The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam filters

PTEC-14637; No of Pages 9 Powder Technology xxx (2019) xxx

Contents lists available at ScienceDirect

Powder Technology journal homepage: www.elsevier.com/locate/powtec

The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam filters L. Ditscherlein ⁎, P. Knüpfer, U.A. Peuker Institute of Mechanical Process Engineering and Mineral Processing, Technische Universität Bergakademie Freiberg, Agricolastraße 1, 09599 Freiberg, Germany

a r t i c l e

i n f o

Available online xxxx Keywords: Nanobubbles Capillary forces Adhesion Atomic force microscopy

a b s t r a c t With decreasing wettability and rough surfaces the adhesion forces between the interacting surfaces shift to higher values. This is due to capillary bridging by nanobubbles which are sitting on one or both rough surfaces and cause capillary interactions. For particles, the coverage with such bubbles for different wettability and gas oversaturation is shown. Also, it is possible to identify three general types of force distance curves: curves with no capillary interactions, curves with capillary interactions but no repulsion during approach and curves with capillary interactions and a small repulsion just before snap-in. Possible reasons for repulsion are analysed and a calculation of Hamaker constants is presented. Furthermore, well-known models for adhesion on rough surfaces are compared with the experimental data. © 2019 Published by Elsevier B.V.

1. Introduction Knowledge about interaction forces and the related influencing parameters is of great interest for various industrial processes like flotation, filtration or product design by agglomeration. In the case of deep bed filtration of liquids, the efficiency of the process depends particularly on the adhesion forces between particles and e.g. foam filters [1]. Also, an agglomeration of the particles upstream before filtration has a positive effect on the separation efficiency [2]. With the developments of the surface force apparatus and the atomic force microscope (AFM) in the second half of the 20th Century [3,4], intensive investigations of adhesive forces between two surfaces were done [5–8]. For instance, theoretical models of van der Waals interactions for specific geometries (homogeneous chemical and morphological properties) were examined and adapted on more realistic surfaces (root mean square (rms) roughness b20 nm) [9–13]. What is common to all of them is a reduction of adhesive force due to the lower contact area between the solids. Models like the ones of Rumpf [14], Hoffmann [15], Rabinovich [9,16], Xie [17] or Fritzsche [18] include roughness as a hemisphere or spherical cap, more or less following the morphology of the real surfaces. One of the systematic problems with these fairly simple models is an overestimation of attractive force for small roughness due to double counting of the fictive roughness, also the asperities is always convex and not concave. Another problem is the exclusive consideration of only one hemisphere or cap. The model of Fritzsche overcomes this issue ⁎ Corresponding author. E-mail address: [email protected] (L. Ditscherlein).

assuming normal distributed asperities. Further, the empirical models have been as long as adjusted (e.g. numerical values of Rabinovich's model or cut off distances) on experimental data that they may work for one substrate surface but fail for another one. Other models, like the model of Cooper [19] or Dagastine [20] approach the problem by other means. Cooper uses cylindrical volume elements to describe his roughness. Unfortunately, in this work they did not use the topographical data of their samples but simulated surfaces. Dagastine's model of layers is quite interesting considering different hamaker constants for every layer depending on the solids volume fraction, but (just as the model by Cooper) not validated for surfaces with high roughness as we have investigated in this study. Bhattacharjee et al. [21] published a model that includes van der Waals as well as electric double layer forces that overcome the restrictions by the Derjaguin approximation. The repulsive barrier is markedly affected by roughness, especially for small rms-values. It is to say that they have used fixed surfaces potentials in this study; in another one they show that roughness is coupled with surfaces charging behaviour and renders the forces attractive or repulsive [22]. So up to know, it is not really clear how real, chemically and morphological complex surfaces can be described exactly. It is seen for many water-based systems and processes that conventional DLVO forces do not explain the interactions between hydrophobic surfaces [23,24]. Besides van der Waals (vdW) interactions there is another attractive force that might influence processes significantly. Israelachvili and Pashley were the first who showed that vdW forces are weaker than so-called hydrophobic interactions [24]. Since then, hydrophobic interactions have been the scope of a variety of investigations [25–31] and many theories about their origin were proclaimed [6,16,32]. Up to

https://doi.org/10.1016/j.powtec.2019.08.077 0032-5910/© 2019 Published by Elsevier B.V.

Please cite this article as: L. Ditscherlein, P. Knüpfer and U.A. Peuker, The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam fi..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.077

2

L. Ditscherlein et al. / Powder Technology xxx (2019) xxx

now, the origin of hydrophobic forces is still under debate. A promising approach is a division of hydrophobic interactions in two parts: • Firstly a short-range true hydrophobic interaction, decaying exponentially and having a range of a few nanometers, caused by a structuring of water molecules near the low energetic surface; • Secondly a long-range interaction, acting up to several hundreds of nm, caused by capillary bridging due to small cap-shaped bubbles, often called nanobubbles [33–35]. The structuring of water molecules near the hydrophobic surfaces occurs due to a re-orientation of the dipoles parallel to the surface because it is energetically more favourable to interact with themselves than with the surface. Consequently, a water depletion layer is generated. In turn, nanobubbles are formed during immersion, because of a gas solubility gradient (temperature or solvent-exchange induced) or by perturbation. As a result of the depletion layer, dissolved gas molecules are enriched in this layer and act as a gas reservoir for the nanobubbles. Their long-term stability, for years subject of discussions, can be explained by a dynamic equilibrium between in- and outflux of gas if the liquid is supersaturated as well as a contact line pinning [36]. Investigations on nanobubbles are usually done on atomically rough surfaces, more precisely samples with rms values below 5 nm. Surfaces in industrial processes are much rougher, e.g. rms N 200 nm, so adhesion models and/or phenomena seen on smooth surfaces might be inexact for technical processes. Interestingly, there is only a small number of published vdW-models for technical rough surfaces yet, e.g. by You et al. [10] and Fritzsche et al. [18]. On the other hand, there are hardly any models that describe short-range hydrophobic interactions on smooth [37] and technical rough surfaces [18,38] and until now no models for long-range “hydrophobic” interactions (nanobubble bridiging) are available. The models that describes such short-range hydrophobic interactions uses the van Oss model for surface energies, but it is questionable if this model is valid [39]. In case of rough surfaces, the impact of both short- and long range interaction has to be estimated.

In this study the authors focus on technical rough hydrophobized ceramic samples in a water-based system described elsewhere [40] to examine adhesion mechanisms and their potential influence on engineering processes like deep bed filtration. The impacts of wetting as well as roughness on measured adhesion forces are investigated. 2. Material & methods Topographical imaging and force spectroscopy were done using the atomic force microscope XE-100 from Park Systems (South Corea). All measurements were carried out with deionized water. Samples in the form of pressed and sintered ceramic tablets were prepared as it is described in [41]. Chosen alumina particles, made by fused-salt electrolysis (Impratex, Switzerland), had diameters between 30 and 40 μm. Due to the hydrophilic character of the used ceramics, both samples and particles were coated with the silane Dynasylan® F8261 of Evonik Industries Germany (see [40]). Silanization leads to an apparent water contact angle of 104° on the sample, respectively the colloidal particles. Alumina particles were glued on tipless cantilevers using a waterinsoluble epoxy resin. Cantilevers that are used in poor wetted systems should be stiffer due to larger adhesive forces, so for total hydrophobic systems AIOAL-TL B cantilevers from Budget Sensors (Bulgaria) were used (calibrated spring constants ranged from 1.55–4.50 N/m) in this study. For small adhesive interactions, for instance observed in entirely hydrophilic systems, soft AIOAl-TL A cantilevers have been used with spring constants between 0.15 and 0.30 N/m. For each sample 64 force distance curves on a 10 × 10 μm2 area on at least 6 different parts of the substrate surface were measured to get statistical valid results. A MatLAB® routine recalculated the raw data and determined the adhesion force, which is defined as the minimum of the retrace for each force distance curve. These pull off forces were normalized by the particle diameter because of the linear relationship between adhesion force and particle size. To distinguish and to classify the force distance curves, the snap-in force of 10 nN is used as criterion based on [23] for whether capillary bridging takes place (snap-in force N10 nN) or not (no preexisting nanobubbles, snap-in force b10 nN). Topographical scans

Fig. 1. SEM and AFM scan of an alumina particle (left) and AFM scans of rough tablet-shaped samples (right; TiO2 (above) and Al2O3 (below)).

Please cite this article as: L. Ditscherlein, P. Knüpfer and U.A. Peuker, The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam fi..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.077

L. Ditscherlein et al. / Powder Technology xxx (2019) xxx

were done using a ContAl-G cantilever from Budget Sensors with a spring constant of 0.20 N/m. With this soft cantilevers it is possible to detect nanobubbles directly, while force spectroscopy is an indirect method. For the topographical investigation and the measurement of particle-particle interactions of alumina particles at different wetting conditions, the particles have been embedded into a thin epoxy layer, whereby these particles were fixed to the grounded glass substrate. By using this method, the particles have been silanized with Dynasylan® F8261 via chemical vapor surface modification (CVSM), described in [42] which is adapted from [43]. A SEM and AFM image of an exemplary colloidal probe and AFM images of rough ceramic surfaces are shown in Fig. 1. 3. Results & discussion 3.1. Particle-plate interactions: impacts of wettability and roughness In a previous study, the influence of wettability on the interaction forces has been studied on sintered alumina samples with and without polishing [44,45]. Unpolished alumina samples are comparable with the sample presented in Fig. 1 (right below) whereas polished ceramic samples show abraded hills and unaffected valleys. For both, poor wettability leads to higher adhesion forces due to the presence of nanobubbles and/or short-ranged hydrophobic interactions. In other words, improved wetting results in a smaller contribution by capillary interactions. In Fig. 2, results for another complex surface (see Fig. 1 right above, rutile with steps on each single particle due to the crystallization, root mean square of a 3 × 3 μm2 area: 0.3 μm) are shown. Clearly visible and in accordance with the previous studies is an increase in adhesion if wettability is decreased. For two hydrophilic surfaces, the force distribution is determined by the changing interaction area due to variations in surface roughness. No nanobubbles are detected onto the surface. A Weibull distribution fits the data very well. Such a distribution is a continuous two-parameter probability distribution, normally used for the determination of failure rates:
x B

−

F ¼ 1−e

A

ð1Þ

1 Here, is the scaling parameter that gives information about the disA tributions width and B is the shape parameter. If the shape parameter

Fig. 2. Force distributions for rutile samples with alumina colloidal probes under variation of wetting behaviour: total hydrophilic (hphilic), hydrophilic sample and hydrophobic particle (hphilic-hphobic) and splitted curve for total hydrophobic systems (hphobic). Splitting is done by separating the data into curves with (capillary interactions that is pre-existing nanobubbles) and without snap-in (short range interactions/nanobubbles by perturbation).

3

has been appropriate selected, a Weibull distribution is similar to others like an exponential (B = 1), a normal (B = 3.6) or a Rayleigh distribution (B = 2). Another Weibull distribution is used to fit the data for the hydrophilic-hydrophobic system. Due to the particle hydrophobicity it is assumed that hydrophobic interactions are present on the particle surface and increase the overall adhesion. For two hydrophobic surfaces, the data is split into a distribution with pre-existing nanobubbles (with snap-in) and without pre-existing ones (no snap-in). Again, clearly visible is an increase in adhesion if capillary interactions occur. If nanobubbles are present on the surface before approaching of the two surfaces, interactions are significantly stronger due to larger size of the bubbles and the capillary interactions. There exists a transition zone between hydrophilic-hydrophobic and total hydrophobic systems. Assuming some, not fully accessible bubbles inside of pores in the case of the total hydrophobic system (here the particles contacts the solid “hills” and not the bubble), it is obvious that adhesion is reduced. On the other hand, there exist a few number of bubbles on the hydrophobic surface in the hydrophilic-hydrophobic case that lead to a large adhesion force because of capillary bridging. Nanobubbles might also be generated during contact of the two surfaces due to perturbation as it is described in literature [46]. Data fitting was done using Weibull distributions, but the accordance between fit and experimental data for large forces without snap-in, respectively small forces with snap-in is unsatisfactory. It is assumed that on the one hand rarely large bubbles are generated by perturbation (distribution without snap-in) and on the other hand some small or poorly accessible bubbles exist (distribution with snap-in). A coupling of two distributions might describe the force distribution better if the coverage and size of the bubbles is known. Another influencing property on adhesion between surfaces is their roughness. Therefore, ceramic samples with different wetting properties were investigated. It is seen for hydrophilic surfaces in liquid phase that higher roughness results in a decrease of adhesion force because of a smaller contact area (Fig. 3 left above). Hydrophilic TiO2 (rms of a 3 × 3 μm2 area: 0.3 μm) shows the largest adhesion forces followed by spinel (rms = 0.6 μm) and alumina (rms = 0.8 μm). Although AC1_0, a sample made of alumina and additives, is the smoothest sample (rms = 0.2 μm) there are only small van der Waals forces detectable. This is because of the different chemical composition of the additives and the lower purity of Al 2 O3 . In Section 3.3, a calculation of vdW interactions of the samples is presented that include the respective Hamaker constants and compare theoretical values with experimental data and mathematical fitting. For the hydrophilic-hydrophobic system (Fig. 3 right above), adhesion is increased compared to the total hydrophilic system and the clear dependence on roughness does not hold. This is due to a very complex interaction caused by roughness, which consist of short range hydrophobic and in some rare cases of capillary interactions. For the interaction of two hydrophobized surfaces, there are no longer differences in the surface chemistry due to the silane layer on both surfaces. The hydrophobized ceramics with varying roughness clearly show an increase of adhesion with increased roughness. This principal change compared to the wetting surfaces derives from the presence of small bubbles inside of asperities and pores: The process of immersion with water is too fast to wet pores, and so there are nano- and also mesobubbles distributed all over the surfaces, depending on the pore size and distribution. They sit stable inside of the asperities and cannot be depinned easily up to scanning forces of 40–50 nN. In a previous study, we have shown that bubble depinning forces needed on smooth hydrophobic surfaces are decreased (below 5 nN) due to the less pinned three phase contact line [44]. For technological processes like deep bed filtration, the impact of roughness might be a crucial factor to control process efficiency. Tailoring the surface morphology as a function of the wetting properties of the process fluid allows for controlling the collection efficiency of a filter surface.

Please cite this article as: L. Ditscherlein, P. Knüpfer and U.A. Peuker, The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam fi..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.077

4

L. Ditscherlein et al. / Powder Technology xxx (2019) xxx

Fig. 3. Force distance distributions for the case sphere-plate under variation of wettability (entirely hydrophilic or hydrophobic (left) and hydrophilic-hydrophobic (right above)) and roughness and data of the curve fittings (right below).

3.2. Particle-particle interactions: impacts of wettability and gas oversaturation Unfortunately, up to now it is not possible to analyse the force data of two hydrophobic surfaces more in detail by using AFM, for instance if bubbles sit only on one or on both surfaces. It is, therefore, highly probable that nanobubbles do not sit exclusively on the rough sample surface as it was observed in [47] but on the rough particle surface, too. To prove this, particles similar to those used as colloidal probe with varying hydrophobicity were scanned in intermittent mode (Fig. 4 top). On the surface of hydrophilic particles no nanobubbles were found. After simply immersing the hydrophobic particles in water, a few gas reservoirs became visible inside the cavities. Finally, after applying solvent exchange to the liquid phase, the gas oversaturation increases and therefore large nanobubbles grow all over the particle surface. In this case, it is highly probable that nanobubbles form a capillary bridge during contact events. Therefore, for force measurements between two hydrophobic particles after solvent exchange it is conceivable is a picking up of bubbles from the grounded surface during contact, since the bubbles stay pinned in asperities. Fig. 4 (below) shows the adhesive force distribution between the CP-particles and the embedded, grounded particles at different conditions. In order to compare the forces, these were normalized to the harmonic mean particle diameter. The hydrophilic combination

provides the lowest adhesion forces, as it is expected. Between hydrophobic particles, the capillary interactions increase the adhesion forces, what is in good agreement with the measurements on the hydrophobic flat substrates. Fig. 4 (right above) shows a significant increase of the number of surface nanobubbles on the particle surface after applying a solvent exchange. The appropriate force measurements exhibit a further increase of the particle interactions in relation to the immersed hydrophobic particles. This is explainable on the one hand due to the extraordinary possibility for forming a capillary between the particles and on the other hand the chance to create multiple capillary contact points. If the size of the nanobubbles has an impact on the resulting capillary force is not completely proved [48]. The results clearly show that engineering processes, for instance particle agglomeration, highly depend on wetting behaviour and gas oversaturation level. 3.3. Cases for force distance curves, calculations and comparison of models A closer look at the force spectroscopy data for rough hydrophobic samples is shown in Fig. 5. An exemplary 2D map of adhesion force, energy and snap-in force shows the relation between these three quantities: The higher the snap-in force during approach, the larger is the adhesion force and adhesive energy (that is the area obtained by integration of the adhesive interaction of the retrace), although there is no linear relation between snap-in and adhesion force. Adhesive

Please cite this article as: L. Ditscherlein, P. Knüpfer and U.A. Peuker, The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam fi..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.077

L. Ditscherlein et al. / Powder Technology xxx (2019) xxx

5

Fig. 4. Phase contrast and topographical images (top) of hydrophilic (left) and hydrophobic particles that are scanned after immersing in water (middle) or solvent exchange (right) and force distributions of sphere-sphere investigations under variation of wettability and gas oversaturation. The domes, clearly visible in phase contrast images, are interpreted as pre-existing nanobubbles.

interactions up to 140 nN for snap-in forces and 600 nN for pull off forces can be measured, which are much larger compared to van der Waals interactions. This is only explainable by capillary interactions. At regions without bubbles, no snap-ins are detected and adhesive interactions are small (case I). If nanobubbles pre-exist onto one or both surfaces, a snap-in can be detected and the retrace curve looks totally different from case I. While the jump-off for case I is sharp, a longranged pull off takes place for retracing the cantilever when capillary interactions are present (case II and III). This is explainable by large bubbles that are deformable. Interestingly, the force distance curves with snap-in differ regarding their behaviour just before the particle jumps into contact. Curves with high snap-in/adhesion force always show a slight repulsion, which has an exponential nature (case III). In case of deep bed filtration or other

engineering processes, this leads to the necessity to provide enough energy, kinetic energy respectively, to overcome this repulsive barrier. Still unclear is the reason for the small repulsion just before a snap-in occurs (case III). An explanation might be a trapped bubble on the particle surface that interacts with nanobubbles sitting on the sample. In the opinion of the authors such repulsive effects just before snap-in might occur due to surface charges of the nanobubbles on the hydrophobic surfaces, hydrodynamic forces because of a deformation of the bubbles surrounded by water or another (additional) repulsive force. Comparable to microbubbles, the nanoscopic gaseous domains are negatively charged [49], whilst uncoated alumina [50,51] or coated surfaces [52] are slightly positive charged in a pH range of 6–7 as used during the measurements. It means in effect that repulsion due to equally charged surfaces can only occur if both interaction parts of the surfaces are

Please cite this article as: L. Ditscherlein, P. Knüpfer and U.A. Peuker, The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam fi..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.077

6

L. Ditscherlein et al. / Powder Technology xxx (2019) xxx

Fig. 5. 2D maps of adhesion and snap-in force as well as adhesion energy between two hydrophobic alumina samples (left), types of force distance curves (I: no capillary interaction, II: capillary interaction without repulsion and III: capillary interaction with repulsive force just before snap-in) and relation between repulsion and potential drop.

covered with bubbles. Shi et al. measured a repulsive force of only ~1 nN between nanobubbles and a microsized bubble [53], however, here in this study repulsive forces up to 9 nN have been observed. Another point is the missing correlation between the number of nanobubbles on the surfaces (indirectly accessible with higher gas oversaturation, larger rough particles etc.) vs. the repulsive force or the snap-in force vs. the repulsive force. During approach, the water film between the bubbles has to get disrupted before a capillary bridge is formed. Film rupture is impaired if both soft surfaces (interphase of the nanobubbles on top of the rigid surfaces) are deformed. A calculation of hydrodynamic interactions [54] for an approach speed of 5 μm/s and a particle radius of 20 μm leads to values of b2 nN, however with larger bubbles and therefore stronger deformation, they can reach 10 nN [53]. Furthermore, an additional repulsive force (e.g. repulsive van der Waals interactions) might occur during approach. For such reasons, Hamaker constants were calculated with Lifshitz theory for the investigated systems. For Dynasylan®-coated alumina we have determined Hamaker constants for Teflon due to the PTFE-like structure of the silane. This simplification was done due to the unknown layer thickness and homogeneity of the silane on the rough surfaces. With the Ninham-Parsegian representation, ε(iξn) is given by Eqs. (2) and (3) [55]:

εðiξn Þ ¼ 1 þ



Cj 2

ξ 1þ ωj

þ

g jξ

ð3Þ

ω2j

where kB is the Boltzmann constant, T represents the temperature, h is Planck's constant, n is the running number, B and Cj are related to the oscillator strength in the microwave, infrared, respectively ultraviolet range, τ and gj are the damping coefficients of the oscillator in the different wavelength ranges and ωj represents the relaxation frequency. The second term is the contribution from the orientation of permanent dipoles and the third term represents the summation of absorption peaks in the infrared and ultraviolet range. Except from water, the second term can be neglected for the materials studied here. The differences in dielectric response Δkl are defined as Δkl ¼

εk ðiξn Þ− εl ðiξn Þ εk ðiξn Þ þ εl ðiξn Þ

ð4Þ

where εk(iξn) and εl(iξn) are the dielectric response function of material k and l. By integrating term by term, AH;132 ¼

4π2 kB T ξn ¼ n h

N X B þ 1 þ ξτ j¼1

∞ ∞ X 3kB T X ðΔ13 Δ23 Þs 0 2 n¼0 s¼1 s3

ð5Þ

ð2Þ is obtained, where s is the number of terms [56]. Non-retarded Hamaker

Please cite this article as: L. Ditscherlein, P. Knüpfer and U.A. Peuker, The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam fi..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.077

L. Ditscherlein et al. / Powder Technology xxx (2019) xxx Table 1 Non-retarded Hamaker constants AH calculated via Lifshitz theory for the used materials. Material (M)

M-vac-M

M-H2O-M

M-H2O-Air

AH in 10−20 J

AH in 10−20 J

AH in 10−20 J

Al2O3 TiO2 MgAl2O4 PTFE H2O

15.20 15.29 12.63 3.80 3.93 (GP) 3.74 (HW) 5.00 (B) System (hydrophilic)

Al2O3-H2O(B)-Al2O3 Al2O3-H2O(B)-TiO2 Al2O3-H2O(B)-MgAl2O4 Al2O3-H2O(B)-PTFE

GP

HW

B

GP

HW

B

4.79 5.98 3.32 0.33

5.01 6.16 3.50 0.34

3.67 5.35 2.44 0.42

−3.67 −3.98 −2.99 0.25

−3.65 −3.97 −2.99 0.15

−3.69 −3.80 −2.88 0.84

AH in 10−20 J 3.67 3.11 2.97 0.98

System (hydrophobic) AH in 10−20 J PTFE-H2O(B)-Al2O3 PTFE-H2O(B)-TiO2 PTFE-H2O(B)-MgAl2O4 PTFE-H2O(B)-PTFE

−0.19 −0.24 −0.06 0.42

Dielectric data is taken from Bergström (B) [48] adapted from [49], Hough et al. (HW) [47] and Gingell et al. (GP) [50]. M-vac-M calculations were done using the data from Hough et al. and Bergström et al.

constants, calculated with Eqs. (2)–(5), n = 2000 and s = 5, are presented in Table 1. Table 1: non-retarded Hamaker constants AH calculated via Lifshitz theory for the used materials; dielectric data is taken from Bergström (B) [57] adapted from [58], Hough et al. (HW) [56] and Gingell et al. (GP) [59]. M-vac-M calculations were done using the data from Hough et al. and Bergström et al. In comparison to vacuum, the Hamaker constants are reduced with water as the intervening medium. Differences for the calculated Hamaker-constants arise due to different spectral data provided in the references. Repulsive van der Waals forces occur for ceramic-water-air systems, whereas the PTFE-water-air system shows attractive forces. Assuming an entirely silane-covered surface and validity of the PTFE-simplification for the Hamaker constant as stated out before, vdW interactions should be attractive. If (in addition to surface charges and hydrodynamic interactions) repulsive vdW forces play a role, then only in the event of an insufficient homogeneity of the silane coverage, e.g. on edges. However, repulsive interactions just before snap-in have been measured only for strong adhesive forces with large deformation, so in the authors opinion the case M-H2O-Air is not valid and repulsive van der Waals interactions are not responsible of the repulsive barrier prior to snap in. In a nutshell, repulsive interactions occur if nanobubbles are sitting on both interacting surfaces and electrostatic forces due to surface charges and hydrodynamic effects take place. Besides this closer examination on reasons for repulsion just before snap in, Hamaker constants of the ceramic systems presented in Section 3.1 are calculated using Lifshitz theory (Table 1) to determine

7

theoretically vdW-forces and to compare these values to the experiF F mental values (median values see Fig. 3 right or Table 2 ð ¼ Þ). D 2R Table 2 shows the results of the calculation of van der Waals interactions involving rough surfaces by using different approaches: Besides theoretical vdW interactions between ideally smooth and homogenous surfaces, three well-known models for rough surfaces were used. Rumpfs model (Eq. (6)) is based on contact of a centered, single hemispherical asperity with a larger spherical particle along a line normal to the surface [14]. Rabinovich et al. modified Rumpfs model (Eq. (7)) by connecting spherical caps with the root mean square roughness of the surface [9]. Fritzsche et al. presented another model (Eq. (8)) based on spherical caps combined with rms-roughness and a structure parameter [18]. 2

3

AH R 6 6 r þ F¼ 4 6D20 r þ R

7 1   7 5 r 1þ 2 D0

ð6Þ

2

3

7 AH R 6 1 1 6   7 þ F¼ 5 24 R 1:48rms 6D0 1 þ 1þ 2 1:48rms D0

ð7Þ

2

3 qffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 −c2 2 r R −c 6 7 AH 6 r A A qffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ  F¼ þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 7 5 ð8Þ 6 4D20 r þ D0 − r 2 −c2A 2 R þ D0 þ hA − R2 −c2 2 A

Where AHis the Hamaker constant of the system, R the particle radius, D0 the cut off distance, r the radius of the asperity, cA the chord radius of the asperity and rms the root mean square roughness. For the entirely hydrophilic system, the only attractive force is the vdW force. Models for ideally smooth and for rough surfaces overestimate the normalized forces measured via AFM extremely and have to be questioned. In the case of the hydrophobic particle (PTFE-like surface) and the hydrophilic surfaces, repulsive van der Waals interactions should occur theoretically. Obviously adhesion is increased compared to the hphilic-hphilic system and a mere description by van der Waals forces is missleading. Assuming correctly determined vdW forces using the models, the additional forces (short range hydrophobic, capillary interactions) can be calculated by simple mathematics. This results in total adhesive forces for hydrophilic-hydrophobic systems between 0.62 mN/m (AC1_0) up to 1.49 mN/m (Al2O3), which are much stronger than any calculated vdW-forces. Except the calculation for smooth surfaces, vdW forces determined with the three models for entirely hydrophobic systems underestimate the measured median values. This is evident because of capillary interactions that are much stronger and

Table 2 Calculated vdW forces for the investigated systems with different models using the Derjaguin approximation [52] (smooth, Rumpf [51], Rabinovich [9], Fritzsche [29]) and experimental overall values. System Hphilic

Hphilic -hphobic

Hphobic

Al2O3-H2O-Al2O3 Al2O3-H2O-Al2O3 Al2O3-H2O-TiO2 Al2O3-H2O-MgAl2O4 PTFE-H2O-Al2O3 PTFE-H2O-Al2O3 PTFE-H2O-TiO2 PTFE-H2O-MgAl2O4 PTFE-H2O-PTFE PTFE-H2O-PTFE PTFE-H2O-PTFE PTFE-H2O-PTFE

rms in μm

Smooth in mN/m

Rumpf in mN/m

Rabinovich in mN/m

Fritzsche in mN/m

F/R50 in mN/m

0.2 0.8 0.3 0.6 0.2 0.8 0.3 0.6 0.2 0.8 0.3 0.6

248.2 248.2 210.3 200.8 −12.8 −12.8 −11.8 −11.8 28.4 28.4 28.4 28.4

2.6 10.1 3.3 6.3 −0.1 −0.5 −0.2 −0.4 0.4 1.4 0.5 1.1

3.8 14.6 4.8 9.0 −0.2 −0.8 −0.3 −0.6 0.5 2.0 0.8 1.5

2.6 10.5 3.3 6.4 −0.1 −0.5 −0.2 −0.4 0.4 1.5 0.6 1.1

0.04 0.05 0.20 0.09 0.60 0.77 1.19 0.76 1.08 5.22 1.81 3.39

(Note that hydrophobic and capillary interactions for hphilic-hphobic and hphobic are included); chosen cut off distance and asperity angle are 0.157 nm and 45°.

Please cite this article as: L. Ditscherlein, P. Knüpfer and U.A. Peuker, The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam fi..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.077

8

L. Ditscherlein et al. / Powder Technology xxx (2019) xxx

not considered. Assuming a certain accordance of calculated vdW interactions on rough hydrophobic surfaces, hydrophobic and capillary interactions increase the total adhesion about 2.2 up to 3.7 times compared to vdW forces and lie between 0.68 mN/m (AC1_0) – 3.82 mN/m (Al2O3). Table 2: calculated vdW forces for the investigated systems with different models using the Derjaguin approximation [60] (smooth, Rumpf [14], Rabinovich [9], Fritzsche [18]) and experimental overall values (note that hydrophobic and capillary interactions for hphilic-hphobic and hphobic are included); chosen cut off distance and asperity angle are 0.157 nm and 45°. It should be noted that the three models for vdW interactions on rough surfaces take only roughness on one of both surfaces into account and the particle roughness of rms = 0.08 μm is not considered. Also, the limitation of Rabinovich's model is rms b 20 nm, that is to say the investigated samples are not suitable for this model. On the other hand, Rumpf and Fritzsche do not give any limitations about their model validity and such a wide range of valid roughness (0.2–0.8 μm) is hardly to imagine. So, in conclusion it is to say that with correctly calculated vdW forces one can determine non-van der Waals attractive forces like short range hydrophobic or capillary forces on rough surfaces, but at the moment no further splitting is possible due to the lack of appropriate models. Fitting the experimental data of sphere-plate interactions with Weibull distributions leads to considerably better accordance (see F/D values in Fig. 3) with the total adhesive force, but it has to be emphasized that this is only a mathematical description without known physical correlations as they are stated in the examined models. Interestingly, the mathematical distribution of Weibull approaches an exponential distribution (B ≈ 1) for the rough surfaces in the case of entirely hydrophilic and hydrophilic-hydrophobic systems. This is different for hydrophobic systems and can be seen for all samples. Further investigations on these observations are intended. 4. Conclusion This study deals with the influence of nanobubbles on rough hydrophobic surfaces. It is shown for rough materials and particles that wetting plays an important role on measured adhesive forces. Adhesion is enhanced for both particle-particle and particle-plate interactions if wettability is improved or a higher gas oversaturation takes place. On the other hand, a higher roughness leads to smaller adhesive forces for good wetting systems while it is the opposite case for the hydrophobic system. Three types of force distance curves are presented. In the case of capillary forces, repulsive interactions just before snap-in are observed and reasons for their appearance are discussed. Also, Hamaker constants of the different interacting systems are calculated and models for van der Waals forces on rough surfaces are validated. Acknowledgements Thanks to Dr. Claudia Voigt (Institute of Ceramic, Glass and Construction Materials of TU Bergakademie Freiberg) for sample preparation of the tablets and to Dr. Christian Weber for constructive discussions and help in calculation of Hamaker constants. The authors would like to thank the German Research Foundation (DFG) for financial support of the subprojects B01 and B04, which are part of the Collaborative Research Center CRC 920. References [1] F. Heuzeroth, J. Fritzsche, U.A. Peuker, Wetting and its influence on the filtration ability of ceramic foam filters, Particuology 18 (2015) 50–57. [2] P. Knüpfer, L. Ditscherlein, U.A. Peuker, Nanobubble enhanced agglomeration of hydrophobic powders, Colloids Surf. A Physicochem. Eng. Asp. 530 (2017) 117–123.

[3] D. Tabor, R.H.S. Winterton, The direct measurement of normal and retarded van der Waals forces, Proc. R. Soc. Lond. A 312 (1511) (1969) 435–450. [4] G. Binnig, C.F. Quate, C. Gerber, Atomic force microscope, Phys. Rev. Lett. 56 (9) (1986) 930–933. [5] M. Hato, Attractive forces between surfaces of controlled "hydrophobicity" across water: a possible range of "hydrophobic interactions" between macroscopic hydrophobic surfaces across water, J. Phys. Chem. 100 (47) (1996) 18530–18538. [6] J.L. Parker, P.M. Claesson, P. Attard, Bubbles, cavities, and the long-ranged attraction between hydrophobic surfaces, J. Phys. Chem. 98 (34) (1994) 8468–8480. [7] N. Ishida, K. Higashitani, Interaction forces between chemically modified hydrophobic surfaces evaluated by AFM-the role of nanoscopic bubbles in the interactions, Miner. Eng. 19 (6–8) (2006) 719–725. [8] N. Ishida, Y. Kusaka, H. Ushijima, Hydrophobic attraction between silanated silica surfaces in the absence of bridging bubbles, Langmuir 28 (39) (2012) 13952–13959. [9] Y.I. Rabinovich, et al., Adhesion between nanoscale rough surfaces. I. Role of asperity geometry, J. Colloid Interface Sci. 232 (1) (2000) 10–16. [10] S. You, M.P. Wan, Modeling and experiments of the adhesion force distribution between particles and a surface, Langmuir 30 (23) (2014) 6808–6818. [11] O. Laitinen, et al., Validity of the Rumpf and the Rabinovich adhesion force models for alumina substrates with nanoscale roughness, Powder Technol. 246 (2013) 545–552. [12] T.D.B. Jacobs, et al., The effect of atomic-scale roughness on the adhesion of nanoscale asperities: a combined simulation and experimental investigation, Tribol. Lett. 50 (1) (2013) 81–93. [13] R.P. Jaiswal, et al., Modeling and validation of the van der Waals force during the adhesion of nanoscale objects to rough surfaces: a detailed description, Langmuir 25 (18) (2009) 10612–10623. [14] H. Rumpf, Particle Technology, Chapman and Hall, London, 1975. [15] B. Hoffmann, S. Weyrauch, B. Kubier, Zur Berechnung von Haftkräften an rauigkeitsbehafteten Oberflächen, Chemie-Ingenieur-Technik 74 (12) (2002) 1722–1726. [16] Y.I. Rabinovich, B.V. Deryagin, Direct measurement of forces of attraction of hydrophobized quartz fibers in aqueous KCl solutions, Colloid J. USSR 49 (4) (1987) 598–602. [17] H.Y. Xie, The role of interparticle forces in the fluidization of fine particles, Powder Technol. 94 (2) (1997) 99–108. [18] J. Fritzsche, U.A. Peuker, Modeling adhesive force distributions on highly rough surfaces, Powder Technol. 289 (2016) 88–94. [19] K. Cooper, A. Gupta, S. Beaudoin, Simulation of the adhesion of particles to surfaces, J. Colloid Interface Sci. 234 (2) (2001) 284–292. [20] R.R. Dagastine, et al., Calculation of van der Waals forces with diffuse coatings: applications to roughness and adsorbed polymers, J. Adhes. 80 (5) (2004) 365–394. [21] S. Bhattacharjee, C.H. Ko, M. Elimelech, DLVO interaction between rough surfaces, Langmuir 14 (12) (1998) 3365–3375. [22] P.K. Das, S. Bhattacharjee, Finite element estimation of electrostatic double layer interaction between colloidal particles inside a rough cylindrical capillary: effect of charging behavior, Colloids Surf. A Physicochem. Eng. Asp. 256 (2–3) (2005) 91–103. [23] H.K. Christenson, P.M. Claesson, Direct measurements of the force between hydrophobic surfaces in water, Adv. Colloid Interf. Sci. 91 (3) (2001) 391–436. [24] J. Israelachvili, R. Pashley, The hydrophobic interaction is long range, decaying exponentially with distance, Nature 300 (5890) (1982) 341–342. [25] P. Attard, Nanobubbles and the hydrophobic attraction, Adv. Colloid Interf. Sci. 104 (1–3) (2003) 75–91. [26] T.D. Blake, J.A. Kitchener, Stability of aqueous films on hydrophobic methylated silica, J. Chem. Soc. Faraday Trans. 1 68 (1972) 1435–1442. [27] A. Carambassis, et al., Forces measured between hydrophobic surfaces due to a submicroscopic bridging bubble, Phys. Rev. Lett. 80 (24) (1998) 5357–5360. [28] Y. Wang, B. Bhushan, Boundary slip and nanobubble study in micro/nanofluidics using atomic force microscopy, Soft Matter 6 (1) (2009) 29–66. [29] X. Cui, et al., Probing interactions between air bubble and hydrophobic polymer surface: impact of solution salinity and interfacial nanobubbles, Langmuir 32 (43) (2016) 11236–11244. [30] W.A. Ducker, Z. Xu, J.N. Isrealachvili, Measurements of hydrophobic and DLVO forces in bubble-surface interactions in aqueous solutions, Langmuir 10 (9) (1994) 3279–3289. [31] M.L. Fielden, R.A. Hayes, J. Ralston, Surface and capillary forces affecting air bubbleparticle interactions in aqueous electrolyte, Langmuir 12 (15) (1996) 3721–3727. [32] E. Ruckenstein, N. Churaev, A possible hydrodynamic origin of the forces of hydrophobic attraction, J. Colloid Interface Sci. 147 (2) (1991) 535–538. [33] M.A. Hampton, A.V. Nguyen, Nanobubbles and the nanobubble bridging capillary force, Adv. Colloid Interf. Sci. 154 (1–2) (2010) 30–55. [34] D. Lohse, X. Zhang, Surface nanobubbles and nanodroplets, Rev. Mod. Phys. 87 (3) (2015). [35] J.R.T. Seddon, D. Lohse, Nanobubbles and micropancakes: gaseous domains on immersed substrates, J. Phys. Condensed Matter 23 (13) (2011). [36] Y. Sun, et al., Stability theories of nanobubbles at solid-liquid interface: a review, Colloids Surf. A Physicochem. Eng. Asp. 495 (2016) 176–186. [37] C.J. Van Oss, M.K. Chaudhury, R.J. Good, Interfacial Lifshitz-van der Waals and polar interactions in macroscopic systems, Chem. Rev. 88 (6) (1988) 927–941. [38] E.M.V. Hoek, G.K. Agarwal, Extended DLVO interactions between spherical particles and rough surfaces, J. Colloid Interface Sci. 298 (1) (2006) 50–58. [39] E. Chibowski, R. Perea-Carpio, Problems of contact angle and solid surface free energy determination, Adv. Colloid Interf. Sci. 98 (2) (2002) 245–264. [40] J. Fritzsche, et al., Impact of wetting to the agglomeration of dispersed particles in an aqueous medium, Adv. Eng. Mater. 15 (12) (2013) 1299–1306.

Please cite this article as: L. Ditscherlein, P. Knüpfer and U.A. Peuker, The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam fi..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.077

L. Ditscherlein et al. / Powder Technology xxx (2019) xxx [41] C. Voigt, et al., Wettability of AlSi7Mg alloy on alumina, spinel, mullite and rutile and its influence on the aluminum melt filtration efficiency, Mater. Des. 150 (2018) 75–85. [42] B. Babel, M. Rudolph, Characterizing mineral wettabilities on a microscale by colloidal probe atomic force microscopy, Miner. Eng. 121 (2018) 212–219. [43] A. Hozumi, et al., Fluoroalkylsilane monolayers formed by chemical vapor surface modification on hydroxylated oxide surfaces, Langmuir 15 (22) (1999) 7600–7604. [44] L. Ditscherlein, et al., Impact of the roughness of alumina and Al2O3-C substrates on the adhesion mechanisms in a model system, Adv. Eng. Mater. 19 (9) (2017) Article number 1700088(1-11). [45] J. Fritzsche, U.A. Peuker, Particle adhesion on highly rough hydrophobic surfaces: the distribution of interaction mechanisms, Colloids Surf. A Physicochem. Eng. Asp. 459 (2014) 166–171. [46] A.C. Simonsen, P.L. Hansen, B. Klösgen, Nanobubbles give evidence of incomplete wetting at a hydrophobic interface, J. Colloid Interface Sci. 273 (1) (2004) 291–299. [47] L. Ditscherlein, J. Fritzsche, U.A. Peuker, Study of nanobubbles on hydrophilic and hydrophobic alumina surfaces, Colloids Surf. A Physicochem. Eng. Asp. 497 (2016) 242–250. [48] J. Fritzsche, U.A. Peuker, Modeling adhesive forces caused by nanobubble capillary bridging, Colloids Surf. A Physicochem. Eng. Asp. 509 (2016) 457–466. [49] R.H. Yoon, J.L. Yordan, Zeta-potential measurements on microbubbles generated using various surfactants, J. Colloid Interface Sci. 113 (2) (1986) 430–438. [50] Y. Hu, J. Dai, Hydrophobic aggregation of alumina in surfactant solution, Miner. Eng. 16 (11) (2003) 1167–1172.

9

[51] M. Kosmulski, The pH dependent surface charging and points of zero charge. VII. Update, Adv. Colloid Interf. Sci. 251 (2018) 115–138. [52] D.S. Wright, B.S. Flavel, J.S. Quinton, Streaming zeta potential measurements of surface-bound organosilane molecular species, Proceedings of the 2006 International Conference on Nanoscience and Nanotechnology, ICONN, 2006. [53] C. Shi, et al., Interaction between air bubbles and superhydrophobic surfaces in aqueous solutions, Langmuir 31 (26) (2015) 7317–7327. [54] A.V. Nguyen, et al., Hydrodynamic interaction between an air bubble and a particle: atomic force microscopy measurements, Exp. Thermal Fluid Sci. 28 (5) (2004) 387–394. [55] B.W. Ninham, V.A. Parsegian, Van der Waals forces: special characteristics in lipidwater systems and a general method of calculation based on the Lifshitz theory, Biophys. J. 10 (7) (1970) 646–663. [56] D.B. Hough, L.R. White, The calculation of hamaker constants from liftshitz theory with applications to wetting phenomena, Adv. Colloid Interf. Sci. 14 (1) (1980) 3–41. [57] L. Bergström, Hamaker constants of inorganic materials, Adv. Colloid Interf. Sci. 70 (1–3) (1997) 125–169. [58] C.M. Roth, A.M. Lenhoff, Improved parametric representation of water dielectric data for Lifshitz theory calculations, J. Colloid Interface Sci. 179 (2) (1996) 637–639. [59] D. Gingell, V.A. Parsegian, Prediction of van der waals interactions between plastics in water using the Lifshitz theory, J. Colloid Interface Sci. 44 (3) (1973) 456–463. [60] B. Derjaguin, Untersuchungen über die Reibung und Adhäsion, IV - Theorie des Anhaftens kleiner Teilchen, Kolloid-Zeitschrift 69 (2) (1934) 155–164.

Please cite this article as: L. Ditscherlein, P. Knüpfer and U.A. Peuker, The influence of nanobubbles on the interaction forces between alumina particles and ceramic foam fi..., Powder Technol., https://doi.org/10.1016/j.powtec.2019.08.077