Hierarchical bubble size distributions in coarsening wet liquid foams

Coarsening of two-phase systems is crucial for the stability of dense particle packings such as alloys, foams, emulsions, or supersaturated solutions. Mean field theories predict an asymptotic scaling state with a broad particle size distribution. Aqueous foams are good model systems for investigations of coarsening-induced structures, because the continuous liquid as well as the dispersed gas phases are uniform and isotropic. We present coarsening experiments on wet foams, with liquid fractions up to their unjamming point and beyond, that are performed under microgravity to avoid gravitational drainage. As time elapses, a self-similar regime is reached where the normalized bubble size distribution is invariant. Unexpectedly, the distribution features an excess of small roaming bubbles, mobile within the network of jammed larger bubbles. These roaming bubbles are reminiscent of rattlers in granular materials (grains not subjected to contact forces). We identify a critical liquid fraction [Formula: see text], above which the bubble assembly unjams and the two bubble populations merge into a single narrow distribution of bubbly liquids. Unexpectedly, [Formula: see text] is larger than the random close packing fraction of the foam [Formula: see text]. This is because, between [Formula: see text] and [Formula: see text], the large bubbles remain connected due to a weak adhesion between bubbles. We present models that identify the physical mechanisms explaining our observations. We propose a new comprehensive view of the coarsening phenomenon in wet foams. Our results should be applicable to other phase-separating systems and they may also help to control the elaboration of solid foams with hierarchical structures.

Coarsening transitions of wet liquid foams under microgravity conditions

We report foam coarsening studies which were performed in the International Space Station (ISS) to suppress drainage due to gravity. Foams and bubbly liquids with controlled liquid fractions ϕ between 15 and 50% were investigated to study the transition between bubble growth laws previously reported near the dry limit ϕ → 0 and the dilute limit ϕ → 1 (Ostwald ripening). We determined the coarsening rates for the driest foams and the bubbly liquids, they are in close agreement with theoretical predictions. We observe a sharp cross-over between the respective laws at a critical value ϕ*. At liquid fractions beyond this transition, neighboring bubbles are no longer all in contact, like at a jamming transition. Remarkably ϕ* is significantly larger than the random close packing volume fraction of the bubbles ϕrcp which was determined independently. We attribute the differences between ϕ* and ϕrcp to a weakly adhesive bubble interaction that we have studied in complementary ground-based experiments.

Daisy-shaped liquid bridges in foam-filled granular packings

HYPOTHESIS

Many applications of liquid foams use them to fill the porosity of various granular media. How is the liquid distributed in such foam-filled systems, in which the geometry of the bubble assembly can be strongly constrained by pore confinement?

EXPERIMENTS

We study how the liquid is distributed in a grain packing filled with liquid foam, as a function of both liquid content and bubble-to-grain size ratio. Moreover, Surface Evolver simulations are carried out at the scale of a single bubble confined into a tetrahedral pore.

FINDINGS

We reveal that foam-filled granular assemblies exhibit a robust pendular-like regime, which is reminiscent of the pendular regime in unsaturated media. The main difference is that here the liquid bridges are daisy-shaped, i.e. with a liquid core bounded by bubbly petals. A simple theoretical model is proposed to describe the foam liquid bridges between contacting grains. In the case of large bubbles, the model is compared with the Surface Evolver simulation. The model is also applied to the case of wall liquid bridge, which is compared with the experimental observation. Beyond their geometrical characteristics, the presence of these liquid bridges, which can represent almost 25% of the liquid contained in the porosity, makes it possible to imagine a new approach (binder foam-based) to bind granular assemblies and turn them to solid materials.

Influence of the Immune Microenvironment Provided by Implanted Biomaterials on the Biological Properties of Masquelet-Induced Membranes in Rats: Metakaolin as an Alternative Spacer

Macrophages play a key role in the inflammatory phase of wound repair and foreign body reactions-two important processes in the Masquelet-induced membrane technique for extremity reconstruction. The macrophage response depends largely on the nature of the biomaterials implanted. However, little is known about the influence of the macrophage microenvironment on the osteogenic properties of the induced membrane or subsequent bone regeneration. We used metakaolin, an immunogenic material, as an alternative spacer to standard polymethylmethacrylate (PMMA) in a Masquelet model in rats. Four weeks after implantation, the PMMA- and metakaolin-induced membranes were harvested, and their osteogenic properties and macrophage microenvironments were investigated by histology, immunohistochemistry, mass spectroscopy and gene expression analysis. The metakaolin spacer induced membranes with higher levels of two potent pro-osteogenic factors, transforming growth factor-β (TGF-β) and bone morphogenic protein-2 (BMP-2). These alternative membranes thus had greater osteogenic activity, which was accompanied by a significant expansion of the total macrophage population, including both the M1-like and M2-like subtypes. Microcomputed tomographic analysis showed that metakaolin-induced membranes supported bone regeneration more effectively than PMMA-induced membranes through better callus properties (+58%), although this difference was not significant. This study provides the first evidence of the influence of the immune microenvironment on the osteogenic properties of the induced membranes.

Stiffening colloidal gels by solid inclusions

The elastic properties of a soft matter material can be greatly altered by the presence of solid inclusions whose microscopic properties, such as their size and interactions, can have a dramatic effect. In order to shed light on these effects we use extensive rheology computer simulations to investigate colloidal gels with solid inclusions of different sizes. We show that the elastic properties vary in a highly non-trivial way as a consequence of the interactions between the gel backbone and the inclusions. In particular, we show that the key aspects are the presence of the gel backbone and its mechanical alteration originating from the inclusions. To confirm our observations and their generality, we performed experiments on an emulsion that presents strong analogies with colloidal gels and confirms the trends observed in the simulations.

Acoustics of monodisperse open-cell foam: An experimental and numerical parametric study

This article presents an experimental and numerical parametric study of the acoustical properties of monodisperse open-cell solid foam. Solid foam samples are produced with very good control of both the pore size (from 0.2 to 1.0 mm) and the solid volume fraction (from 6% to 35%). Acoustical measurements are performed by the three-microphone impedance tube method. From these measurements, the visco-thermal parameters-namely, viscous permeability, tortuosity, viscous characteristic length, thermal permeability, and thermal characteristic length-are determined for an extensive number of foam samples. By combining Surface Evolver and finite-element method calculations, the visco-thermal parameters of body centered cubic (bcc) foam numerical samples are also calculated on the whole range of solid volume fraction (from 0.5% to 32%), compared to measured values and to theoretical model predictions [Langlois et al. (2019). Phys. Rev. E 100(1), 013115]. Numerical results are then used to find approximate formulas of visco-thermal parameters. A systematic comparison between measurements and predictions of the Johnson-Champoux-Allard-Lafarge (JCAL) model using measured visco-thermal parameters as input parameters, reveals a consistent agreement between them. From this first step, a calculation of the optimal microstructures maximizing the sound absorption coefficient is performed.

Well-controlled foam-based solid coatings

Foam-based solid coatings appear to be a simple solution for giving new properties to solid surfaces. An efficient method is presented for producing open-cell foam coatings having a tunable pore radius distribution (i.e. monodisperse within the range 100-1000 μm, bidisperse or fully polydisperse), tunable thickness, and tunable bulk and surface porosities. This is achieved by mixing a precursor aqueous foam and particle suspension (here a micrometer-sized polyurethane dispersion), and by spreading with a nozzle the resulting particle-loaded foam on the solid surface to be coated. It is shown that the bubble size distribution of the precursor foam can be preserved in the final solid coating. This is highlighted by using a monodisperse aqueous foam, for which coatings showed a polycrystalline structure, as well as bidisperse or fully polydisperse foams. As a major advantage of our method, the bubble size and solid volume fraction are shown to be independent parameters, allowing the size of the microstructural elements to be tuned easily, and so the expected functional properties of the coating. Results obtained with the studied polyurethane dispersion are expected to be reproduced with other dispersions.

Viscous friction of squeezed bubbly liquid layers

Shear viscosity of bubbly liquids is known to depend on both the gas volume fraction and the capillary number. Here, we study the impact of confinement on their behavior by investigating the viscosity of semi-dilute bubbly liquid layers confined between two plates and characterized by a ratio of the undeformed bubble diameter to the layer thickness equal to or larger than unity. For all the studied confinement ratios, viscosity is shown to be smaller than the viscosity of the suspending liquid for capillary numbers larger than 0.1. Measurements of bubble deformations show that this behavior is related to bubble stretching in the direction of shear induced flow. In the limit of high capillary numbers, viscosity reaches values predicted for unconfined bubbly liquids. On the other hand, our results for smaller capillary numbers, i.e. within the range 0.001-0.1, reveal a non-monotonic variation of the viscosity as a function of the confinement ratio, exhibiting a well-defined maximum value for the ratio close to 1.8. This behavior differs strongly from the reference case of unconfined bubbly liquid, and it is shown to result from both bulk and wall drag forces on the squeezed bubbles.

Synergistic actions of mixed small and large pores for capillary absorption through biporous polymeric materials

Water absorption in porous media is an important process involved in numerous materials for various applications, such as in the building industry, food processing and bioengineering. Designing new materials with appropriate absorption properties requires an understanding of how absorption behavior depends on both the material's morphology and the properties of the solid matrix, i.e. hydrophilic/hydrophobic nature and swelling/deformation properties. Although the basic principles of imbibition are well-known for simple porous systems, much less is known about absorption in complex porous systems, in particular those containing several coexisting porous phases, such as wood for example. Here, water absorption is studied for model porous organic materials exhibiting several degrees of hydrophobicity and two pore size levels, either as monoporous materials (large or small pores) or as biporous materials (mixed large and small pores). The interconnected biporous structure is designed via a double porogen templating approach using cubic sodium chloride particles as templates for the generation of the larger pore size (250-400 μm) and i-PrOH as a porogenic solvent for the smaller pore size (2-5 μm). While absorption for the small pore material is well described by the classical Washburn theory, the large pore material shows a drastic reduction in the imbibition rate. This behavior is attributed to the slow breakthrough mechanism for the water interface at sharp edge connections between pores. Remarkably, this slow regime is suppressed for the biporous material and the imbibition rate is even higher than the sum of rates obtained for its monoporous counterparts, which highlights the synergistic action of mixed small and large pores.

Permeability of solid foam: Effect of pore connections

In this paper, we study how the permeability of solid foam is modified by the presence of membranes that close partially or totally the cell windows connecting neighboring pores. The finite element method (FEM) simulations computing the Stokes problem are performed at both pore and macroscopic scales. For foam with fully interconnected pores, we obtain a robust power-law relationship between permeability and aperture size. This result is due to the local pressure drop mechanism through the aperture as described by Sampson for fluid flow through a circular orifice in a thin plate. Based on this local law, pore-network simulation of simple flow is used and is shown to reproduce FEM results. Then this low computational cost method is used to study in detail the effect of an open window fraction on the percolation properties of the foam pore space. The results clarify the effect of membranes on foam permeability. Finally, Kirkpatrick's model is adapted to provide analytical expressions that allow for our simulation results to be successfully reproduced.

Elasticity of particle-loaded liquid foams

Mixing solid particles with liquid foam is a common process used in industry for manufacturing aerated materials. Desire for improvement of involved industrial processes and optimization of resulting foamed materials stimulates fundamental research on those complex mixtures of grains, bubbles and liquid. In this paper, we generate well-controlled particle-loaded liquid foams and we determine their elastic behavior as a function of particle size (6-3000 μm) and particle volume fraction (0-6%). We focus on both the elastic modulus exhibited by the material at small strain and the strain marking the end of the linear elastic regime. Results reveal the existence of a critical particle-to-bubble size ratio triggering a sharp transition between two well-defined regimes. For small size ratios, the behavior is governed by the mechanical properties of the solid grains, which have been proved to pack in the shape of a foam-embedded granular skeleton. In contrast, bubbles elasticity prevails in the second regime, where isolated large particles contribute only weakly to the rheological behavior of the foamed material. The modeling of elasticity for each regime allows for this transition to be normalized and compared with previously reported particle size-induced effects for foam drainage (Haffner et al. J. Colloid Interface Sci., 2015, 458, 200-208) and solid foam mechanics (Khidas et al., Compos. Sci. Technol., 2015, 119, 62-67). This highlights that rheology and the other properties of particle-loaded foams are subjected to the same size-induced morphological transition.

Optimal strengthening of particle-loaded liquid foams

Foams made of complex fluids such as particle suspensions have a great potential for the development of advanced aerated materials. In this paper, we study the rheological behavior of liquid foams loaded with granular suspensions. We focus on the effect of small particles, i.e., particle-to-bubble size ratio smaller than 0.1, and we measure the complex modulus as a function of particle size and particle volume fraction. With respect to previous work, the results highlight a new elastic regime characterized by unequaled modulus values as well as independence of size ratio. A careful investigation of the material microstructure reveals that particles organize through the network between the gas bubbles and form a granular skeleton structure with tightly packed particles. The latter is proven to be responsible for the reported new elastic regime. Rheological probing performed by strain sweep reveals a two-step yielding of the material: The first one occurs at small strain and is clearly attributed to yielding of the granular skeleton; the second one corresponds to the yielding of the bubble assembly, as observed for particle-free foams. Moreover, the elastic modulus measured at small strain is quantitatively described by models for solid foams in assuming that the granular skeleton possesses a bulk elastic modulus of order 100 kPa. Additional rheology experiments performed on the bulk granular material indicate that this surprisingly high value can be understood as soon as the magnitude of the confinement pressure exerted by foam bubbles on packed grains is considered.

On the collapse pressure of armored bubbles and drops

Drops and bubbles wrapped in dense monolayers of hydrophobic particles are known to sustain a significant decrease of their internal pressure. Through dedicated experiments we investigate the collapse behavior of such armored water drops as a function of the particle-to-drop size ratio in the range 0.02-0.2. We show that this parameter controls the behavior of the armor during the deflation: at small size ratios the drop shrinkage proceeds through the soft crumpling of the monolayer, at intermediate ratios the drop becomes faceted, and for the largest studied ratios the armor behaves like a granular arch. The results show that each of the three morphological regimes is characterized by an increasing magnitude of the collapse pressure. This increase is qualitatively modeled thanks to a mechanism involving out-of-plane deformations and particle disentanglement in the armor.

Foam clogging

To what extent are aqueous foams prone to clogging? Foam permeability is measured as a function of particulate loading (trapped hydrophilic particles) under conditions where the particle to bubble size ratio is allowed to increase when the number of particles per bubble is fixed. In addition to experiments performed on the foam scale, we investigated experimentally and numerically the hydrodynamic resistance of a single foam node loaded with one particle. It is shown that, with respect to solid porous media, aqueous foams clog more efficiently due to two reasons: (i) the deformation of interfaces allows for larger particles to be incorporated within the interstitial network and (ii) the interfacial mobility contributes to lowering of the reduced permeability.

Coupling of elasticity to capillarity in soft aerated materials

We study the elastic properties of soft solids containing air bubbles. Contrary to standard porous materials, the softness of the matrix allows for a coupling of the matrix elasticity to surface tension forces acting on the bubble surface. Thanks to appropriate experiments on model systems, we demonstrate how the elastic response of the soft porous solid is governed by two dimensionless parameters: the gas volume fraction and a capillary number comparing the elasticity of the matrix with the stiffness of the bubbles. Furthermore, we show that our experimental results are accurately predicted by computations of the shear modulus through a micro-mechanical approach.

Capture-induced transition in foamy suspensions

We investigate the drainage behaviour of foamy granular suspensions. Results reveal large fluctuations in the drainage velocity as bubble size, particle size and gas volume fraction are varied for a given particle volume fraction. Particle capture is proved to control the overall drainage behaviour through the parameter λ, which compares the particle size to the size of passage through constrictions within the foam pore space. λ highlights a sharp transition: for λ < 1 particles are free to drain with the liquid, which involves the shear of the suspension in foam interstices, for λ > 1 particles are trapped and the resulting drainage velocity is strongly reduced. A phenomenological model is proposed to describe this behaviour.

Flow and jamming of granular suspensions in foams

The drainage of particulate foams is studied under conditions where the particles are not trapped individually by constrictions of the interstitial pore space. The drainage velocity decreases continuously as the particle volume fraction φ(p) increases. The suspensions jam--and therefore drainage stops--for values φ*(p) which reveal a strong effect of the particle size. In accounting for the particular geometry of the foam, we show that φ*(p) accounts for unusual confinement effects when the particles pack into the foam network. We model quantitatively the overall behavior of the suspension--from flow to jamming--by taking into account explicitly the divergence of its effective viscosity at φ*(p). Beyond the scope of drainage, the reported jamming transition is expected to have a deep significance for all aspects related to particulate foams, from aging to mechanical properties.

Foam invasion through a single pore

We investigate experimentally the behavior of liquid foams pumped at a given flow rate through a single pore, in the situation where the pore diameter is smaller than the bubble diameter. Results reveal that foam invasion can be observed only within a restricted range of values for the dimensionless flow rate and the foam liquid fraction. Within this foam invasion regime, the liquid content of invading foams is measured to be three times higher than the initial liquid content. Outside this regime, both gas alone and liquid alone invasion regimes can be observed. The gas invasion regime results from the rupture of foam films during local T1, during bubble rearrangements events induced by foam flow, whereas the liquid invasion regime is allowed by the formation of a stable cluster of jammed bubbles at the pore's opening.

How topological rearrangements and liquid fraction control liquid foam stability

The stability of foam is investigated experimentally through coalescence events. Instability (coalescence) occurs when the system is submitted to external perturbations (T1) and when the liquid amount in the film network is below a critical value. Microscopically, transient thick films are observed during film rearrangements. Film rupture, with coalescence and eventual collapse of the foam, occurs when the available local liquid amount is too small for transient films to be formed. Similar experiments and results are shown in the two-bubble case.

Capture of particles in soft porous media

We investigate the capture of particles in soft porous media. Liquid foam constitutes a model system for such a study, allowing the radii of passage in the pore space to be tuned over several orders of magnitude by adjusting the liquid volume fraction. We show how particle capture is determined by the coupling of interstitial liquid flow and network deformation, and present a simple model of the capture process that shows good agreement with our experimental data.

Shear induced drainage in foamy yield-stress fluids

Shear induced drainage of a foamy yield-stress fluid is investigated using MRI techniques. Whereas the yield stress of the interstitial fluid stabilizes the system at rest, a fast drainage is observed when a horizontal shear is imposed. It is shown that the sheared interstitial material behaves as a viscous fluid in the direction of gravity, the effective viscosity of which is controlled by shear in transient foam films between bubbles. Results provided for several bubble sizes are not captured by the R2 scaling classically observed for foams. Furthermore, foam films are found to be responsible for the unexpected arrest of drainage, thus trapping irreversibly a significant amount of interstitial liquid.

Recirculation model for liquid flow in foam channels

Although extensively studied in the past, drainage of aqueous foams still offers major unaddressed issues. Among them, the behaviour of foam films during drainage has great significance as the thickness of the films is known to control the Ostwald ripening in foams, which in turn impacts liquid drainage. We propose a model relating the films' behavior to the liquid flow in foam channels. It is assumed that Marangoni-driven recirculation counterflows take place in the transitional region between the foam channel and the adjoining films, and the Gibbs elasticity is therefore introduced as a relevant parameter. The velocity of these counterflows is found to be proportional to the liquid velocity in the channel. The resulting channel permeability is determined and it is shown that Marangoni stresses do not contribute to rigidify the channel's surfaces, in strong contrast with the drainage of horizontal thin liquid films. New experimental data are provided and support the proposed model.

Foam drainage in the presence of nanoparticle-surfactant mixtures

The drainage of SiO(2) nanoparticle-cationic surfactant (TTAB) mixtures through calibrated aqueous foams had been studied by combining several approaches on both the macroscopic and the local scale. Macroscopic measurements reveal a strong stabilizing effect arising for nanoparticle concentrations as low as 2 wt % mainly because of a drainage kinetic slow-down dependent on the nanoparticle concentration. We show that the variation of the viscous parameters (bulk viscosity, interfacial viscosity, or both) in the classical theoretical models of foam drainage, mainly developed for aqueous surfactant solutions, does not enable fitting experimental data obtained via steady- or free-drainage strategies for [SiO(2)] > or = 2 wt %. In contrast, the quantitative analysis of the data obtained from front propagation velocities has revealed a drainage regime transition from a node-dominated regime toward a Plateau-border-dominated regime upon nanoparticle concentration increase. Observations performed at the Plateau border scale brought to light the drainage kinetic slow-down process by evidencing that the presence of insoluble aggregates induces traffic jamming and even cork formation for silica concentrations above 2 wt %. Considering these observations, a simple mechanism of aggregate growth and cork formation is proposed. Finally, we analyze the discrepancy between experiments (steady- and free-drainage methods) and theory by pointing out that the hypothesis relative to the foam structure that is usually assumed for both the liquid fraction calculation and the determination via conductivity measurements is strongly modified when large insoluble aggregates are present in the system. In this view, the method based on the liquid fraction determination through the measurement of the front propagation velocity seems to be the most suitable for studying the drainage of colloidal dispersion because of the lower dependence of this approach toward hypothesis on the local geometry of the foam continuous phase.

Permeability of aqueous foams

We perform forced-drainage experiments in aqueous foams and compare the results with data available in the literature. We show that all the data can be accurately compared together if the dimensionless permeability of the foam is plotted as a function of liquid fraction. Using this set of coordinates highlights the fact that a large part of the published experimental results corresponds to relatively wet foams (epsilon approximately 0.1). Yet, most of the foam drainage models are based on geometrical considerations only valid for dry foams. We therefore discuss the range of validity of the different models in the literature and their comparison to experimental data. We propose extensions of these models considering the geometry of foam in the relatively wet-foam limit. We eventually show that if the foam geometry is correctly described, forced drainage experiments can be understood using a unique parameter --the Boussinesq number.

Specific surface area model for foam permeability

Liquid foams were recognized early to be porous materials, as liquid flowed between the gas bubbles. Drainage theories have been established, and foam permeability has been modeled from the microscopic description of the equivalent pores geometry, emphasizing similarities with their solid counterparts. But to what extent can the theoretical work devoted to the permeability of solid porous materials be useful to liquid foams? In this article, the applicability of the Carman-Kozeny model on foam is investigated. We performed measurements of the permeability of foams with nonmobile surfactants, and we show that, in introducing an equivalent specific surface area for the foam, the model accurately describes the experimental data over two orders of magnitude for the foam liquid fraction, without any additional parameters. Finally, it is shown that this model includes the previous permeability models derived for foams in the dry foams limit.

Liquid drainage through aqueous foam: study of the flow on the bubble scale

Macroscopic properties of foams are highly dependent on the liquid volume fraction, which has motivated many studies on foam drainage in the last decade. Theoretical developments and recent experimental results have suggested that two macroscopic drainage regimes could be expected, in relation with flow transitions occurring at the microscopic level, essentially in the Plateau border channels. We have constructed a setup, the Plateau border apparatus, to study the hydrodynamics of a single Plateau border channel, focusing on the surface properties of the foaming solution. Experimental results have shown that the actual theoretical models only partially predict the dissipation of liquid flow through a Plateau border channel. The major discrepancies can be explained considering additional dissipation processes related to the properties of the interface, and to the liquid flows induced in adjoining films as the liquid flows in the channel. Evidence of the hydrodynamic coupling between the channel and the adjoining films is given in the paper.

Experimental impact of the history of packing on the mean pressure in silos

The role played by the history of packing in the behaviour of a granular material confined in a column is studied experimentally. The mean pressure applied by the granular assembly to the base is measured as a function of the height of material poured in the column. We obtain reproducible mean vertical normal stress measurements without using a particular procedure to mobilise the wall friction. We focus on the influence of the filling method on the mean vertical normal stress. Filling the column via the edges induces a higher apparent mass of grain than filling it via the centre. Particular attention is devoted to the measurement of the effect of the force sensor stiffness. We show that the lower the base stiffness, the lower the mean pressure on the base. We also vary the packing fraction. We obtain an increasing relation between the apparent mass and the mean packing fraction, and show that this relation depends on the filling method.

Quasistatic detachment of a sphere from a liquid interface

In this paper the problem of removing a spherical particle initially attached to a liquid-gas interface is analytically treated. In particular, the Derjaguin equation for small radii is used to derive a closed-form approximate expression for the work of detachment of the sphere from the interface. Expressions corresponding to the prescribed displacement condition and the applied force condition, which seems to be the relevant condition for the flotation separation process, are presented. A special effort has been made to closely compare analytical results with data obtained through the exact numerical treatment of the detachment process. Results show that proposed expressions are sufficiently accurate to calculate the energy required to detach the sphere from the interface as soon as the sphere radius is small compared to the capillary length. Validity limits are specified.

Liquid Bridge between Two Moving Spheres: An Experimental Study of Viscosity Effects

The effects of viscosity on the mechanical response of a liquid bridge are investigated in the case of small amounts of liquid axially strained between two moving spheres. An experimental setup allows the measurement of capillary and viscous forces exerted on the spheres as a function of the spheres separation distance and the spheres velocity. The experimental results are found to be accurately described over a large range in spheres velocity and liquid viscosity by a simple closed-form expression. In addition, the bridge rupture distance is found to increase like the square root of the separation velocity. Copyright 2000 Academic Press.