A General Equation for Fitting Contact Area and Friction vs Load Measurements

The variation of contact area with load between adhesive elastic spheres depends upon the effective range of attractive surface forces. Relatively simple forms to describe limiting cases exist, but the general intermediate case requires a more complex analysis. Maugis, using a Dugdale model [D. Maugis, J. Colloid. Interf. Sci. 150, 243 (1992)], provides an analytic solution, but the resulting equations are cumbersome if one wishes to compare with experimental data such as atomic force microscope measurements. In this paper we present a simpler general equation that approximates Maugis' solution extremely closely. The general equation is amenable to conventional curve fitting software routines and provides a rapid method of determining the value of the "transition parameter" which describes the range of surface forces. Copyright 1999 Academic Press.     

Adhesion maps of spheres corrected for strength limit

Present understanding of adhesion is mostly due to the well-known contact theories for spheres, including JKR (Johnson-Kendall-Roberts), DMT (Derjaguin-Muller-Toporov) and MD (Maugis-Dugdale). Since most of the models exhibit their optimal applicability only in a specific regime, an adhesion map has been developed [K.L. Johnson, J.A. Greenwood, J. Colloid Interface Sci. (1997)] to guide the selection among different models. In the JG (Johnson-Greenwood) map, however, an important physical fact has been neglected that the adhesion strength must not exceed the theoretical strength; thereby the applicability of the classical adhesion models is overestimated and misguidance may arise from the JG map. To avoid this limitation, in this paper we introduce the strength limit into the adhesion map and find that the selection of adhesion models depends not only on the Tabor number but also on the ratio of the theoretical strength to the stiffness. Given this ratio, there exists a critical Tabor number or the size of the sphere, below which adhesion is dominated by the limiting strength and the classical adhesion models are no longer appropriate for spheres. These results eventually lead to a corrected adhesion map for spheres.     

Can we predict the spreading of a two-liquid system from the spreading of the corresponding liquid-air systems?

We present new data obtained from the spreading of a series of oil droplets, on top of a hydrophobic grafted silicon substrate, in air and immersed in water. We follow the contact angle and radius dynamics of hexane, dodecane, hexadecane, dibutyl phthalate, and squalane from the first milliseconds to approximately 1 s. Analysis of the images allows us to make several hundred contact angle and droplet radius measurements with great accuracy. The G-Dyna (Seveno et al. Langmuir 2010, 25, 13034) software is then used to fit the data with one of the wetting theories, the molecular-kinetic theory (MKT) (Blake et al. J. Colloid Interface Sci.1969, 30, 421), which takes into account the dissipation at the three-phase zone at the contact line. This theory allows us to extract the coefficient of friction of the contact line, which expresses the relationship between the driving force, that is, the unbalanced Young force, and the contact-line velocity V. It is first shown that the MKT is appropriate to describe the experimental data and then that the contact-line friction is a linear function of the viscosity as theoretically predicted. This is checked for oil-air and oil-water systems. A linear relation between the contact-line friction measured in oil-water systems and the contact-line frictions of the parent single liquid system seems plausible. To the best of our knowledge, this is the first trial to establish a link between the dynamics of wetting in liquid-liquid and in liquid-air systems.     

Response to the comment on [J. Colloid Interface Sci. 253 (2002) 196] by J. Eggers and R. Evans

We examine the comment on our paper [J. Colloid Interface Sci. 253 (2002) 196] by Eggers and Evans and show that the assertions made there have no foundation in fact nor in scientific substance.     

Ions at the air/water interface

In a recent review of this topic [B.C. Garett, Science 303 (2004) 1146] the emphasis was on some recent experiments, in which it was found that some anions accumulate at the air/water interface and not in the bulk, as usually happens to the cations, and on some simulations which explained those positive surface adsorption excesses. Because a large number of these experiments could be explained on the basis of some simple physical models proposed by the authors for the interaction between the ions and the air/water interface [M. Manciu, E. Ruckenstein, Adv. Colloid Interface Sci. 105 (2003) 63; Adv. Colloid Interface Sci. 112 (2004) 109; Langmuir 21 (2005) 11312], those models are reviewed in the present note, the goal being to draw attention to them.     

Electrophoresis of ionic microgel particles: from charged hard spheres to polyelectrolyte-like behavior

We perform electrophoretic mobility measurements of ionic microgel particles in the deswollen and swollen phases. The results show that microgels behave as charged hard spheres in the first case and as free-draining spherical polyelectrolytes in the latter. A unified theory for the electrophoresis of polyelectrolyte-coated particles [H. Ohshima, Adv. Colloid Interface Sci. 62, 189 (1995)] is shown to contain the essential physics for describing the experiments, upon adequate consideration of the particles swelling behavior and network-solvent friction variations.     

The validity of Cassie's law: a simple exercise using a simplified model

The contact angle of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model which can lead to the augmented Young-Laplace equation. Droplets under the condition of constant volume as well as constant vapor pressure are considered. By assuming a cylindrical liquid-vapor surface (meniscus) and minimizing the total free energy of the interface displacement model, we derive an equation which is similar but different from the well-known Cassie's law. Our modified Cassie's law is essentially the same as the formula obtained previously by Marmur [J. Colloid Interface Sci. 168 (1994) 40]. A few consequences from this modified Cassie's law are briefly described in the following sections of this paper. Several sets of recent experimental results seem to support the validity of our modified Cassie's law.     

Comments on "a study of the collisional fragmentation problem using the gamma distribution approximation"

M. Kostoglou and A.J. Karabelas [J. Colloid Interface Sci. 303 (2006) 419-429] proposed using a gamma distribution approximation to study a collisional fragmentation problem. This approximation involved two types of integrals and the use of continued fraction expansions for their computation. In this Comment, explicit expressions are derived for computing the integrals.     

Effect of capillary element aspect ratio on the dynamic imbibition within porous networks

The Washburn equation is widely accepted for describing capillary imbibition. It has, however, been shown to be insufficient at very short times due partly to the lack of inertial terms. Bosanquet (C. H. Bosanquet, Philos. Mag. ser. 645, 525 (1923)) applied an inertial term via momentum, Szekely et al. (J. Szekely, A. W. Neumann, and Y. K. Chang, J. Colloid Interface Sci.35, 273 (1971)) examined single capillaries based on a revised boundary-condition model, and Sorbie et al. (K. S. Sorbie, Y. Z. Wu, and S. R. McDougall, J. Colloid Interface Sci. 289 (1995)) reviewed and applied Szekely's work to examine the effects of comparative imbibition into a parallel pore doublet. The study here extends the work of Sorbie et al. by applying the equation of Bosanquet to a three-dimensional network model, Pore-Cor. All authors agree that, with the inclusion of inertial terms at short times, smaller radius capillaries will initially fill faster than larger radius capillaries which disagrees with the Washburn equation. It is shown that the aspect ratio of a capillary, defined as its length divided by its radius, plays an important role, in combination with the capillary radii themselves, in determining the filling rate of individual elements. The distribution of this ratio associated with the capillary throat elements within a network structure is investigated. The result is that a preferred pathway of permeation is observed under supersource imbibition conditions in the case where a broad size distribution of capillary elements occurs within a network structure.     

Surfactant solutions and porous substrates: spreading and imbibition

In Section 1, spreading of small liquid drops over thin dry porous layers is investigated from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. Drop motion over a porous layer is caused by an interplay of two processes: (a) the spreading of the drop over already saturated parts of the porous layer, which results in an expanding of the drop base, and (b) the imbibition of the liquid from the drop into the porous substrate, which results in a shrinkage of the drop base and an expanding of the wetted region inside the porous layer. As a result of these two competing processes, the radius of the drop goes through a maximum value over time. A system of two differential equations has been derived to describe the evolution with time of radii of both the drop base and the wetted region inside the porous layer. This system includes two parameters, one accounts for the effective lubrication coefficient of the liquid over the wetted porous substrate, and the other is a combination of permeability and effective capillary pressure inside the porous layer. Two additional experiments were used for an independent determination of these two parameters. The system of differential equations does not include any fitting parameter after these two parameters are determined. Experiments were carried out on the spreading of silicone oil drops over various dry microfiltration membranes (permeable in both normal and tangential directions). The time evolution of the radii of both the drop base and the wetted region inside the porous layer were monitored. All experimental data fell on two universal curves if appropriate scales are used with a plot of the dimensionless radii of the drop base and of the wetted region inside the porous layer on dimensionless time. The predicted theoretical relationships are two universal curves accounting quite satisfactory for the experimental data. According to theory predictions [1]: (i) the dynamic contact angle dependence on the same dimensionless time as before should be a universal function, and (ii) the dynamic contact angle should change rapidly over an initial short stage of spreading and should remain a constant value over the duration of the rest of the spreading process. The constancy of the contact angle on this stage has nothing to do with hysteresis of the contact angle: there is no hysteresis in the system under investigation. These conclusions again are in good agreement with experimental observations [V.M. Starov, S.R. Kosvintsev, V.D. Sobolev, M.G. Velarde, S.A. Zhdanov, J. Colloid Interface Sci. 252 (2002) 397]. In Section 2, experimental investigations are reviewed on the spreading of small drops of aqueous SDS solutions over dry thin porous substrates (nitrocellulose membranes) in the case of partial wetting [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]. The time evolution was monitored of the radii of both the drop base and the wetted area inside the porous substrate. The total duration of the spreading process was subdivided into three stages-the first stage: the drop base expands until the maximum value of the drop base is reached; the contact angle rapidly decreases during this stage; the second stage: the radius of the drop base remains constant and the contact angle decreases linearly with time; the third stage: the drop base shrinks and the contact angle remains constant. The wetted area inside the porous substrate expends during the whole spreading process. Appropriate scales were used with a plot of the dimensionless radii of the drop base, of the wetted area inside the porous substrate, and the dynamic contact angle on the dimensionless time. Experimental data showed [S. Zhdanov, V. Starov, V. Sobolev, M. Velarde, Spreading of aqueous SDS solutions over nitrocellulose membranes. J. Colloid Interface Sci. 264 (2003) 481-489]: the overall time of the spreading of drops of SDS solution over dry thin porous substrates decreases with the increase of surfactant concentration; the difference between advancing and hydrodynamic receding contact angles decreases with the surfactant concentration increase; the constancy of the contact angle during the third stage of spreading has nothing to do with the hysteresis of contact angle, but determined by the hydrodynamic reasons. It is shown using independent spreading experiments of the same drops on nonporous nitrocellulose substrate that the static receding contact angle is equal to zero, which supports the conclusion on the hydrodynamic nature of the hydrodynamic receding contact angle on porous substrates. In Section 3, a theory is developed to describe a spontaneous imbibition of surfactant solutions into hydrophobic capillaries, which takes into account the micelle disintegration and the concentration decreasing close to the moving meniscus as a result of adsorption, as well as the surface diffusion of surfactant molecules [N.V. Churaev, G.A. Martynov, V.M. Starov, Z.M. Zorin, Colloid Polym. Sci. 259 (1981) 747]. The theory predictions are in good agreement with the experimental investigations on the spontaneous imbibition of the nonionic aqueous surfactant solution, Syntamide-5, into hydrophobized quartz capillaries. A theory of the spontaneous capillary rise of surfactant solutions in hydrophobic capillaries is presented, which connects the experimental observations with the adsorption of surfactant molecules in front of the moving meniscus on the bare hydrophobic interface [V.J. Starov, Colloid Interface Sci. 270 (2003)]. In Section 4, capillary imbibition of aqueous surfactant solutions into dry porous substrates is investigated from both theoretical and experimental points of view in the case of partial wetting [V. Straov, S. Zhdanov, M. Velarde, J. Colloid Interface Sci. 273 (2004) 589]. Cylindrical capillaries are used as a model of porous media for theoretical treatment of the problem. It is shown that if an averaged pore size of the porous medium is below a critical value, then the permeability of the porous medium is not influenced by the presence of surfactants at any concentration: the imbibition front moves exactly in the same way as in the case of the imbibition of the pure water. The critical radius is determined by the adsorption of the surfactant molecules on the inner surface of the pores. If an averaged pore size is bigger than the critical value, then the permeability increases with surfactant concentration. These theoretical conclusions are in agreement with experimental observations. In Section 5, the spreading of surfactant solutions over hydrophobic surfaces is considered from both theoretical and experimental points of view [V.M. Starov, S.R. Kosvintsev, M.G. Velarde, J. Colloid Interface Sci. 227 (2000) 185]. Water droplets do not wet a virgin solid hydrophobic substrate. It is shown that the transfer of surfactant molecules from the water droplet onto the hydrophobic surface changes the wetting characteristics in front of the drop on the three-phase contact line. The surfactant molecules increase the solid-vapor interfacial tension and hydrophilise the initially hydrophobic solid substrate just in front of the spreading drop. This process causes water drops to spread over time. The time of evolution of the spreading of a water droplet is predicted and compared with experimental observations. The assumption that surfactant transfer from the drop surface onto the solid hydrophobic substrate controls the rate of spreading is confirmed by experimental observations. In Section 6, the process of the spontaneous spreading of a droplet of a polar liquid over solid substrate is analyzed in the case when amphiphilic molecules (or their amphiphilic fragments) of the substrate surface layer are capable of overturning, resulting in a partial hydrophilisation of the surface [V.M. Starov, V.M. Rudoy, V.I. Ivanov, Colloid J. (Russian Academy of Sciences English Transaction) 61 (3) (1999) 374]. Such a situation may take place, for example, during contact of an aqueous droplet with the surface of a polymer whose macromolecules have hydrophilic side groups capable of rotating around the backbone and during the wetting of polymers containing surface-active additives or Langmuir-Blodgett films composed of amphiphilic molecules. It was shown that droplet spreading is possible only if the lateral interaction between neighbouring amphiphilic molecules (or groups) takes place. This interaction results in the tangential transfer of "the overturning state" to some distance in front of the advancing three-phase contact line making it partially hydrophilic. The quantitative theory describing the kinetics of droplet spreading is developed with allowance for this mechanism of self-organization of the surface layer of a substrate in the contact with a droplet.     

Diffuse Double-Layer Interaction between Two Identical Spherical Colloidal Particles

A simple method is given for calculating the potential energy of the diffuse double-layer interaction between two identical spherical colloidal particles in a symmetrical electrolyte solution with the help of Derjaguin's approximation. This method uses accurate analytic expressions for the corresponding interaction energy between two parallel similar plates obtained previously (Colloids Surf. A Physicochem. Eng. Asp. 146, 213 (1999); J. Colloid Interface Sci. 212, 130 (1999)). Agreement with numerical data provided by Honig and Mul (J. Colloid Interface Sci. 36, 258 (1971)) is excellent particularly for small particle separations. Copyright 2000 Academic Press.     

Analytical expressions for the electrical potential near planar, cylindrical, and spherical surfaces for symmetric electrolytes

The conjecture of Tuinier (J. Colloid Interface Sci. 258 (2003) 45) for the electrical potentials near a cylindrical surface and near a spherical surface under the conditions of symmetric electrolyte and large scaled radius are derived by solving the corresponding Poisson-Boltzmann equation. The surface charge density-surface potential relations for these surfaces are also derived under the conditions of constant surface potential. We show that the level of surface charge density for planar, cylindrical, and spherical surfaces follows the order spherical surface > cylindrical surface > planar surface.     

A numerical study of the effect of insoluble surfactants on the stability of a viscous drop translating in a Hele-Shaw cell

A circular drop is a linearly stable solution for the buoyancy-driven motion of drops in a Hele-Shaw cell [Gupta et al. J. Colloid Interface Sci.218(1), 338 (1999)]. In the absence of surface-active agents, an initially prolate drop always goes to a steady circular shape while initially oblate drops exhibit complex dynamics [Gupta et al. J. Colloid Interface Sci.222, 107 (2000)]. In this study, the effect of insoluble surfactant impurities on the critical conditions for drop breakup is explored by using the Langmuir adsorption framework in conjunction with a physically based expression for the depth-averaged tangential stress exerted on a two-phase interface in a Hele-Shaw cell. It is shown that the presence of surfactants can have both a stabilizing and a destabilizing effect on the shape of the drop, depending on the Bond number, the magnitude of the initial perturbation, and the strength of surface convection. Similar to the clean drop dynamics, two marginally stable branches are found. Increasing the surface Peclet number results in the stabilization of the main branch while the secondary branch shifts to higher Bond numbers. The mode of breakup is also found to be strongly influenced by the strength of surface convection.     

Comment on "Two touching spherical drops in uniaxial extensional flow: analytic solution to the creeping flow problem"

From an analysis of tangent spherical drops in straining flow, Baldessari and Leal conclude that the drop-scale internal circulation, driven by the ambient flow, has a negligible influence on the drainage of the thin liquid film between drops under small-deformation conditions [F. Baldessari, L.G. Leal, J. Colloid Interface Sci. 289 (2005) 262]. However, their conclusion is incorrect as explained in this letter.     

Effect of friction between particles in the dynamic response of model magnetic structures

A simple particle-level simulation model that takes into account interparticle friction forces is developed to describe the dynamic response of magneto-rheological fluids. The results obtained for single-width particle chains are found to be in good agreement with slender body theory predictions [J. de Vicente, M.T. López-López, J.D.G. Durán, G. Bossis, J. Colloid Interface Sci. 282 (2005) 193]. The addition of side chains to a single-width one results in one order of magnitude increase of storage modulus and relaxation. The double logarithmic plot of storage and loss moduli vs frequency gives a limiting slope of one when including friction forces between particles. Simulation results are found to be in agreement with experimental measurements on an iron/kerosene model MR-fluid.     

pH-dependent surface charging and points of zero charge. III. Update

The recently published points of zero charge (PZC) of various materials are compiled to update previous compilations [M. Kosmulski, Chemical Properties of Material Surfaces, Dekker, New York, 2001; M. Kosmulski, J. Colloid Interface Sci. 253 (2002) 77; M. Kosmulski, J. Colloid Interface Sci. 275 (2004) 214]. The recent results corroborate the previously found PZC with a few exceptions. The PZC of alumina obtained from the second-harmonic generation response is substantially lower than the PZC obtained by means of standard methods, while for titania the difference is less significant. PZC of Tl2O3 at pH 7.9 was reported for the first time. A surprisingly insignificant temperature effect on the IEP of rutile was found. Recent model studies aimed at explanation of the effect of the nature of 1-1 electrolytes on the course of charging curves and of discrepancies in the PZC of different materials having the same chemical formula are summarized.     

Numerical calculation of the electrophoretic mobility of concentrated suspensions of soft particles

The electrophoretic mobility of spherical soft particles in concentrated colloidal suspensions is numerically calculated. The particle is modeled as a hard core coated with an ion-penetrable membrane bearing a uniform distribution of fixed charges, while the high particle concentration is taken into account by means of a cell model. The network simulation method used makes it possible to solve the problem without any restrictions on the values of the parameters such as particle concentration, membrane thickness, fixed charge density in the membrane, viscous drag in the membrane, number and valence of ionic species, electrolyte concentration, etc. The theoretical model used is similar to the one presented by Ohshima [H. Ohshima, J. Colloid Interface Sci. 225 (2000) 233], except for the use of the Shilov-Zharkikh, rather than the Levine-Neale, boundary condition for the electric potential, and the inclusion in the force balance equation of an additional term corresponding to the force exerted by the liquid on the core of the moving particle [J.J. López-García, C. Grosse, J. Horno, J. Colloid Interface Sci. 265 (2003) 327]. The obtained results only coincide with existing analytical expressions for low particle concentrations, low particle charge, and when the electrolyte concentration is high, the membrane is thick, and its resistance to the fluid flow is high. This suggests that most interpretations of the electrophoretic mobility of soft particles in concentrated suspensions require numerical calculations.     

Studies on the Spontaneous Evolution of Small Particle Aggregations

On the basis of the criteria for spontaneous evolution of small particle aggregations, which are described by D. Zhaojing, L. Yiping, and L. Cunye [J. Colloid Interface Sci.173,79 (1995)], and according to the results of the experiments and simulations, the spontaneous evolution process of small particle aggregations is further discussed in detail.     

On structural forces in thin fluid films at the critical point

Smooth approximations for structural force in thin fluid films near the critical point are presented to facilitate the usage of formulas derived in [J. Colloid Interface Sci. 278 (2004) 173-183] in experimental studies.