Pressure and relative motion in colloidal suspensions

Abstract

We examine the nature of relative motion in colloidal suspensions. By distinguishing carefully between the thermodynamic pressure of a mixture, defined by Gibbs, and the pressure measured by Darcy in porous media, we resolve apparent contradictions between the results and interpretations of different experiments. We show that Fick's and Darcy's laws, two empirical equations thought to describe different and complementary physical phenomena, are in fact particular limits of a single, unifying thermodynamic equation which can be used more generally to describe transport in colloidal systems. Importantly, this equation relates macroscopically measurable quantities. We use it to provide new interpretations of experiments in ultrafiltration.

Solidification of colloidal suspensions

“…where P is the pressure of the mixture as a whole and p is the pervadic pressure of the pure fluid separated from the suspension by a rigid semi-permeable partition (Peppin et al 2005). As noted by Batchelor and others (Batchelor 1976;Auzerais, Jackson & Russel 1988), the osmotic pressure is equivalent to the transmitted stress in a concentrated suspension of particles in which the pervadic pressure is equivalent to the Darcy pressure.…”

“…(2.12) Equation (2.12), which has appeared several times in the literature (Auzerais et al 1988;Petsev, Starov & Ivanov 1993;Peppin et al 2005), relates the transport coefficients D and k to the same underlying physical variables. As we illustrate in § 3, whether one chooses to speak in terms of a diffusion coefficient D or a permeability k depends partly on convention and partly on the closeness of the particular system under consideration to a solution or a porous medium, respectively.…”

“…An equation describing the motion of the spheres relative to the suspending medium (Batchelor 1976;Peppin, Elliott & Worster 2005…”

In Situ X‐Ray Radiography and Tomography Observations of the Solidification of Aqueous Alumina Particles Suspensions. Part II: Steady State

“…If some common characteristics between these two systems are encountered, such as the relationship between the structural wavelength and the interface velocity [7], it is nevertheless necessary to incorporate the specificities associated to particles in the analysis. Such an effort is under way, under the so-called "colloidal alloys" designation [8][9][10][11]. Experimental results gathered so far concentrated on low interface velocities systems (<1 micron/s), which are hardly relevant to the conditions encountered in the materials processing route called freeze-casting.…”

Plasticity and Fracture in Drying Colloidal Films

“…The film's upper surface is exposed to air, and evaporating at a rate _ E. Darcy's law, rp ¼ Àð=Þv, describes how the resulting gradient of the capillary (or pervadic [15]) pressure drives flow of a fluid of viscosity at a superficial velocity v in a film of permeability . Averaging over the height h of the film, and considering flow only along the x direction, mass conservation requires that @v x =@x ¼ À _ E=h.…”