water–solids interaction: deliquescence, Annu. Rev. Food Sci. Technol. 1 (2010) 41–63.
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[8] S. Palzer, Agglomeration of dehydrated consumer foods, in: M. Hounslow, A. Salman (Eds.), Handbook on Granulation, Elsevier, 2006, pp. 730–801. [9] J. Tomas, Zum Verfestigungsprozeß von Schüttgütern - Mikroprozesse, Kinetikmodelle und Anwendungen, Schüttgut 2 (1) (1996) 31–50. [10] J. Schwedes, Review on testers for measuring flow properties of bulk solids, Granular Matter 5 (2003) 1–43. [11] H. Rumpf, Zur Theorie der Zugverfestigung von Agglomeraten bei Kraftübertragung an Kontaktpunkten, Chem.-Ing.-Techn. 42 (8) (1970) 538–540. [12] E. Lifshitz, The theory of molecular attraction forces between solids, Soviet. Phys. JETP 2 (1) (1956) 73–83. [13] H. Hamaker, The London–Van der Waals attraction between spherical particles, Physica 4 (10) (1937) 1058–1072. [14] H. Weisser, in: M. Maguer, P. Jelen (Eds.), Influence of Temperature on Sorption Isotherms, Transport Phenomena, Vol. 1, London and New York, 1986. [15] S. Brunauer, P. Emmett, E. Teller, Adsorption of gases in multimolecular layers, J. Am. Chem. Soc. 60 (1938) 309–319. [16] Palzer, S., in press: Supra-molecular structure and material properties of water soluble solid food substances — relating of structural characteristics with physical properties of powders. Trends in Food Science and Technology, in press. [17] M. Gordon, J. Taylor, Ideal copolymers and the second order transition of synthetic rubbers. 1. Non-crystalline copolymers, J- Appl. Chem. 2 (1993) 493–500. [18] S. Palzer, U. Zürcher, Bedeutung und Berechnung des Glasübergangs komplexer amorpher Lebensmittelkomponenten Teil II, Lebensmitteltechnik 9 (2004) 70. [19] S. Palzer, Contrôle de l'agglomération de polymères de dextrose par l'application du concept de la transition vitreuse, Ind. Alimentaires et Agricoles 12 (2006) 20–27. [20] S. Khalloufi, Y. El-Maslouhi, C. Ratti, Mathematical model for prediction of glass transition temperature of fruit powders, J. Food Sci. 65 (5) (2000) 842–848. [21] E. Schreyer, K. Sommer, Effect of crystalline NaCl on sorption, sintering and caking of amorphous dextrose syrup, Bulk Europe 2008, Prag., , 2008. [22] Schreyer, E., expected 2010. Water sorption, sintering and caking of binary mixtures of amorphous and crystalline particles. PhD thesis at the Lehrstuhl für Verfahrenstechnik disperser Systeme, Wissenschaftszentrum Weihenstephan, für Ernährung, Landnutzung und Umwelt/Germany. [23] M. Williams, R. Landel, J. Ferry, The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids, J. Am. Chem. Soc. 77 (1955) 3701–3707. [24] T. Soesanto, M. Williams, Volumetric interpretation of viscosity for concentrated and diluted sugar solutions, J. Phys. Chem. 85 (1981) 3338–3341. [25] A. Ollett, R. Parker, The viscosity of supercooled fructose and its glass transition temperature, J. Texture stud. 21 (1990) 335–362. [26] G. Kuczynski, Self-diffusion in sintering of metallic particles, metals transaction, J. Met. 1 (2) (1949) 169–178. [27] W. Schatt, Sintervorgänge - Grundlagen, VDI Verlag Düsseldorf, Germany, 1992. [28] Wagner, T., 1997. Kaltsprühen ein- und mehrphasiger Flüssigkeiten. PhD thesis at the chair for Food Process Engineering, Department of Food Science ETH Zürich/ Switzerland. [29] J. Frenkel, Viscous flow of crystalline bodies under action of surface tension, J. Phys. 5 (1945) 385–391. [30] H. Rumpf, K. Sommer, K. Steier, Mechanismen der Haftkraftverstärkung bei der Partikelhaftung durch plastisches Verformen, Sintern und viskoelastisches Fliessen, Chem.-Ing.-Tech. 48 (4) (1976) 300–307. [31] S. Palzer, Influence of the material properties on the agglomeration of watersoluble amorphous particles, Powder Technol. (2008). [32] S. Palzer, Influence of supra-molecular structure and storage conditions on the caking of powders, 5th World Congress on Particle Technology 2006, 2006, paper 231a. [33] G. Downtown, J. Flores-Luna, C. King, Mechanism of stickiness in hygroscopic, amorphous powders, Ind. Eng. Fundam. 21 (1982) 447–451. [34] M. Röck, M. Ostendorf, J. Schwedes, Development of an uniaxial caking tester, Chem. Eng. Technol. 29 (6) (2006) 679–685. [35] D. Schulze, Powders and Bulk Solids: Behavior, Characterization, Storage and Flow, Springer, Berlin/Germany, 2007. [36] A. Jenicke, R. Shield, On the plastic flow of coulomb solids beyond original failure, J. Appl. Mech. 26 (81) (1959) 599–602. [37] S. Palzer, U. Zürcher, Kinetik unerwünschter Agglomerationsprozesse bei der Lagerung und Verarbeitung amorpher Lebensmittelpulver, Chem. Ing. Tech. 76 (2004) 1594–1599. [38] E. Teunou, J. Fitzpatrick, Effect of relative humidity and temperature on food powder flowability, J. Food Eng. 42 (1999) 109–116.
Contents lists available at ScienceDirect
Powder Technology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / p ow t e c
Caking of amorphous powders — Material aspects, modelling and applications Markus Hartmann a,⁎, Stefan Palzer b a b
Nestlé Product Technology Centre, Lange Straße 21, 78224 Singen, Germany Nestlé Research Center, Vers-Chez-Les-Blanc, 1000 Lausanne 26, Switzerland
a r t i c l e
i n f o
Available online 24 April 2010 Keywords: Caking Amorphous powders Sintering Time consolidation
a b s t r a c t Caking of powders and bulk granules and adhesion of powders on equipment surfaces is a serious problem in the food, chemical and pharmaceutical industries. While caking of crystalline particles is tackled only briefly, this publication deals mainly with caking of water-soluble amorphous particles. Caking of amorphous particles starts with stickiness of the powder surface and can result in a collapse of the powder structure. The powder bulk turns from a free flowable powder bulk composed of single particles into a massive block. The material aspects (hygrocapacity, hygrosensitivity and viscosity) of water-soluble amorphous materials and sintering are discussed. The increase of the sinter bridges during caking could be modelled through the known sinter equations and measured by carrying out experiments in a ring shear cell. The calculated sinter bridge diameter could be correlated with the strength of the caked powder bulk measured in a ring shear tester. © 2010 Elsevier B.V. All rights reserved.
1. Introduction
1.1. Powders affected by caking
A number of powders are agglomerated to provide superior dispersibility. They should rehydrate and/or dissolve quickly without forming lumps. In addition, agglomeration improves the flowability of powders significantly. Another aspect is that more and more consumers prefer agglomerated to powdery products because of their more intense colour, the different visual aspect and the reduced dustiness. Sometimes also undesired agglomeration effects can be observed while processing food powders. The following undesired agglomeration phenomena are observed during handling, processing and storing of powders:
Time consolidation during storage, often referred to as caking, is a major problem when handling powders. Caking requires grinding to transform the powder cake into single particles or agglomerates. But in some cases, however, a grinding procedure is not effective because the structure of the agglomerates will be destroyed. Sometimes even whole silos are blocked by caked powder and the content of the silos can only be removed manually by mining techniques. Furthermore, the quality of packed powder products is negatively affected by caking during storage or transport. To reduce processing costs for posttreatment and to increase the quality of the end products such caking has to be avoided. Mainly powders which contain a major amount of water-soluble amorphous substances are sensitive to caking. The following amorphous food powders tend to consolidate during storage: powdered vegetable, yeast and meat extracts, hydrolysed fish proteins, meat powders, hydrolysed plant proteins, flavour powders containing such hydrolysates, maltodextrins and sugar syrups, organic acids used as food additives, spray-dried dairy powders, brown sugar and all food powders containing a significant amount of the mentioned ingredients [1–4]. In the chemical and pharmaceutical industries, e.g. urea, dextrose, citric acid and other organic acid are prone to caking. The main mechanism responsible for caking of such powders is sintering. Occasionally, also caking of fine, water-soluble crystalline powders is observed. The reason for caking of such crystalline powders is a partial dissolution and re-crystallisation of the crystalline substance [5–7]. In some cases also a partial melting and re-crystallisation of triglycerides can be the reason for caking of fat-containing powders. The chemical composition, the supra-molecular structure and the micro-structure as well as external factors like stress, humidity and
⋅ Stickiness and lumping of amorphous powders at high humidity and/or high temperature ⋅ Collapse of a fluid bed at high air humidity ⋅ Lumping of carrier powders due to over-saturation with nondissolving liquids ⋅ Post-hardening of amorphous or crystalline tablets during storage ⋅ Caking of amorphous or crystalline powders during storage ⋅ Soiling of equipment. With the exception of lumping due to an over-saturation with non-dissolving liquids all these undesired agglomeration phenomena can be explained with accelerated sinter processes or dissolution of crystalline substances at high relative humidity. This study focuses mainly on the caking of amorphous powders during storage.
⁎ Corresponding author. E-mail address: [email protected] (M. Hartmann). 0032-5910/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2010.04.014
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temperature are decisive for the caking mechanism and the caking kinetics. Fig. 1 shows scanning electron microscopic pictures of different caked food powders containing major amounts of amorphous substances. Several sinter bridges (highlighted by white circles) are clearly visible. In the current article the mechanisms and kinetics of caking will be discussed, test methods will be introduced and an approach for predicting the intensity of caking is presented. 2. Basics 2.1. Caking mechanisms Several mechanisms can lead to a time consolidation of powders [9]. It will be demonstrated in the frame of the current study that mainly sintering is responsible for the observed caking of amorphous food powders. Macroscopically, several stages of caking can be distinguished (Fig. 2). In the initial phase of the process the powder starts to get sticky and particles adhere to each other which leads to a reduced flowability of the powder bulk (which is often described as “stickiness”). They form brittle lumps and with progressing sintering a mechanically stable powder cake is obtained. In a later phase of sintering, particles missing a stabilising inner structure, which are built of non-dissolving substances lose their structure and shape. The powder structure collapses, open pores in the particle package disappear and, finally, a highly viscous, foam-like, amorphous melt is obtained. The shape of some particles (e.g. dehydrated vegetable pieces) is preserved due to an insoluble matrix (e.g. composed of cellulose, silicate, fat or proteins) and, thus, no collapse of the powder structure is observed.
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When water-soluble amorphous substances are stored in an environment with a high humidity, they absorb water and, thus, their viscosity decreases. Although sintering is accelerated due to the decreasing viscosity, the tensile strength of the sinter material/ bridge decreases with increasing water content. Due to the progressing absorption of water the strength of the powder cake first increases and in a later phase of the progress decreases again. Explanation: At low moisture content or in the early phase of the sintering process the diameter of the sinter bridges limits the stability of the particle cake. The growing diameter of the sinter bridges leads to an increasing strength of the cake. With progressing moisture absorption the viscosity of the bridge decreases and, thus, the strength of the powder cake decreases again. Finally, the powder structure collapses and a pasty mass is obtained. The viscosity of amorphous substances is also reduced at higher temperatures leading to an accelerated sintering of the particles and a steadily increasing strength of the powder cake. Crystalline water-soluble powders behave differently while they are exposed to a high humidity or temperature. If their critical humidity is temporarily exceeded, they will partially dissolve. The formed low-viscosity liquid bridges are rather fragile. However, a stable powder cake can be formed if the absorbed water evaporates again enabling a re-crystallisation of the dissolved substance. Accordingly, caking of crystalline powders stored in closed containers can be induced by condensation and evaporation of moisture due to temperature variations. The condensate builds liquid bridges between the particles. After a short time span the liquid forming these bridges is saturated with the dissolving substance. If the water is evaporated out of this liquid later, stable bridges between the particles are formed.
Fig. 1. Scanning electron microscopic pictures of caked powders (sinter bridges highlighted by white circles) [8].
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Fig. 2. Different phases of the sintering process.
Finally, also melting and following re-crystallisation of fat (e.g. cocoa, palm fat, etc.) due to temperature variations can cause caking of fat-containing powder masses. 2.2. Adhesion principles relevant for caking Increasing adhesion forces between particles are prerequisite for agglomeration and caking. Adhesion can be linked to the development of material bridges or increasing Van der Waals forces between neighbouring particles. For caking of water-soluble amorphous particles the following adhesion mechanisms are relevant: ⋅ ⋅ ⋅ ⋅ ⋅
Increasing Van der Waals forces due to plastic deformation Increasing Van der Waals forces due to visco-elastic deformation Liquid bridges with low viscosity Amorphous bridges with high viscosity Crystalline solid bridges
In specific cases also inter-locking might contribute to the tensile strength of powder bulks. Electrostatic forces are not relevant for caking since the particles are in continuous contact. Only with nonconducting plastic particles electrostatic charges could cause caking problems, but no relevant experiments and results are known [10]. The above-mentioned mechanisms increase the adhesion force F holding two neighbouring particles together. The tensile strength of the powder cake depends on the strength of these adhesion forces between the primary particles. According to Rumpf [11] the tensile strength of a powder cake composed of spheres with a diameter a can be estimated through the following equation. σt =
1−ε F ⋅k⋅ a2 k⋅ε≈3:1≈π: π a
ð1Þ
Fa is the adhesion force between two particles (spheres), ε the porosity of the agglomerate and k represents the coordination number of the primary particles building the agglomerate. For spherical particles k is approximately equal to π/ε [11]. In the following, the different adhesion mechanisms and their relevance for the caking of particles are discussed/explained. 2.3. Increased Van der Waals forces by particle deformation Adhesion between particles can be linked to increasing Van der Waals forces. The Van der Waals forces between two deformed particles can be estimated according to Lifshitz [12] and Hamaker [13]. Except for plastically deformable particles most caking processes are not caused by increasing Van der Waals forces. However, plastic or visco-elastic deformation of particles leading to increasing contact points and decreasing distance between neighbouring particle surfaces might enhance caking caused by sintering or dissolution and following re-crystallisation. 2.4. Hygrocapacity of water-soluble substances The water activity at a given moisture content is a function of the chemical composition, the supra-molecular structure and the microstructure of the powder. The sorption isotherm describes the relation
between water content and water activity for a given temperature. The sorption isotherm of a product can be modelled according to Guggenheim, Anderson and deBoer (GAB) [14] or according to Brunauer, Emmett and Teller (BET) [15]. Establishing the sorption isotherm of a crystalline (e.g. crystalline lactose, NaCl) and water-soluble material it can clearly be seen that the water capacity of crystalline materials is rather low. Below a critical relative humidity leading to dissolution of the crystalline substance a significant quantity of water can only be stored in the crystal matrix in form of crystal water. Apart from crystal water nearly no water can be stored within the crystalline structures. Crystalline substances do not absorb water until they dissolve at a specific relative humidity (e.g. 73– 75% RH for NaCl or 83–85% RH for sucrose) [16]. Amorphous hydrophilic substances behave differently when they are exposed to an increasing relative humidity. They absorb increasing amounts of water with increasing relative humidity. The water molecules are stored within the free volume left within the amorphous matrix. In contrast to crystalline materials a critical humidity at which particles might dissolve cannot be defined. With increasing water content the viscosity of the amorphous melt decreases and, finally, a diluted solution of the substance is obtained. Due to differences in the hygrocapacity observed between watersoluble amorphous and crystalline solids, re-crystallisation of the metastable amorphous form liberates moisture. The liberated water affects the crystallisation velocity of the remaining amorphous fraction. This might also lead to caking of the powder. 2.5. Effects of water on water-soluble amorphous substances (hygrosensitivity) Changes in the physico-chemical properties of materials linked to changing water content are referred to as hygrosensitivity. Amorphous and crystalline substances demonstrate a significantly different hygrosensitivity. Crystalline substances preserve their mechanical properties with increasing humidity until they dissolve at a substance-specific critical relative humidity of the surrounding air. In most cases the resulting solution has a low or medium viscosity. Such crystalline watersoluble substances, amongst them various minerals, mono- and disaccharides, do not provide a high viscosity due to their low molecular weight. Amorphous water-soluble materials do not dissolve like crystalline substances as their water content increases. They already have a liquidlike supra-molecular structure although they are perceived as solids. Water does not dissolve amorphous particles, but it migrates into the amorphous molecular matrix. Water stored in the amorphous matrix has a plastifying effect on the amorphous structure. The viscosity and elasticity of the material decrease with increasing water content. In parallel the glass transition temperature decreases due to the absorption of water. The well-known Gordon and Taylor equation (Eq. 2) describes the dependency between the glass transition temperature Tg and the water content w (as a percentage on wet basis) of an amorphous watersoluble substance.
Tg =
ð1−wÞ⋅Tg;s + w⋅k⋅Tg;w : ð1−wÞ + w⋅k
ð2Þ
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Tg,s is the glass transition temperature of the dry solid, Tg,w represents the glass transition temperature of pure water commonly considered equal to −135 °C. Although the Gordon and Taylor constant k [17] can be calculated theoretically (equations not shown), k is mostly used as a fitting parameter after Tg measurement. The k values of different materials can also be found in literature. In a powder mix in equilibrium the water activity is the same for all components although they might have different individual water contents. Therefore, it is useful to measure the glass transition temperature of powders depending on their water activity in order to identify the most critical component in the blend. Obviously, the powder fraction with the lowest glass transition temperature of the mix is the most sensitive component within the blend. Combining the GAB equation and Eq. 2, the dependence of the glass transition temperature on the water activity can be modelled according to Eq. 3 [18,19].
contact with amorphous particles, crystalline substances exhibit a lower deliquescence point, i.e. they start earlier to dissolve, coinciding with the glass transition of the amorphous component in the mix [21]. Dissolution of KCl or NaCl attracts a great amount of water in the powder mix and, as a consequence, the amorphous substance absorbs more water. Consequently, the mix of an amorphous and a crystalline substance has a greater water sorption capacity and is plasticized faster than the pure amorphous substance. Its glass transition temperature decreases strongly according to the Gordon–Taylor equation. With increasing water content the function Tg = f(aw) for mixes of amorphous and crystalline particles is not linear anymore in the water activity range between 0.2 and 0.7. It presents an inflection point coinciding with the glass transition where the crystalline material starts to dissolve. At this point the Tg = f(aw) curve drops sharply [22].
ð1−K⋅aw Þ⋅ð1 + ðC−1Þ⋅K⋅aw Þ⋅Tg;s + k⋅wm ⋅C⋅K⋅aw ⋅Tg;w Tg aw;22 ∘C = : ð1−K⋅aw Þ⋅ð1 + ðC−1Þ⋅K⋅aw Þ + k⋅wm ⋅C⋅K⋅aw
2.6. Effects of the water content and the temperature on the viscosity
ð3Þ A similar approach was taken by Khalloufi et al. [20] to describe the dependency of the glass transition temperature on the water activity of different fruit powders. Plotting the function Tg = f(aw) a sigmoidal-shaped curve, which can be approximated in the water activity range from 0.2 to 0.7 by a straight line, is observed. Fig. 3 shows the glass transition temperature and the water content of dextrose syrup (DE 21) and a tomato powder depending on their water activity. However, in the case of binary powder mixtures of crystalline and water-soluble amorphous particles, it has been shown with maltodextrin/dextrose syrup (DE 6, 21, 47) together with KCl or NaCl that the behaviour of the mix follows not a sorption isotherm obtained by a linear combination of both single sorption isotherms. In fact, in
Most substances, amongst them various amorphous water-soluble materials, deform visco-elastically. The deformation and relaxation behaviour of food materials can be described through various viscoelastic models. Depending on the nature of the stress/strain applied either the storage and loss modulus or the elasticity and the viscosity are included as material parameters. All these material parameters depend on the temperature and the plasticiser content of the viscoelastic substance as well as on the applied strain rate. Because of the relatively long time required for caking only the viscosity is relevant and the elasticity can be neglected. To model the temperature dependence of visco-elastic material parameters the time–temperature superposition principle is applied [23]. According to this principal visco-elastic data (like viscosity, compliance or modulus) obtained for one temperature and time or frequency can be extrapolated to a different temperature by multiplying the logarithmic time or frequency values with a temperature-
Fig. 3. Glass transition temperature and water content of dextrose syrup (DE 21) depending on the water activity (DSC onset of the second scan at a heating rate of 5 °C/min; water content analysed according to Karl–Fischer) [19].
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dependent shift factor. Especially in the case of the viscosity η it can be shown that the following equation is valid: −C⋅ T−Tg η for 0 K≤ T−Tg ≤100 K: log = ηg B + T−Tg
ð4Þ
This is a frequently applied form of the Williams, Landel and Ferry (WLF) equation where Tg is the reference temperature and C and B (in K) are constant factors [24,25]. 2.7. Sinter bridges between amorphous particles In general, in literature sintering is not considered as an important adhesion mechanism. This study demonstrates that sintering is in fact a ubiquitous process of striking importance for various powder processing operations. In the authors' opinion sintering is the main adhesion mechanism for many desired and undesired agglomeration processes related to powders. Especially in agglomeration of amorphous powders at elevated humidity or temperature the adhesion forces between the particles are generated by growing sinter bridges. In the following paragraph the mechanism of sintering is explained. All materials have the tendency to reduce their free surface area which is associated with the specific energy of the system. Like lowviscosity liquid droplets, amorphous particles tend to adopt a spherical shape. By bringing two amorphous particles into contact with each other, they can be considered as one new single particle. To minimise the free surface area of this newly created particle, molecules are transported to the contact point between the two primary particles (Fig. 4). Such a process is called sintering. The driving force for the sinter process is the difference between the capillary pressure at the contact point between the particles and the laplace pressure in the volume of the two initial particles. Eq. 5 enables the calculation of this pressure difference for two spherical primary particles attached to each other. Δpc = pc1 −pc2 =
4⋅γ 2 1 −γ ⋅ − : a x s
ð5Þ
pc1 represents the capillary pressure in the volume of the primary particles, pc2 is the capillary pressure in the sinter bridge and a is the diameter of the primary particles. γ is the surface tension of the amorphous substance, x the diameter of the sinter bridge and s represents the radius of the curvature of the meniscus of the viscous bridge. Since the capillary pressure is directly linked to the vapour pressure in the continuous gas phase surrounding the particles, a gradient of the vapour pressure across the particles exists. Based on these local differences in capillary and vapour pressure different molecular transport mechanisms are observed. The relevant literature [26–28] distinguishes between a transport through the vapour phase, surface diffusion and volume diffusion (Fig. 4). Diffusion of molecules inside the particles, sometimes also referred to as viscous flow, seems to be the relevant mechanism for caking of most amorphous water-soluble substances caused by sintering.
The kinetics of such transport processes strongly depends on the diffusion coefficient which is a function of viscosity. As discussed, the viscosity of amorphous solids depends on the temperature as well as on the plasticiser content of the material. Thus, sintering of amorphous water-soluble particles can be controlled by adjusting the temperature and/or the water content of system. 2.8. Modelling sinter bridges between amorphous particles For modelling the sintering of organic particles by viscous flow, Frenkel [29] published the following equation. Assuming spherical particles of a diameter a, the diameter of the sinter bridge x can be calculated depending on the sinter time t, the surface tension γ and the viscosity η. x2 a
=
1 γ t : 6⋅ a⋅η
ð6Þ
Alternatively, the sinter kinetics can be predicted according to Rumpf et al. [30]. Assuming a punctual contact between the particles and neglecting changes in the particle geometry during sintering, Rumpf et al. modelled the viscous flow based on the Navier–Stokes equation. Ft represents the force with which particles are pressed together. x2 a
=
4 γ 2⋅Ft t ⋅ + ⋅η: 2 5 a 5⋅π⋅a
ð7Þ
Both equations are valid only for the initial phase of the sinter process. For non-spherical particles the relevant radius a has to be estimated based on the curvature radius at the contact point between the particles. A prerequisite for a sinter process is a molecular contact between the particles. A moderate force (e.g. caused by the weight of the particles) pressing the particles together ensures a continuous contact between the particles during sintering. In most systems variations in surface tension with increasing solvent content or presence of surface ingredients are limited. Hence, in most applications the viscosity which might vary by magnitudes governs the sinter kinetics [31,32]. As already elaborated the viscosity of water-soluble amorphous substances depend on the moisture (plasticiser) content w and the temperature T. Combining Eqs. 4 and 7 and considering the fact that due to sorption or desorption processes the humidity of the amorphous substance might change as a function of time, Eq. 8 is obtained. x2 a
tmax
= ∫ t =0
−C ⋅ðT−Tg ðt ÞÞ 4 γ 2⋅Ft 1 B+ T−T ðt Þ + ⋅ ⋅ ⋅10 ð g Þ ⋅dt 5 a 5⋅π⋅a2 ηg
where tmax is the time available for the sinter process.
Fig. 4. Sintering mechanisms.
ð8Þ
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By combining Eq. 8 with Eq. 1 the tensile strength of sintering agglomerates can be estimated. tmax −C ⋅ðT−Tg ðt ÞÞ ð1−εÞ⋅π 4 γ 2⋅Ft 1 σs ðT; w; ωÞ⋅ ∫ + 10 B+ ðT−Tg ðtÞÞ ⋅dt: σt = ⋅ ⋅ ⋅ ⋅ 2 ε 5 a ηg 5⋅π⋅a t=0 ð9Þ However, in practice it remains difficult to predict the tensile strength of sintered agglomerates because of the geometrical diversity of primary particles and the visco-elastic nature of the built sinter bridges. According to Downtown et al. [33] a significant adhesion force F between particles should be observed if the diameter ratio x/a exceeds a value of 0.01. Wallack and King [2] reported a value x/a of 0.1 required for adhesion. For practical applications these empirical value was found to be useful in order to estimate whether a stable powder cake can be expected. 2.9. Methods for measuring caking One possibility for measuring caking is to fill powder samples in a container and store this container under a certain temperature and relative humidity. After a defined time the evaluation is done visually by using a qualitative evaluation scale. These results are only meaningful for this special setup and hardly transferable to other situations and dimensions. More advanced caking test methods include time consolidation trials. The powder sample is stored under defined conditions and the mechanical strength of the obtained powder cake is measured. One of the more scientific time consolidation tests is the uniaxial tester which exists in different design variations. A sample is filled into a cylinder, consolidated without wall friction by applying normal consolidating stress σ1,c and stored under a defined temperature and relative humidity. After removing the cylinder the sample is loaded again with an increasing normal stress up to the point of failure, leading to the unconfined yield strength σc [10,34]. The disadvantage of a uniaxial tester is that there is no consolidation of the bulk solids sample up
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to steady state flow and that it is not possible to measure the yield loci (τ = f (σc)) of powders as it is the case in a ring shear cell (see below). A more accurate and reproducible way to quantify caking are time consolidation experiments performed in ring shear cells. After preconsolidation under steady flow conditions and storage under defined settings the strength of the powder cake within the ring cells is measured by shearing [35]. One of the major drawbacks of time consolidation experiments in the almost closed cells is the hampered exchange of moisture between the air and the sample during the consolidation phase. Contrary to such test conditions, moisture absorption and time consolidation are often parallel processes which are difficult to separate from each other in practice. To quantify the caking intensity the unconfined yield strength σc of the initial and the stored powder have to be compared with each other. The increase in unconfined yield strength σc or the decrease of the flow factor ffc [36] can both be used for quantifying the degree of caking. Empirically, it has been found that strong caking corresponds to an increase in unconfined yield strength of more than 1000 Pa [37]. Fig. 5 shows the shift of the yield locus and the increase in unconfined yield strength σc of yeast extract with a water activity of 0.17 stored for 4 days at 10 °C above its glass transition temperature. The yeast extract shown exhibits a strong caking corresponding to an increase of unconfined yield strength of roughly 1000 Pa. 3. Material and methods For the trials spray-dried dextrose syrup with a dextrose equivalent (DE) of 20–23 (DE 21, Roquette GmbH, Frankfurt, Germany) was used. The dextrose syrup powder has a water content of 4% (db) (water activity aw = 0.18) and a medium particle size x50,3 of 150 µm. Furthermore, spray-dried tomato powder (Transa/Badojoz/Spain and Conesa/Villafranco del Guadiana Badajoz/Spain) produced on a Filtermat® spray dryer was used for the time consolidation experiments. In addition, a series of time consolidation trials was performed with powdered yeast extract (Biospringer, Maison-Alsort, France).
Fig. 5. Initial shear locus of yeast extract and shear locus of yeast extract stored for 4 days at 10 °C above Tg (ring shear tester; T = 25 °C; aw = 0.17; t = 96; consolidation stress 1200 Pa).
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The glass transition temperature was measured by Differential Scanning Calorimetry (DSC) with a heating gradient of 5 °C/min (STARe SW 8.10 from Mettler-Toledo GmbH, Switzerland). The onset of the resulting thermogram was defined to be the glass transition temperature Tg. The water activity was measured using a capacitive sensor equipped with hygroscopic material (HygroPalm AW1 from Rotronic, Ettlingen, Germany) at a temperature of 20–25 °C. The water content of the samples was analysed by titration according to the method of Karl–Fischer. The time consolidation measurements were performed using a ring shear tester (RST-01.pc from Schulze-Schüttgutmesstechnik, Wolfenbüttel, Germany). Three samples were stored at different relative humidity for one week. The preconditioned samples were filled into a ring cell and the cover of the cell was loaded with a defined weight. After the consolidation time the flowability of the product was measured in the ring shear cell tester. The yield locus was established and the unconfined yield stress was determined. By definition a sample providing an unconfined yield strength of more than 1000 Pa is considered to be caked. For the scanning electronic microscopy (SEM) images of crystals about 10 g of NaCl crystals (X50,3 = 420 µm) were filled in a thin layer in small petri-dishes and stored for different periods (1, 2 and 5 days) at 25 °C and various relative humidity in desiccators containing saturated salt solutions from Fluka Chemie AG of known values (62% RH, NH4NO3; 75% RH, NaCl; KNO3, 88% RH). After the treatment the samples were dried in a chamber with 20 °C at 20% RH for several days and observed with a SEM.
4. Results and discussion 4.1. Sintering of pairs of single amorphous particles The sintering of two amorphous dextrose syrup particles (DE 21) which were exposed to a relative humidity of 70% was investigated.
Both particles were placed on a silanised hydrophobic glass plate and the relative humidity of the surrounding air was adjusted by a saturated salt solution. Fig. 6 shows the water content of the particles depending on the storage time and images of the sinter bridge developed between the two particles. The absorbed moisture leads to a decreasing viscosity of the amorphous matrix and, thus, sintering is accelerated. A stable sinter bridge is already obtained after 3 to 6 h of storage. Finally, the two particles coalesce and form a single viscous droplet. Fig. 7 shows a comparison of the calculated sinter bridge diameter with the measured sinter bridge diameter between two dextrose syrup (DE 21) particles stored at 30 °C and 70% RH values for bridge diameter corresponding to Fig. 6. The calculated kinetics of sintering is in good agreement with the measured increase of the diameter of the sinter bridge. Despite the various assumptions and simplifications made, Eq. 8 allows a satisfying prediction of the sinter kinetics of amorphous water-soluble particles. Possibly the accuracy of the prediction can be further improved by taking into account a moisture gradient along the particle diameter. Establishing the Navier–Stokes equation for a pair of sintering particles the viscosity gradient corresponding to the moisture distribution inside the particles has to be considered.
4.2. Caking of a bulk of amorphous particles As already mentioned, different mechanisms might be responsible for the observed caking of powders. In case of amorphous, water-soluble solids, sintering is supposed to be the main mechanism responsible for increasing adhesion forces between the particles. Assuming a constant viscosity of the amorphous substance forming the bridge, the unconfined yield strength should be a function of the average sinter bridge diameter (Eq. 7). In Fig. 8 the unconfined yield strength of spray-dried tomato powder, dextrose syrup and hydrolysed whey permeate is plotted against the calculated squared ratio between the diameter of the sinter bridge and the particle diameter (x/a)2. The ratio (x/a)2 is
Fig. 6. Moisture content and images of two dextrose syrup particles (DE 21) stored at 30 °C and 70% RH.
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Fig. 7. Comparison between calculated and measured sinter bridge/particle diameter ratio for pairs of spray-dried dextrose syrup particles (DE 21) stored at 30 °C and 75% RH (Tg = −4 °C; γl,g = 70 mNm, η = 106 Pa s) [31].
calculated through Eq. 7. According to the results obtained, the unconfined yield strength increases with increasing ratio (x/a)2 more or less linearly for (x/a)2 values exceeding 0.05. This result is in agreement with the studies of Downtown et al. [33], Wallack and King [2] and Aguilera et al. [3] who observed a caking if the ratio between the radius of the sinter bridge and the particle diameter x/a exceeds a value of 0.01 to 0.1. According to Eq. 9 the unconfined yield strength of the powder cake should theoretically increase linearly with (x/a)2. Such
correlation can be confirmed for values (x/a)2 exceeding 0.05 (Fig. 8). In the initial phase of the storage process the growth of the sinter bridge might be delayed because of the incomplete contact between the particles. The gap at the contact points between single particles has to be bridged before the development of the bridge is initiated. Such a delay of the sinter process might explain why a theoretical value of (x/a)2 of 0.05 has to be exceeded before a linear increase in tensile strength is observed. Another explanation is that the initial powder is
Fig. 8. Measured unconfined yield strength of tomato powder, dextrose syrup DE 21 and hydrolysed whey permeate plotted against ratio (x/a)2 (Eq. 9) [8,38].
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in disequilibrium with the surrounding air and in the early phase of the experiments moisture still migrates into the particles. On the one hand, the moisture content on the particle surface is used for calculating the diameter of the sinter bridge. On the other hand, also the viscosity of the particle inside is relevant for sintering by viscous flow. Hence, a calculation based on the initial moisture content of the particle surface yields for the beginning of the process a too large bridge diameter. Apparently, the risk of caking can be predicted through the calculated sinter bridge diameter. It is important to remember that Eq. 9 used for calculating the theoretical ratio (x/a)2 is valid only for the initial phase of the sintering process. Furthermore, dehydrated cell structures, which bind the strongly plastified amorphous substance through capillary forces or crystallisation processes, might limit the availability of amorphous material for building the sinter bridge. Thus, the real growth kinetics of the sinter bridge might deviate significantly from the predicted growth rate. Despite these effects, it has been demonstrated that the risk of caking of water-soluble amorphous powders can be predicted by calculating the theoretical sinter bridge diameter. When the calculated x/a value exceeds 0.01 caking of the powder can be expected. 4.3. Caking of a bulk of crystals Crystalline particles show no time consolidation at constant moisture content. However, if the relative humidity of the air temporarily or locally exceeds the critical humidity of the crystalline substance, a partial superficial dissolution is observed. For sodium chloride this critical relative humidity leading to dissolution is in the range of 73–76% RH. As it can be seen in Fig. 9 sodium chloride crystals
stored at 60–62% and 71–73% RH for 120 h are not dissolving. Contrarily, sodium chloride crystals exposed to a relative humidity of 80–83% RH for 120 h dissolve partially and a saturated sodium solution builds liquid bridges between the cubic crystals. When decreasing the relative humidity the generated liquid bridges dry out again. During the drying the sodium chloride dissolved within the liquid crystallizes in form of small cubic fractal structures. Some of these cubic crystals build bridges between the larger initial crystals. Finally, a porous cake built of larger crystals which are connected by re-crystallized sodium chloride remain. When exposing a thick layer of crystals to an elevated relative humidity the outer layer of crystals dissolves first. The generated saturated sodium chloride solution builds a liquid film limiting diffusion of moisture into the core of the particle bulk. Accordingly, a caked powder layer is obtained after decreasing the relative moisture again. Exposing crystalline sodium chloride for a longer time to a relative humidity above 75% leads to the entire dissolution of the material. Caking of crystalline material might be observed especially when storing the powder in closed storage containers excluding a convective moisture transfer to the environment. To estimate the risk of caking, it is sufficient to analyse the expected variations in temperature and to estimate the corresponding changes in relative humidity of the air through the Mollier diagram for humid air. If the predicted maximum relative humidity inside the powder bulk exceeds the critical humidity of the crystalline substance, the probability of caking is high. 5. Conclusion and outlook Generally, it seems to be highly feasible to predict the caking of crystalline and amorphous water-soluble particles. For amorphous
Fig. 9. Scanning electronic microscope images of NaCl crystals stored at different relative humidity and different times.
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substances the viscosity of the material is estimated by considering the temperature and the moisture content. Based on the viscosity the kinetics with which the diameter of the sinter bridge increases with time can be predicted. The calculated average sinter bridge diameter could be linked qualitatively to the strength of the powder cake. Further improvement of the precision of this estimation is possible by considering the moisture exchange between particles and the surrounding air. Furthermore, the tridimensional distribution of the bridge diameters between the particles of a caked powder bulk has to be considered for establishing a relation between sinter bridge diameter and the unconfined yield strength. Caking of crystalline powders is simply linked to a partial dissolution and re-crystallisation of the crystalline substance. Such caking is only observed while temporarily exceeding the substancespecific critical relative humidity. Nomenclature list a Diameter of a sphere/particle aw Water activity B Constant factor in the WLF equation C Constant factor in the WLF equation Flow factor ffc F Adhesion force Adhesion force between two particles Fa Ft Force with which particles are pressed together k Coordination number k Gordon and Taylor constant K Parameter (GAB equation) Capillary pressure in the volume of primary particles pc1 Capillary pressure in a sinter bridge pc2 Plastic yield pressure ppl s Radius of the curvature of a meniscus of a bridge t Sinter time Time available for a sinter process tmax T Temperature Glass transition temperature Tg Glass transition temperature of a dry solid Tg,s Glass transition temperature of pure water Tg,w w Water/plasticiser content x Diameter of a sinter bridge γ Surface tension ε Porosity η Viscosity Unconfined yield strength σc Consolidating stress (steady flow conditions) σ1 Consolidating stress (uniaxial tester) σ1,c
[m] [–] [K] [–] [–] [N] [N] [N] [–] [–] [–] [N/m2] [N/m2] [N/m2] [m] [s] [s] [T] [K] [K] [K] [–] [m] [N/m] [–] [Pa·s] [N/m2] [N/m2] [N/m2]
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