The exchange of fines between carriers in adhesive particle mixing: A study using DEM simulation

Powder Technology 288 (2016) 266–278

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The exchange of fines between carriers in adhesive particle mixing: A study using DEM simulation Duy Nguyen a, Anders Rasmuson a,⁎, Kyrre Thalberg b, Ingela Niklasson Björn b a b

Chemical and Biological Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden AstraZeneca R&D Centre, SE-431 83 Mölndal, Sweden

a r t i c l e

i n f o

Article history: Received 29 July 2015 Received in revised form 2 October 2015 Accepted 30 October 2015 Available online 1 November 2015 Keywords: DEM Adhesive particle mixing The transfer of fines Dry particle coating Dry powders for inhalation

a b s t r a c t This study employs DEM simulations to investigate the transfer of fine particles between carrier particles, which is one of the important mechanisms governing adhesive particle mixing. Single collisions between a carrier coated with fines and a non-coated carrier were simulated, in which the interaction between particles was modelled using the JKR theory. Detailed post-impact analysis was carried out to characterise the transfer mechanism and the effects of interface energy between particles, impact velocity and impact angle on the transfer process. It was found that fines are transferred between carriers and are restructured with different patterns according to the relative magnitude of the kinetic energy and the interface energies of particles, both between fines and between fine–carrier. The impact angle, which is closely related to mixer type, has a significant influence on the transfer of fines when the kinetic energy is able to be dissipated into adhesive bonds between fines (which strength is characterised by the corresponding interface energy). The correlation of the particle properties (e.g. interface energies), the processing parameters (e.g. the impact velocity), and the type of mixer (e.g. the impact angle) in characterising the transfer mechanism is established. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Particle mixing is often encountered in a wide array of industrial processes. It can be described by the random mixing theory when interparticle interaction is excluded [1]. With the addition of fine particles, a particulate flow will exhibit behaviour differing from that of large and cohesionless particles. While the contribution of gravitational and inertia forces to the total force acting on fines can be neglected, interparticle attraction leads to the adhesion of fine particles onto coarse ones during particle collisions. This interaction is beneficial for handling properties, and it can also be utilized to obtain a high degree of uniformity, i.e. adhesive mixing [2,3]. Although end-use properties, e.g. mixing homogeneity, exist in a triangle relationship with particle properties and processing conditions, the latter is poorly documented as regards the mixing process. A few studies on mixing times [4], mixing rate [5,6], and DEM simulations of fines — carrier adhesion [7–9] have been carried out in an effort to understand the effects of mixing on the performance of desired products. While the homogeneity of random mixing obeys the law of probability and is determined by a statistical distribution, adhesive particle mixing is governed by different mechanisms due to complex interparticle interactions. Several such mechanisms have been documented in the literature; namely (i) random mixing (ii) de-agglomeration (iii) ⁎ Corresponding author. E-mail address: [email protected] (A. Rasmuson).

http://dx.doi.org/10.1016/j.powtec.2015.10.048 0032-5910/© 2015 Elsevier B.V. All rights reserved.

adhesion, and (iv) redistribution and compression [10]. A recent study by [11] has demonstrated a methodology for characterising the relative importance of the first three mechanisms to the overall mixing process. The last mechanisms, i.e. the redistribution and the compression of fines on carrier surfaces, have not been taken into account although these mechanisms are critical regarding the microstructure of mixtures [12, 13]. There are a few studies in the literature that confirm the redistribution of fines among carriers. de Boer et al. have evaluated the transfer of fines between dissimilar carrier fractions, and have shown that fines migrate from small to large carrier particles due to differences in surface properties [14]. The mixing time to achieve equilibrium state was also reported in that study to be 30 min, which was actually determined for an extreme case since such a large difference in the surface energy of carrier particles would not be expected in a real mixture (prepared from the same carrier batch). The transfer of fines between similar carrier particles, which acts as an adhesive mixing mechanism, therefore needs further investigation. The kinetics of this kind of transfer using a population balance-based model has been reported previously [15]; however, a detailed description of such mechanisms and the resulting structures of adhesive mixtures have not been established. The aim of this study is thus to investigate the redistribution of fines, in particular carrier-to-carrier transfers, in an attempt to improve the overall understanding of the adhesive mixing process. In this study, the collisions between carriers with the addition of fine particles have been simulated using the Discrete Element Method (DEM). The influence of interface energies between particles, impact velocity, and

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Fig. 1. The initial state and simulation setup, (a) even three-layer fines-distribution on a spherical segment (fine particle layer exaggerated), (b) random fines-distribution.

impact angle, as well as that of their correlation on the resulted structure after impact has been characterised. 2. Method The deposition of fine particles on the carrier and particle impacts were simulated using DEM in which the movement of individual particles is tracked using Newton's Equation of Motion 2

mi

Ii

d xi dt

2

¼ F ijcontact þ F igravity þ F ifluid

dωi ¼ T icontact dt

ð1Þ

ð2Þ

ij i i , Fgravity , Ffluid are the contact force between particles i–j, where Fcontact the gravity force and the fluid force that act on particle i. Ii, ωi, and Ti are the inertia moment, the angular velocity and the torque that act on particle i. The gravitational and the fluid forces have been neglected in this study. The elastic–cohesive contact force between two particles has been modelled using the JKR model [16], which describes the contact radius a as

a3 ¼

3Ri j 4Ei j

 F ne þ 3πΓ i j Ri j þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  2 6πΓ i j Ri j F ne þ 3πΓ i j Ri j

ð3Þ

where Γi–j is the adhesion work, i.e. the work per unit area needed to separate two surfaces in vacuum, and Fne is the normal elastic–cohesive contact force. The effective radius Ri–j and the effective Young modulus Ei–j are defined as 1 Ei j

1  v2i 1  v j þ Ei Ej

2

¼

1 1 1 ¼ þ Ri j Ri R j

ð4Þ

ð5Þ

where Ei, Ri νi are the Young modulus, the radius and the Poisson ratio of particle i. The model and the simulation strategy have been adopted from [17]. To set up the initial state, 1800 fine particles (lactose, 5 μm) were guided to form 3 layers with an even distribution on a spherical section of a carrier particle of which radius was one third of the carrier radius (mannitol, 200 μm). This was done by first positioning fines in three spherical segments of which each thickness was equal to the size of

fines. The first segment was positioned very close to the surface of the carrier but not touching the carrier to prevent fine–carrier interactions occur. The second and the third segments were respectively positioned on top of the first one with a small gap to also prevent fine–fine interactions. A centripetal force field which magnitude was one order of magnitude less than particle gravity was applied to all fines to make them move toward the carrier to form three layers on the carrier surface. This centripetal force field was then removed and the simulation was continued until all particles reached their stable positions with extremely low velocities to ensure that most kinetic energy was dissipated. This initial state is illustrated in Fig. 1 and is regarded as an ideal model mixture resulting from an agglomerate impact. A second uncoated carrier particle was introduced and forced to collide with the first one at different impact velocities and angles (see also Fig. 1). A time step of 0.2 ns was used for all simulations. The interface energies between fine–fine particles and between fine–carrier particles were varied for each simulation. The physical and simulation parameters (see Table 1) were adopted from relevant studies in the literature [18–22]. In a real context, there is always a certain random distribution of fine–particle fragments on the carrier surface. For this reason, the simulation setup in this study must be regarded as an ideal model which mimics an adhesive mixture. Only a spherical section has been considered since this is the region in which all particles have the possibility to interact with a new carrier, i.e. this is the region in which competing mechanisms can be evaluated. A more realistic case in which fine particles are randomly distributed on the carrier was simulated for comparison. In this case, the fine–carrier assembly at the initial state was adopted from the result of the impact of an agglomerate with a carrier particle (see Fig. 1b). Particle properties, simulation parameters and procedure were identical for both cases. Table 1 Physical and simulation parameters. Parameters

Fine particle (lactose)

Carrier particle (mannitol)

Particle size Particle density Young modulus [18,21,22] Poisson ratio [18,21,22] Friction coefficient [18,21] Rolling friction coefficient [18] Impact velocity Impact angle

5 μm 1520 kg/m3 4 GPa 0.12 0.26 (fine–fine) 0.002 (fine–fine) 0.01 m/s to 2.5 m/s 0 (normal), π/4, π/2 (shear, d = 12.5 μm) 0.005 to 0.03 J/m2 0.001 to 0.03 J/m2

200 μm 1490 kg/m3 0.1 GPa 0.29 0.3 (fine–carrier) 0.002 (fine–carrier)

Interface energy between fines (Γ1–1) Interface energy between fine–carrier (Γ1–2)

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transferred to a second carrier and is called “transfer ratio”. The third parameter, the “remove ratio”, represents the fraction of free fines removed from the first carrier but not adhered to the second. In addition, other parameters including the damage ratio [23], energy dissipation, and the tensile strength of fragments were also employed to characterise the nature of the collision between two carrier particles. 3. Results and discussion 3.1. How fines are transferred between carriers

Fig. 2. The fraction of fines that stay, are removed and are transferred in the final state for a normal impact with Γ1–1 = 0.01 J/m2, Γ1–2 = 0.03 J/m2.

The resulting structure of fine–particle fragments on each carrier particle in the final state was evaluated in terms of three parameters. The first one, the “stay ratio”, is defined as the fraction of fines that remain on the first carrier after a collision to the total number of loaded fines. The second parameter was calculated as the fraction of fines

In order to provide the first picture of the collision and the transfer of fine particles between two carrier particles (as illustrated in Fig. 1), the final structure of such a particulate system represented in terms of stay ratio, transfer ratio and remove ratio is shown as functions of impact velocity in Fig. 2 for a normal impact (α = 0). As can be seen, a redistribution of fines among carriers did occur with great variation with changes in impact velocity. At low impact velocity, the transfer started with a small fraction, then gradually increased to achieve a maximum value at 1.2 m/s before being reduced at higher impact velocities. The stay ratio continuously decreased, whilst the remove ratio gradually increased with a local collapse corresponding to the maximum point of the transfer ratio. Similar tendencies were also obtained for impacts

Fig. 3. Snapshots (a, b, c, d) and velocity profiles (e, f, g, h) during a normal impact. The snapshots are of a central slice cut and are set opaque for easy visibility. The velocity profiles are illustrated both in terms of vectors and particle colours for Γ1–1 = 0.01 J/m2, (g) Γ1–2 = 0.03 J/m2, (h) Γ1–2 = 0.01 J/m2. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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from different angles although the relative contribution of each mechanism varied, e.g. the number of fines that remained on the coated carrier was large even at high impact velocities when α = π/2. Snapshots of the impact at certain time points are shown in Fig. 3 to illustrate the dynamics of fines transfer. A fragmentation of the fines cluster can be observed in Fig. 3b where the new carrier had just hit the coated one. Two major fragments can be distinguished in the figure; one that stays on the coated carrier and one that shows a tendency to move toward the non-coated carrier. The corresponding particle velocity distribution at this time point shows a large velocity gradient between these two parts, (see Fig. 3e, Γ1–1 = 0.01 J/m2, Γ1–2 = 0.03 J/ m2), which acts as a driving force for the fragmentation. In fact, the characteristic of these fragments depends on interparticle interactions and kinetic energy. The velocity distribution in cases of smaller Γ1–2 (0.01 J/m2) shows a different pattern where most of the fines are removed from the coated carrier (see Fig. 3g). At later time points (Fig. 3c, d), the major fragment moving toward the new carrier continues to be fragmented, which is seen clearly in the velocity pattern in Fig. 3f, h. This step can be regarded as an agglomerate impact in which the target is the new carrier. The breakage–capture behaviour

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of such an agglomerate, as documented by [17], is a function of impact velocity (bouncing velocity from the first collision in this case), and interparticle interaction. Therefore, it can be interpreted that upon impact at a certain velocity between two carriers, the fines are transferred between carriers in three steps: i) being separated from the initial fragment, (ii) being fragmented, and iii) being attached onto the uncoated carrier. In other words, the number of transferred fines depends on three components, i.e. the incident kinetic energy, the fine–fine interface energy Γ1–1, and the fine–carrier interface energy Γ1–2. Low kinetic energy will be dissipated entirely into fine–fine bonds with minor breakage, which results in a low transfer ratio. The transfer ratio is increased when larger daughter fragments are removed from the initial one with the kinetic energy that can be handled by the fine–uncoated carrier interaction. The optimization of those three parameters makes the maximum value. When the kinetic energy of daughter fragments cannot be dissipated entirely into fine–uncoated carrier bonds, the transfer ratio will be reduced as a consequence. It should be noted that the impact velocity also influences the spreading angle of daughter fragments and, in turn, the potential for contact with the uncoated carrier. Those fines that are removed

Fig. 4. (a) The energy dissipation and (b) the normalized energy loss for a normal impact with Γ1–1 = 0.01 J/m2, Γ1–2 = 0.03 J/m2.

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and those that stay on the coated carrier are only governed by the strength of the fine–fine and the fine–coated carrier attraction, respectively. Their behaviour responding to the change in impact velocity can be explained as higher kinetic energy results in greater breakage performance. Energy dissipation can be utilized to obtain further insight into the impact event. The total energy loss and the amount of energy spent in breaking fine–fine and fine–carrier bonds [19,24] are depicted in Fig. 4 for a normal impact. An interesting point is that at low impact velocities, the energy spent for breaking fine–fine adhesion bonds is negative. This can be understood by considering that, although being fragmented, the overall structure of daughter fragments in this state is denser than the original one (i.e. new fines–fines bonds are created). This fact is one of the mechanisms to formulate the microstructure of adhesive mixtures. In general, all energy losses increases with the impact velocity, but with a complex pattern. According to [19], the impact may involve different breakage regimes within the evaluated range, and therefore, the dimensionless number proposed by [25] is no longer valid for the whole range. The contributions of the energy spent breaking each pair of interparticle contacts to the total energy loss (see Fig. 4b) illustrate how kinetic energy is distributed upon impact. At low velocities, most kinetic energy is used to break fine–carrier bonds, and this fraction gradually decreases at higher velocities. Since such an impact is governed by impact velocity and the interface energies, it should be

kept in mind that the relative comparison between the studied parameters may change subject to a specific condition. The tendency of those parameters, however, are of interest and reflect the behaviour of the collisions. 3.2. Effects of interface energy between fine and carrier particles Γ1–2 Transfer ratios corresponding to different values of Γ1–2 have been plotted as functions of the impact velocity in Fig. 5a for a normal impact. As the transfer of fines is also a result of how fines are kept on the coated carrier, the stay ratio is also shown in Fig. 5b to give a better understanding of the process. At low impact velocities, the cases with small Γ1–2 possess a distinct behaviour which shows that most fines have been transferred to the uncoated carrier (see Fig. 5a). Other cases with higher Γ1–2, however, possess the same tendency as discussed earlier. Although this observation seems to contradict the fact that fines are better captured at higher Γ1–2, it may be explained by taking into account the effect of the impact angle. When the fine–carrier attraction is notably weaker than the fine–fine attraction, a sufficient impact velocity tends to break fine–carrier bonds rather than breaking the fine–particle fragment. This is evident by the evolution of interparticle bonds illustrated in Fig. 6 where a dramatic decrease of the number of contacts between fines and the coated carrier, and a gradual increase of the number of contacts between fines, can be observed. This breakage behaviour

Fig. 5. Effects of the fine–carrier interface energy on (a) the transfer ratio, (b) the stay ratio for a normal impact, Γ1–1 = 0.01 J/m2.

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Fig. 6. The evolution of interparticle bonds for normal impacts at 0.4 m/s, Γ1–1 = 0.01 J/m2, with two different Γ1–2 (0.001 J/m2 and 0.03 J/m2).

resulted in the removal of the whole fragment from the coated carrier, as indicated by the low stay ratio in Fig. 6 and illustrated in Fig. 3g and h. In the case of normal impact, such a removed fragment makes another normal impact with the uncoated carrier and is trapped there due to its low kinetic energy. This secondary impact thus results in an extraordinary high transfer ratio. When two carrier particles collide at low velocities and with high Γ1–2, the fragment is better retained by the coated carrier, as being evident also by the evolution of interparticle bonds in Fig. 6. This breakage behaviour results in a low transfer ratio as seen in Fig. 5a. It should be noted that the capability of the uncoated carrier to capture fines also increases at the same time but the carrier has less possibility to make contact with fines in this case. At higher impact velocities in which fine–fine bonds are broken sufficiently, the transfer ratio shows the behaviour discussed in the previous section, i.e. the transfer ratio gradually increases and achieves a maximum value, owing to the optimization of the kinetic energy and the interface energies, before it gradually becomes reduced. In general, the use of high Γ1–2 results in a better transfer of fines owing to two contributions: i) an uncoated carrier can capture more fines since the fine–carrier bonds can dissipate higher kinetic energy, and ii) a stronger attraction between a coated carrier and fines results in better breakage

performance of the fragment, which generates more fines to be captured by the uncoated carrier. This tendency is obtained for both normal and shear impacts, however, a normal impact accommodates for more fines being transferred owing to higher breakage performance (a coated carrier receives more kinetic energy from an uncoated one in a normal impact). The thresholds in the stay ratio indicate that significant damage occurs in fine–carrier bonds when sufficient kinetic energy is reached. Beyond these thresholds, the stay ratio is gradually reduced with the increase in the impact velocity. This is not only due to the fact that fine–carrier attraction cannot entirely dissipate the kinetic energy, but it is also due to the increase in broken fine–fine bonds. The latter contributes to reducing the size of daughter fragments that remain on the surface of the coated carrier. The transfer of fines in a case in which fine particles are randomly distributed on the whole surface of the carrier at the initial state is shown in Fig. 7. The corresponding data is more scattered than that was obtained from even distribution cases, and the effect of interparticle interaction is difficult to observe. In adhesive mixtures, what actually plays the role in interparticle bonding is the total force that acts on particles, which is a function of the coordination number and interface energy for a mono-dispersed system. When fine particles are evenly

Fig. 7. The transfer ratio of fines which were randomly distributed in the initial state, Γ1–1 = 0.01 J/m2.

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Fig. 8. Effects of the fine–carrier interface energy on the damage ratio for a normal impact, Γ1–1 = 0.01 J/m2. Compression behaviour can be observed (damage ratio b 0).

distributed, the total force acting on individual particles has a narrow distribution. In order words, this fact reduces the overlapping of the distributions of the force corresponding to different values of the interface energy of particles. The effects of interface energy on the impact are thus possible to distinguish. When fines are randomly positioned, changes in interface energy can shift the entire force distributions but cannot diminish their overlap. Therefore, it is difficult to distinguish the behaviour for each change in interface energy. However, a maximum transfer ratio obtained at appropriate conditions is reflected in Fig. 7. It was also checked that in the case of that fines are evenly distributed on the entire surface of a carrier (not only on a spherical segment), the reflected tendency of each mechanism, e.g. transfer and stay, is similar to the earlier discussed cases (the results are not shown here). Therefore, the main conclusion which relates the interaction of fines– fines and fines–carrier and the impact velocity to the transfer of fines between carriers is valid for the different structures of adhesive mixtures that can be expected in a real mixing process. Although using solely the damage ratio [23] is not sufficient for characterising the fragmentation of agglomerates, it can be used as a quick tool to evaluate the packing status of such a particulate system. The damage ratio that resulted from the impacts corresponding to

different Γ1–2 is shown as a function of the impact velocity in Fig. 8. It should be noted that this damage ratio only accounts for fine–fine bonds, and a negative damage ratio indicates that there are more fine–fine bonds in the final state than in the initial state, i.e. the daughter fragments have a higher packing density. Fig. 8 shows that in most of the cases, i.e. Γ1–2 b 0.01 J/m2, the daughter fragments are compressed even at high impact velocities. At higher Γ1–2, the daughter fragments are only compressed at low velocities. This is consistent with the previous observation that the use of high fine–carrier interaction accommodates for better breakage. The main feature of Fig. 8 is that although the initial agglomerate has been broken into some fragments, the daughter fragments have a higher packing density than the original fragment. The damage ratio; however, just reflects the packing property of the overall system rather than the mechanical strength of individual fragments. To further explore agglomerate compression, the tensile strength of fragments can be used as a quantitative parameter and can be defined as Np 1 N σ t ¼ ∑ Ri ∑ nij F ij V i¼1 j¼1

! ð6Þ

Fig. 9. Tensile strength of the largest fragment on the coated carrier, on the new carrier, and that of the initial fragment. The size of the largest fragment is normalized by the initial fragment size. Normal impact with Γ1–1 = 0.01 J/m2, Γ1–2 = 0.03 J/m2.

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Fig. 10. Effects of fine–fine interface energy on the transfer ratio for a normal impact, Γ1–2 = 0.03 J/m2.

where V is the fragment volume, N and Np are the number of particles in the fragments and the number of neighbours around particle i, respectively, Fij is the force acting on the i–j pair connected by unit vector nij.

The tensile strength of fragments that stay on the coated carrier and that are transferred to the new carrier is plotted and is compared to the tensile strength of the original fragment in Fig. 9 (for α = 0). In the final state, there is a certain distribution of fragments on both carriers, but

Fig. 11. Effects of fine–fine interface energy on the stay ratio for normal impacts with (a) Γ1–2 = 0.03 J/m2, (b) Γ1–2 = 0.02 J/m2.

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only the largest fragments are considered here for the case Γ1–2 = 0.03 J/m2. As shown, the daughter fragments on both carriers have a higher tensile strength than the original fragment, especially those that resulted from impacts at high velocities. The drawback of using the damage ratio to evaluate particulate structure is also revealed by comparing Figs. 8 and 9. In the cases in which the damage ratio is positive, indicating agglomerate deformation, daughter fragments also have higher tensile strength than the original fragment. The fact that the resulting fragments have higher tensile strength, i.e. have been compressed, has been documented in the literature [13] where the press-on force during mixing can be related to the force exerted on fragments during carrier collisions in current simulations. This fact contributes as a significant mechanism that forms the final structure of adhesive mixtures in which tensile strength plays an important role in delivering product performance, e.g. dry powders for inhalation. Tensile strength also shows variation corresponding to change in the impact velocity, i.e. higher tensile strength was recorded at high impact velocity in the present study. This fact is in agreement with the observation from the agglomerate impact [17] which relates the impact velocity to the total force acting on particles. There is also a difference in the tensile strength of the fragments on the two carriers where higher strength was observed for those on the new carrier. This observation can be explained if the number of collisions for those two fragments is considered.

3.3. Effects of interface energy between fine particles Γ1–1 The transfer ratio and the stay ratio that resulted from the normal impacts corresponding to different values of Γ1–1 are shown in Figs. 10 and 11, respectively. The influence of the interface energy Γ1–1 can be expected to be more complicated since it must always be considered to be in a relative relationship with Γ1–2 [9]. It is obvious that Γ1–1 represents the breakage of agglomerates, Γ1–2; however, makes two contributions in the capturing of fine particles. The first one, as earlier discussed, Γ1–2 affects the breakage of agglomerates; and the second one is the capability to handle broken fragments. In fact, a low value of Γ1–1 gives high breakage performance which produces finer fragments. For the transfer ratio, a sufficiently high Γ1–2 can capture large fragments and, therefore, a higher Γ1–1 will give a higher transfer ratio at an impact velocity which is sufficient to break the initial agglomerate (see Fig. 10). When the Γ1–2 is not sufficient, only small fragments with low kinetic energy are attached by the carrier, which results in a higher transfer ratio for smaller Γ1–1. The transfer of fines is a dynamic process and is dependent on the combination of the interface energies and the impact velocity. Therefore, the maximum transfer ratio and its difference between cases should be considered as a reference to understand the process. Extensive simulations must be carried out at higher resolutions in order to determine the conditions for a “real” maximum transfer ratio unless a detailed mechanistic description is to be achieved. It should also

Fig. 12. (a) Transfer and (b stay ratio for the case of α = π/2, Γ1–1 = 0.01 J/m2.

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be noted that although a high Γ1–2 can capture large fragments, it also increases breakage performance which, in turn, produces finer fragments. Therefore, it is always necessary to consider both breakage and adhesion in a single context, and the stay ratio in Fig. 11 is a good illustration of this. As it can be seen, a higher Γ1–1 gives larger daughter fragments, and at low impact velocity, the coated carrier can retain these larger fragments, i.e. a higher stay ratio. At higher impact velocities, the coated carrier only can retain smaller fragments which results in a higher stay ratio for lower Γ1–1. The dependence of this transition on the impact velocity and Γ1–2 is reflected in a comparison of the data obtained from two cases with different Γ1–2 (Fig. 9a, Γ1–2 = 0.03 J/m2 and 9b, Γ1–2 = 0.02 J/m2) in which the transition point moves to a lower impact velocity when Γ1–2 decreases. This observation is in agreement with experimental findings based on the cohesion–adhesion balance theory, that the relative magnitudes of the cohesion and adhesion strengths significantly affect the de-agglomeration performance of fine–particle agglomerates [26,27]. 3.4. Effects of impact angle The transfer and stay ratio resulting from impacts with α = π/2 (i.e. tangential impact) are depicted in Fig. 12 for different Γ1–2. The corresponding data for the case α = π/4 is shown in Fig. 13. In general, the effect of interface energies and incident velocity on the impact in these cases is consistent with that which was observed for a normal

275

impact. That is, an appropriate combination of them would yield the highest transfer ratio, and the use of a high Γ1–2 results in a better capture of fines by the second carrier. The most interesting point is the behaviour revealed at low velocities, which reflects the effect of the impact angle on the transfer of fines between carriers. As discussed in Section 3.3, a secondary normal impact is responsible for the extremely high transfer ratio obtained. In the case of shear impact (α = π/2), this secondary normal impact did not occur in order to capture the fragment which was also totally removed from the coated carrier (see Fig. 12b). The transfer in this case was solely caused by the adhesion of disintegrated fragments onto the uncoated carrier; and thus, the transfer behaviour is in agreement with the cases at high impact velocity and interface energy. The impacts with α = π/4; however, illustrate this distinct behaviour more clearly than the cases of normal impact. The remove–capture of the whole fragment due to insufficient fine–carrier interaction occurred even at Γ1–2 = 0.01 J/m2 (see Fig. 13). Such behaviour can explained by a coupling with the effect of the impact angle on the agglomerate breakage reported by [18]. According to their findings, breakage performance greatly varies with the impact angle, and the greatest damage was recorded at the angle α = π/4. This can be interpreted to mean that, at this angle, stronger fines–carrier bonds can be broken upon impacts subject to the fact that an identical velocity magnitude is used for all impacts at different angles. The same observation can be made regarding the damage ratio plotted for three different angles in Fig. 14a. At one specific impact velocity, the damage ratio had

Fig. 13. (a) Transfer and (b) stay ratio for the case of α = π/4, Γ1–1 = 0.01 J/m2.

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Fig. 14. (a) Damage ratio and (b) stay and transfer ratio for three impact angles with Γ1–1 = 0.01 J/m2 and Γ1–2 = 0.03 J/m2.

Fig. 15. Relationship of variables in the transfer of fines among carriers.

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increased in the order of α = π/2, α = 0, α = π/4. This also applies to the region in which the fragments were compressed (negative damage ratio). In other words, compression is less pronounced in cases of impact with α = π/4. A comparison of the transfer and stay ratio corresponding to the three angles is plotted in Fig. 14b for impacts with Γ1–1 = 0.01 J/m2 and Γ1–2 = 0.03 J/m2. As shown, fines preferably stay on the carrier in the case of shear impact (α = π/2), i.e. higher stay ratio than that yielded from other angles. This is due to the poor breakage performance accommodated by shear impacts, as reflected by the damage ratio (Fig. 14a). The stay ratio also varied less with impact velocity for the shear impact while a threshold was observed for other cases at the point where the kinetic energy was sufficient to boost agglomerate damage. Although this threshold was also observed for the shear impact (see Fig. 12b), it requires a lower fines–carrier interface energy and higher impact velocity. The transfer ratio for this value of Γ1–2; however, shows the opposite behaviour. Consequently, more fines are transferred to the new carrier when α = π/4 than in the other cases, which is due to the breakage performance. It should be noted again that the variation in the transfer and the stay ratio of fines must be considered together with the ratio of ΓΓ11 at a certain impact velocity. Additional research with the 12 purpose of obtaining a mechanistic description of such a relationship thus is needed.

3.5. Relationship between particle properties and operating conditions Fig. 15 shows an interpretation of the correlation of the investigated parameters, i.e. the interface energies, the impact velocity, and the impact angle, on the collision and the transfer of fines between two carrier particles. For the purpose of discussion, the ratio of incident kinetic energy to the interface energy has been used to characterise the breakage of fragments. The normal and the shear impact at a given set of conditions are compared to characterise the effect of the impact angle. At low impact velocities, there is no transfer of fines until a certain velocity is reached (point 1), which is not sufficient to break fine–fine bonds within the agglomerate but is sufficient to break fine–carrier bonds between the agglomerate and the carrier. It should be noted that the onset of this depends on the size of the initial agglomerates coated on the carrier, i.e. the larger the agglomerate is, the easier it is removed from the carrier. From this point, there is a dramatic increase in the transfer ratio due to the removal of large fragments caused by a normal impact since such an impact produces a secondary normal impact whilst the shear impact does not. Consequently, the impact angle becomes significant. At the point where the kinetic energy is sufficient to break fine–fine bonds (point 2), the transfer ratio starts to decrease due to the production of smaller fragments. The transfer ratio in the shear impact gradually increases within this range owing to better breakage performance. When the kinetic energy is high enough to fragmentize the initial agglomerates (point 3), the interaction between uncoated carrier and fine particles comes into play and gradually increases the transfer of fines for the normal impact. From this point, the tendency of the transfer ratio in the normal and shear impacts is consistent. The maximum point (point 4), as earlier discussed, is a consequence of the utilization of both breakage and adhesion. An additional increase in impact velocity will decrease the transfer ratio due to the reduction of adhesion capability. The main feature of this illustration is that the transfer of fines among carriers occurs with different behaviours depending on the relationships between the kinetic energy, the interface energies and the impact angle. In fact, all of these scenarios can be expected in a real mixing process in which a large velocity gradient and wide angle distributions are encountered. Among the mechanisms involved in adhesive mixing, the deagglomeration has been reported to be the time-limiting step in achieving the homogeneity of fines [11]. The time scale of the transfer of fines; however, is the key to answering whether or not the microstructure and

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micro-homogeneity of fines have been established. The observation in Fig. 15 can be interpreted to roughly evaluate how different processing conditions can affect this time scale. Indeed, neither the extreme transfer limited between points 1 and 3 in the case of normal impact, nor no transfer at all, as to the left of point 1, would be advantageous for establishing an equilibrium state. In these cases, additional energy input would be required, either in terms of increasing mixing speed or longer mixing time, to deform fine–particle fragments or to break fine–carrier bonds to transform them to the regime beyond point 3. Within this regime, most fines would remain as “free” particles after early collisions and would be deposited onto carriers through their own collisions with the carriers, which is supposed to be advantageous for an even distribution of fines. This is, however, a very rough estimation of the transfer time for different cases. Such time scale should always be considered together with a suitable condition to obtain the desired structures. For instance, a mixing speed that is too high is inefficient for dispersing fines during the inhalation of dry powders due to the increase of tensile strength of fine–particle fragments. The main point here is that the type of mixer is of importance from the perspective of collision angle. For instance, in a high shear mixer where tangential collisions dominate, the transfer of fines is not really sensitive to the impact velocity, i.e. no extreme transfer occurs at low velocities. For other devices in which normal collisions are noticeable, the impact velocity would have a major influence on the transfer time scale. In fact, the limits pointed out in Fig. 15 would shift depending on the relationship of all the parameters used in the mixing process. This motivates the need for a mechanistic description that relates particle properties and processing conditions to the transfer of fines in order to better predict an adhesive particle mixing process. 4. Conclusions DEM simulations were carried out to investigate the transfer of fines between carriers, which is one of the important mechanisms in formulating the microstructure of adhesive mixtures. Extensive analysis was performed to characterise the effects of the interface energies, the impact velocity and the impact angle on the transfer process. It was found that fines are transferred by means of carrier collisions in different patterns according to the relative magnitude of the kinetic energy and the interface energies both between fines and between fines and carrier. The impact angle introduces a significant effect when the kinetic energy is able to be dissipated into adhesive bonds between fines which strength are represented by the interface energy. Fine–particle fragments are also restructured after a collision in which both of the fragments that remain on the initial carrier and that are transferred to another carrier have higher tensile strength than the original fragment, i.e. fine–particle fragments are compressed by collisions. The correlation of particle properties (e.g. interface energies), processing parameters (e.g. the impact velocity), and the type of mixer (e.g. the impact angle) in characterising the transfer mechanism was introduced to characterise the coupling effect of those governing parameters. The finding of this paper motivates further research to develop a mechanistic description that better predicts the mixing process and the resulting structures of fine particles adhering to the carriers. References [1] P. Lacey, The mixing of solid particles, Chem. Eng. Res. Des. 75 (1997) S49–S55. [2] V.K. Vikas, A. Saharan, M. Kataria, V. Kharb, P.K. Choudhury, Ordered mixing: mechanism, process and applications in pharmaceutical formulations, AJPS 3 (2008) 240–259. [3] J.A. Hersey, Ordered mixing: a new concept in powder mixing practice, Powder Technol. 11 (1975) 41–44. [4] H. P., F. Grasmeijer, H.W. Frijlink, H.A. de Boer, Mixing time effects on the dispersion performance of adhesive mixtures for inhalation, PLoS One 8 (2013). [5] A. Sato, E. Serris, P. Grosseau, G. Thomas, A. Chamayou, L. Galet, M. Baron, Effect of operating conditions on dry particle coating in a high shear mixer, Powder Technol. 229 (2012) 97–103.

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