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This study addresses the electrostatic and van der Waals interactions at the aqueous interface of large area CVD graphene, 1-3 layers thick on a silica support and assessed by Raman spectroscopy to have exclusive sp2 character. Ionic strength was found to substantially alter the interactions of silica microspheres with silica-supported graphene. Particles were nonadhesive at large Debye lengths but became irreversibly adherent at reduced Debye lengths about 2nm or less. This was demonstrated to be qualitatively parallel to the influence of ionic strength on silica-silica interactions. The observed ionic strength effects are best explained by negative charges in the vicinity, within a few nanometers, of the supported graphene. DLVO-based modeling of the silica-water-supported graphene interaction suggests that van der Waals interactions drive particle capture and that the surface potential at the supported graphene surface is at least -10 to -15mV (corresponding to a charge density of 0.02-0.06/nm2). This charge could result from ion adsorption or from charges on silica beneath the graphene. The conclusions are not substantially affected by inclusion of nanometer-scale interfacial roughness in the modeling.

Hypothesis High and medium internal phase Pickering emulsions stabilized with cellulose nanocrystals (CNCs) exhibited very different performance compared to their peers stabilized with a surfactant. In this paper, we ascribed the difference to the formation of hydrogen bonding and van der Waals interactions between the CNC nanoparticles on adjacent oil droplets. Experiments Rheological properties of CNC-stabilized oil-in-water medium internal phase emulsions (MIPEs, oil content = 65% v/v) and high internal phase emulsions (HIPEs, oil content = 80% v/v) were comprehensively characterized using both oscillatory and rotational tests. Findings It was found that in the MIPEs, the van der Waals and hydrogen bonding interactions dominate the emulsion properties, whereas the compact structure of oil droplets plays a more important role in the HIPEs. CNC concentration in the aqueous phase also affects the emulsion properties, especially for the HIPEs, and the results can be correlated to the stabilization mechanisms we previously reported. The information from these tests provides a much-needed guidance for the practical application of CNC-stabilized emulsions.

Whether surfaces are characterized from experimental gas-phase adsorption coefficients of probe molecules with known properties (as is done in inverse gas chromatography (IGC)) or whether adsorption coefficients are to be predicted from known properties of the adsorbate and the adsorbent (as is desirable in environmental chemistry) in both cases a correct quantitative description of the van der Waals and acid-base interactions of organic molecules at surfaces is necessary. The model used to date in IGC for the van der Waals interactions tacitly assumes that the interactions of a dilute gas with a surface can be treated like the interactions between two condensed phases. This only works if the contact area of the adsorbed molecule is treated as an adjusted parameter which makes up for the occurring discrepancies. In this paper an improved equation for the van der Waals interactions will be suggested which works without adjusted parameters. For describing acid-base interactions of dilute gases at surfaces Gutmann's donor and acceptor numbers have found wide use in the IGC literature. However, these parameters are related to the heats of the acid-base interactions rather than the free energies. Thus this approach has the disadvantage of putting the acid-base characterization of surfaces in IGC on a different basis than the van der Waals characterization, and it also does not allow the prediction of gas-phase adsorption coefficients. Here, a different approach will be discussed that was originally introduced by van Oss and coworkers for the acid-base interactions between condensed phases (1). This approach uses acceptor and donor parameters that are free energy related. Validation with experimental data from the literature shows a good performance of the equations introduced in this paper for IGC purposes as well as for the prediction of gas-phase adsorption coefficients.

This paper discusses the role of the structural disjoining pressure exerted by nanoparticles on the spreading of a liquid film containing these particles. The origin of the structural disjoining pressure in a confined geometry is due to the layering of the particles normal to the confining plane and has already been traced to the net increase in the entropy of the system in previous studies. In a recent paper, Wasan and Nikolov (Nature, 423 (2003) 156) pointed out that the structural component of the disjoining pressure is strong enough to move a liquid wedge; this casts a new light on many applications-most notably, detergency. While the concept of spreading driven by the disjoining pressure is not new, the importance of the structural disjoining pressure arises from its long-range nature (as compared to the van der Waals' force), making it an important component of the overall force balance near the contact line. In this paper, we report on a parametric study of the spreading phenomena by examining the effects of nanoparticle size, concentration and polydispersity on the displacement of an oil-aqueous interface with the aqueous bulk containing nanoparticles. The solution of the extended Laplace-Young equations for the profile of the meniscus yields the position of the nominal contact line under the action of the structural disjoining pressure. Simulations show that the displacement of the contact line is greater with a high nanoparticle volume fraction, small particles for the same volume fraction, monodispersed (in size) particles rather than polydispersed particles and when the resisting capillary pressure is small, i.e., when the interfacial tension is low and/or the radius of the dispersed phase drop/bubble is large.

Exfoliation and dispersion of two dimensional (2D) transition metal dichacogenides (TMDCs) such as MoS2 in water are highly demanded. In this paper, we exfoliate MoS2 nanosheets in pure water via ultrasonication and attempt to understand the exfoliation process and the dispersion behavior of hydrophobic MoS2. Cavitation-induced exfoliation leads to thinning and fragmentation of MoS2 flakes. Formation of mesoporous MoS2 sheets suggests that the exfoliation initiates from the basal planes. As for the dispersion of MoS2 nanosheets in water, we find that higher centrifugation rate and thus smaller lateral size, results in improved stability. This can be attributed to the enhanced edge effects. Fragmentation of MoS2 flakes generates many edges, to which hydrophilic and ionizable groups are attached. Herein, the edge effects include two aspects. On the one hand, edge-attached polar and hydrophilic groups promote interactions of MoS2 nanosheets with water molecules and result in better wettability, which can be explained by the hemi-wicking model. On the other hand, dissociation of these groups makes MoS2 sheets negatively charged. It is found that edge charge dominates. As the flake size reduces, attractive van der Waals force and hydrophobic force can be overcome by electrostatic repulsions, which prevent MoS2 nanosheets from aggregation. This study opens a new vista on exfoliating and dispersing hydrophobic 2D nanomaterials in water.

The aim of this paper is to present a method for predicting the effect of temperature on contact angles and wetting transitions for n-alkanes on PTFE. The analysis is based on the effect of temperature on two closely related phenomena, which are critical in the determination of contact angles: intermolecular forces and the thickness of an adsorbed film in the region adjacent to the three-phase contact. Considering solely van der Waals forces, it is possible to reproduce the experimental temperature dependence of contact angles. At low temperature values, contact angles show a small and linear decrease with temperature. For higher temperature values, substantially larger decreases are exhibited by the more volatile alkanes. In the case of n-octane, a single transition from partial to total wetting is found at 443K. This transition, which arises from the vanishing of the effective Hamaker constant at 430K, is characterized by a surface specific heat exponent close to one, indicating the existence of a first order wetting transition. For the less volatile alkanes, the contact angle decrease is progressively less pronounced as the volatility decreases in such a way that for n-hexadecane the contact angle remains approximately constant throughout the temperature range under study.

Scale dependence in friction is studied in the present paper using the newly developed mesoscale friction tester (MFT). A transition in frictional shear strength from several hundreds of MPa to several tens of MPa was observed over a very limited range of contact radii (20-30 nm) in both ambient and dry environments. Thus, a single apparatus has been able to establish these two limits which are consistent with the values previously obtained from friction experiments using atomic force microscopy (AFM) and the surface force apparatus (SFA), respectively. Consequently, it is hypothesized here that a shear strength in the hundreds of MPa results from intimate contact (solid-solid) and a shear strength in the tens of MPa results from a monolayer-lubricated contact. Furthermore, both the probe size and the normal pressure govern the interfacial conditions in the contact zone and it is these conditions, rather than the nominal environment, which in turn determine the resulting shear strengths. A continuum analysis based on the Lifshitz theory for van der Waals interactions is used to explain the quantized shear strengths which were obtained from our experiments and previous AFM and SFA friction experiments. This quantized friction behavior [J.N. Israelachvili, P.M. McGuiggan, A.M. Homola, Science 240 (1988) 189] results from the discrete separation due to the different interfacial conditions that can arise between two sliding surfaces. The consistency between the analysis and the experimental results shows that this analysis is applicable for nonwear friction with single asperity contact.

The structure of colloidal clusters observed at the air-water interface is studied theoretically in this paper using a recently developed global optimization routine based on a genetic algorithm. A model potential with a secondary minimum produced from the attractive van der Waals interaction and repulsive dipolar interaction is used for the colloid-colloid interaction. The structures predicted from the genetic algorithm are not always consistent with the experimental observations; the theoretical results predict the growth of cluster as a spreading of triangular networks, however, the experimental observations seem to suggest the formation of a circular shell structure. More thorough theoretical as well as experimental studies are called for in order to obtain more conclusive evidence regarding these matters.

This work develops models for calculating the disjoining pressures of a cylindrical fluid "plug", specifically in submicrometer cylindrical pores. This modeling produces closed-form, cylindrical-pore disjoining pressures for London/van der Waals and solute/pore-wall adsorption interactions, which are the slit-pore models with the characteristic pore size replaced by the radius and multiplied by 6, resulting in a 48-fold or more increase in magnitude. In addition, this work contains a numerical solution for electrostatic interactions. The result of the numerical solution was a 9-fold increase in the modeled disjoining pressure compared to that in the slit-pore model. The cylindrical models may apply to the chemical coating of the interior walls of cylindrical pores or to the thermodynamics within droplets after the breakup of a fluid coating a surface. However, the application used as the base case in this paper is the extension of transport and thermodynamic laws for porous media, previously developed with capillary pressure models, to fully saturated porous media with submicrometer-sized pores. As such, the models could apply to mass transport in ultrafiltration, nanofiltration, and reverse-osmosis membranes. Copyright 2001 Academic Press.

The van der Waals interaction between perfectly spherical, infinitely hard spheres is well understood. Unfortunately, real powder particles are not infinitely hard and rarely spherical. Those particles that are approximately spherical are often covered in small asperities. It is often believed that the size of these asperities dominates the cohesive force between powder particles. This paper rigorously examines this phenomenon and demonstrates the regimes over which the asperities dominate the cohesive force and when the particle size dominates. Deformation of particles is also investigated with a simple model and is shown to produce a significant increase in cohesive force. We demonstrate that previous simple models for calculating the effect of deformation are inadequate, as they ignore effects that can be as large as the correction they suggest. This can lead to an underestimation of the cohesive force by a factor of approximately 2. Copyright 2000 Academic Press.

This paper develops the theory of slow motion of a thin wetting liquid film attached to a meniscus on a solid surface; the liquid is assumed to be completely wetting. The film spreads under Van der Waals forces. To describe the film dynamics, a problem for the evolution equation with boundary conditions at the (unknown) contact line and at the meniscus edge is formulated. The self-similar solution is studied. Wetting diffusion kinetics equations are derived. The influence of the curvature radius of an immovable meniscus on the contact line dynamics is described analytically. Wetting is shown to terminate at a certain short radius. A phenomenon of weightlessness of films over a meniscus near a vertical flat wall is demonstrated. Gravitation does not affect the film profile when the film length exceeds the meniscus radius by an order of magnitude. Such an effect is significant only when the film length is much longer.

In this paper, we provide an analytical derivation to show that the interfacial electrostrictive effects may modify the liquid–vapor surface tension. We propose that at the liquid vapor interface, there is possibility of an electrostatic field, which in conjunction with the inherent density and permittivity variations across the interface, will lead to an electrostrictive force. This force will act in tandem with the intermolecular van der Waals (vdWs) interactions and will modify the expression of the interfacial density profile as well as the surface tension. The final result is found to have very similar mathematical forms as that corresponding to the classical square gradient theory (with only vdW intermolecular interactions), allowing an easy estimation of the role of the electrostrictive effects on the overall surface tension. Depending on the parameters, the contribution of electrostriction in surface tension can be of the same order as the classical non-electrostrictive surface tension.

A new and single correction function which could be used with the London equation to account for the retardation effect on van der Waals attraction, was recently proposed. The function is simple enough to permit closed-form solutions to be obtained by the Hamaker–De Boer approach for macrobodies of a few different shapes. In this paper, closed-form solutions are presented for sphere–half space and sphere–sphere systems. The results are shown to agree well with those which employ Overbeek correction functions.

The detailed description of the influence of a chemical reaction on the dynamic behavior of a thin liquid film is of significant importance in many engineering and biological applications. In this paper, the dynamics of a thin liquid film on a solid substrate is followed until film rupture or formation of local contacts. A surface chemical reaction between insoluble surfactant molecules (receptors) on the free surface of the film and binding sites on the solid substrate is considered. Asymptotic expansion of the equations for fluid motion with van der Waals, capillary, and Marangoni forces leads to a model with three nonlinear evolution equations describing the dynamics of the surface deformation and the kinetics of free and bound receptors. Chemical and hydrodynamic modes are predicted and simulated numerically with different stability regimes: for a simple linear surface reaction, the concentration of receptors follows the deformation of the surface; for a nonlinear surface reaction with affinity enhanced at small distances, a clustering of receptors is observed at the local points of contact. A completely new regime is also obtained where the rupture (or contact) time is delayed by several orders of magnitude, and the concentrations and film thickness may oscillate. This study could be relevant to biological applications where adhesion between cells and substrates can be modeled by considering the dynamics of the thin film between them. The results are first compared with experiments on biological cells adhering to glass or other solid substrates where periodic patterns (wavelike morphologies) are observed with a clustering of adhesion receptors at the local contact points. A second possible application is the activation of T lymphocytes, a major immunological cell type, which requires the clustering of cell surface receptors by interaction of T-cell receptors with surface-bound ligands.

The electrophoretic penetration of colloidal ceramic particles into an impermeable porous graphite substrate is investigated. The substrate is immersed in a suspension containing the particles and positioned between two electrodes. An electric potential gradient between the electrodes is used to drive the ceramic particles into the pores which are closed at the far end not allowing fluid permeation. Three driving mechanisms are identified: the hydrodynamic drag force exerted on the particles due to the electroosmotic flow of the solvent inside the pores, the electrophoretic force exerted on the particles, and the stochastic Brownian force due to thermal fluctuations of the solvent molecules. While subjected to these forces, the particles may reach the walls of the pore and the short range van der Waals forces may cause their capturing and deposition onto the walls. The objectives of this paper are (a) to predict the penetration depth of a single ceramic particle moving inside an impermeable porous substrate under the effect of an electric potential gradient, (b) to derive the nondimensional parameters characterizing the motion of the ceramic particles, and (c) to gain a physical insight on the relative significance of the various mechanisms governing penetration. Qualitatively, the results are that penetration depths are governed by a favorable (if large) Peclet number and unfavorable (if large) Damkohler number. The closed pore structure of the substrate causes diminished particle penetration due to a less effective electroosmotic force. Quantitative results for the mean penetration depths and the dispersion about the mean are also provided.

Due to the inherent complexity of the general Lifshitz theory, the Hamaker–De Boer approach is still used in computing the van der Waals attractive force in systems with macrobodies of complex shapes. To account for the retardation of force computed by this approach, the London equation has in the past been modified by introducing correction functions. However, the functions proposed in the past are either piece-wise in nature or valid for a restricted range of separation distances, making it difficult to carry out the necessary integrations in cases involving complex macrobodies. In this paper, a single correction function is proposed. First, the correction function is shown to represent the retardation effect reasonably well by comparing the proposed function with those proposed in the past. Then, the retarded van der Waals energy is computed for nine different systems involving mica, quartz, pyrophyllite, water, polystyrene, and air for the case of two semi-infinite parallel plates separated by a medium. Experimental data found in the literature on the dielectric frequency spectra are utilized. The results are compared with those computed by the general Lifshitz theory and are shown to agree reasonably well.

A theoretical investigation of particle deposition onto a permeable surface in a parallel-plate channel is presented in this paper. The convective diffusion equation is rigorously formulated with the inclusion of lateral transport due to permeation drag and inertial lift, and transport due to gravitational, double layer, and van der Waals forces. A numerical procedure for solving the governing equation is also presented. The effects of particle size, permeation velocity, solution ionic strength, cross-flow velocity, and particle density on the initial rate of particle deposition are investigated. Results point out that the local and average particle deposition rates onto a permeable surface are determined by an interplay between several transport and interaction mechanisms, among which permeation drag, electric double layer repulsion, and inertial lift are most important.

In this paper the particle volume fraction and temperature dependence of the dynamic viscosity of highly concentrated transformer oil based magnetic nanofluids was investigated in the absence of an external magnetic field. The solid particle volume fraction dependence of the relative viscosity was found to be very well fitted by the Krieger-Dougherty formula, whence the mean ellipticity of the colloidal particles and the effective surfactant layer thickness were obtained. Using the information on the particles' size and shape statistics obtained from TEM, DLS and magnetogranulometry investigations, it was concluded that the magnetite nanoparticles agglomerate in small clusters of about 1.3 particles/cluster, due to the van der Waals interactions. The effective thickness of the oleic acid surfactant layer was estimated as about 1.4 nm, in very good agreement with the value resulted from previous SANS investigations.

In addition to be an environmentally friendly material, hemp fibres are also inexpensive reinforcements in thermoplastics or concrete composites, due to their intrinsic mechanical, thermal and acoustic properties. The morphology of hemp fibres has been chemically modified in order to enhance the matrix/fibre interface and has been examined by Scanning Electron Microscopy (SEM). In this paper, Gas Chromatography (GC) and Atomic Force Microscopy (AFM) were used to investigate the influence of treatments on the composition of hemp fibres and also on the micro-adhesive interactions between a silica colloidal probe and the surface of the fibres using Chemical Force Microscopy (CFM). Microscopy studies and chemical analysis showed that each treatment tends to lead to a morphology of interconnected web-like structure of hemp fibres. It was found that on an average, the adhesion force, contribution of capillary force and Van der Waals' forces, is higher in the case of NaOH treatment.

The determination of molecular interaction forces, e.g., van der Waals force, between macroscopic bodies is of fundamental importance for understanding sintering, adhesion and fracture processes. In this paper, we develop an accurate, general procedure for van der Waals force calculation. This approach extends a surface formulation that converts a six-dimensional (6D) volume integral into a 4D surface integral for the force calculation. It uses non-uniform rational B-spline (NURBS) surfaces to represent object surfaces. Surface integrals are then done on the parametric domain of the NURBS surfaces. It has combined advantages of NURBS surface representation and surface formulation, including (1) molecular interactions between arbitrary-shaped objects can be represented and evaluated by the NURBS model further common geometries such as spheres, cones, planes can be represented exactly and interaction forces are thus calculated accurately; (2) calculation efficiency is improved by converting the volume integral to the surface integral. This approach is implemented and validated via its comparison with analytical solutions for simple geometries. Calculation of van der Waals force between complex geometries with surface roughness is also demonstrated. A tutorial on the NURBS approach is given in Appendix A.

The deformability of droplets is accounted for as a new effect in the statistical mechanics of microemulsions. It is assumed that a plane-parallel film is formed between two colliding microemulsion droplets. The collision is accompanied by deformation of the droplets and by an increase of their interfacial area. The increased interfacial energy gives rise to an effective soft repulsion between the two droplets. In addition, the deformed droplets, having the shape of spherical segments, exhibit considerably greater van der Waals attraction than two spheres of the same volume, separated at the same surface-to-surface distance. The superposition of these two effects leads to the appearance of a potential well in the energy of droplet—droplet interaction. The latter depends on the droplet interfacial tension, the Gibbs elasticity, the Hamaker constant, and the thickness of the liquid film separating the droplets. The soft repulsion and the increased attraction predicted by this model lead to pronouncedly lower values of the calculated second virial coefficient in comparison with the hard sphere model of microemulsions. The deformable droplet model proposed in this paper allows the explanation of experimental findings such as the abnormally low measured values of the second virial and diffusion coefficients as well as the dimer formation in microemulsions.

Coagulation between a charged particle and an uncharged particle arises in ionic aerosol clustering and in ion-induced nucleation. In this paper, we obtain an analytical expression for the image potential for situations of charged-uncharged particle coagulation. The interparticle coagulation rate enhancement in the presence of the newly derived image potential over the entire range of Knudson number is calculated. A simultaneous potential composed of the image potential and a van der Waals potential is subsequently considered. Conditions in which each of the component potentials predominates are determined.

In the present paper we analyze the effect of infinitesimal non-axisymmetric perturbations in determining the critical gap thickness at which a draining, finite radius thin-film becomes unstable. The film is part of the suspending fluid trapped between two approaching deformable drops under the action of a flow field. We carry out a linear stability analysis in the context of a quasi-static approximation where the rate of growth of the disturbances is assumed to be much faster than the rate of film drainage. An analytical solution is derived for the model in the special case of a uniformly thick film, for two types of perturbation: fixed-end and free-end. It is shown, for this special case, when the hydrodynamic force pushing the drops together from the external flow is constant, that the four most unstable disturbances are of the free-end kind, associated with the lowest frequency modes of azimuthal variation in the film thickness. Higher modes are stabilized by surface tension. Our analysis also shows that adopting the unretarded form of the van der Waals disjoining pressure yields results similar to the analysis when electromagnetic retardation effects are included in the calculation. A second case is analyzed where the film is also of uniform thickness but its lateral extent and the gap thickness are both time-dependent. This case was included to extend the predictions to glancing drop-collisions where the external hydrodynamic force is time-dependent. We find that there is a maximum capillary number below which the film becomes unstable, and that there is range of angles in the trajectory where the film becomes unstable, but that outside this range the film is stable.

This paper presents a numerical study of the pore structure of fine particles. By means of granular dynamics simulation, packings of mono-sized particles ranging from 1 to 1000 μm are constructed. Our results show that packing density varies with particle size due to the effect of the cohesive van der Waals force. Pores and their connectivity are then analysed in terms of Delaunay tessellation. The geometries of the pores are represented by the size and shape of Delaunay cells and quantified as a function of packing density or particle size. It shows that the cell size decreases and the cell shape becomes more spherical with increasing packing density. A general correlation exists between the size and shape of cells: the larger the cell size relative to particle size, the more spherical the cell shape. This correlation, however, becomes weaker as packing density decreases. The connectivity between pores is represented by throat size and channel length. With decreasing packing density, the throat size increases and the channel length decreases. The pore scale information would be useful to understand and model the transport and mechanical properties of porous media.

When small particles are added to a colloidal dispersion of large particles, a depletion interaction between large particles occurs because the small ones are depleted from the gaps between the former particles. In the present paper, a cell model is employed to examine the behavior of a dispersion of large particles immersed in an electrolyte solution containing small particles. In this model, each cell consists of one large particle in its center and an associated atmosphere. Double-layer, van der Waals, and depletion interactions, as well as entropic effects, have been taken into account. When the change of the free energy with respect to that of the electrolyte solution is negative (and this happens in most cases), the dispersions of large particles are stable from a thermodynamic point of view. With increasing volume fraction of the small particles, the free energy change becomes more negative. The formation of gels observed experimentally in concentrated emulsions is explained through the formation of a thermodynamically stable dispersion.

Based on the well-known Debye-Huckel approximation and the Derjaguin's integration method, this paper presents an integral solution for the electrical double-layer (EDL) interaction between a spherical particle and a cylinder. The effects of the relative dimensions of the cylinder to the sphere on the EDL interaction are studied using this numerical solution. The detailed numerical results indicate that, in general, the curvature effect on the EDL interaction cannot be neglected at small separation distances. The widely used sphere-flat plate approximation will considerably overestimate the actual EDL interaction between a spherical particle and a cylinder. The ratio of the radius of the particle to the EDL thickness, tau=kappaa(p), also plays an important role in determining the EDL interaction at small dimensionless separation distances (

This paper describes an effort to measure and model changes in the adhesion of micron-scale particles to substrates in systems in which chemical reactions are occurring. Contact interactions between polystyrene latex spheres and silicon substrates (with surface oxide) immersed in aqueous KNO(3) solutions were studied. Two important results were obtained. First, it was shown that the AFM can be employed to monitor, in situ, changes in adhesive interactions induced by surface chemical reactions in this system. Second, the morphology of the interacting surfaces plays a controlling role in particle adhesion. In particular, for this system, changes in roughness of the substrate changed the interaction force by nearly 90%. Copyright 2000 Academic Press.

Presented in this paper are first-principle-based approximate macroscopic models of the van der Waals adhesion force for a variety of particle shapes interacting with an infinite cylinder. In particular, expressions for the van der Waals adhesion force and interaction energy are developed for a (1) spherical particle/infinite cylinder, (2) disk-like particle/infinite cylinder, (3) disk-like particle oriented edgewise to an infinite cylinder, and (4) a deformed slice/infinite cylinder. The models presented depict expected trends in the behavior of both the force of adhesion and the interaction energy between different geometric configurations. These results are also used to demonstrate the impact of contact time on the adhesion force for cylindrical fibers in contact with a disk-shaped particle. After long time intervals where the disk-like particles have remained in contact with the cylinder, the adhesion force may lead to significant deformation of the attached particle. Hence, the adhesion force for a fourth geometric set which represents the most likely scenario for attached particles with long contact times is developed. As will be shown, this scenario results in the highest values of adhesion force and interaction energy. Copyright 2000 Academic Press.

Based on the Hamaker approach, this paper presents a general method to compute the retarded van der Waals (vdW) interaction potential and force between a spherical particle and a cylinder. The effects of the relative dimensions of the cylinder to the sphere were examined by this general method. First, the unretarded vdW interaction potential between these two bodies is obtained by pairwise summation of all the relevant intermolecular interactions and evaluated by accurate multiple numerical integrations. The interaction potential is then modified to account for the retardation effect by incorporating a correction factor which depends on the separation distance and the characteristic wavelength of the interactions. The numerical predictions indicate that the vdW interaction between a sphere and a finitely long cylinder can be approximated as the interaction between a sphere and an infinitely long cylinder only if the ratio of the cylinder length to its radius, B = L/R, is greater than a certain lower limit, say, B10. At smaller dimensionless separation distances, H = D/a/= 1, the vdW interaction between a sphere and a cylinder can be approximated by that between a sphere and a flat plate. However, such a commonly used flat plate approximation is found to be acceptable only if the ratio of the cylinder radius to the sphere radius, A = R/a, is larger than 10, regardless of the B value. Otherwise, it will seriously overestimate the vdW interaction for the sphere-cylinder system. Copyright 1999 Academic Press.

The hydrodynamic interaction between two unequal spheres is derived through the standard method which uses bispherical coordinates. Brenner's matrix formulation of the hydrodynamic resistances is used to obtain numerical data. The influence of the radius ratio on the relative trajectories of the two spheres is then given for both simple shear and extensional flows. The equivalent axis ratio r e of secondary doublets is deduced. The hydrodynamic resistance of rigid asymmetric dumbbells can then be derived from the general results; the equivalent axis ratios are detailed and the motion of the center of free rotation is illustrated by several examples. The influence of van der Waals and Coulombic double-layer forces is finally detailed; several examples of relative trajectories are given to illustrate the influence of the radius ratio when the electrochemical conditions are constant and to illustrate the influence of the colloidal forces for a given radius ratio. The results of this paper are important to understand heterocoagulation in flowing colloidal dispersions.

This paper describes recent studies of the forces between surfaces for separations of the order of tens to hundreds of angstroms. The first part deals with the direct measurement of forces between molecularly smooth mica sheets and shows that normal van der Waals' forces operate for separations less than 100 A, retarded van der Waals' forces for separations greater than 200 A. The second part describes a direct study of the repulsive forces exerted by charged double layers residing on solid surfaces. By using the contact between a soft optically smooth rubber hemisphere and a flat glass surface repulsive forces of the order of 10 5 dyne/cm −2 have been measured for film thicknesses of about 150 A. The equilibrium film thickness decreases with increasing ion concentration and the results are in broad agreement with measurements by Mysels and others on black soap films.