A Simple Calculation of Structural and Depletion Forces for Fluids/Suspensions Confined in a Film

Abstract

By use of the analytic result for the Laplace transform of the radial distribution function for two large hard spheres dispersed in a fluid of the smaller hard spheres, simple equations for the film interaction energy and film disjoining pressure, due to the structural and depletion forces, are derived. The proposed equations satisfy some known exact results and explicitly express the energy and pressure as a function of the film thickness and volume fraction of the small hard spheres. The predicted results for the film energy and film disjoining pressure are compared with existing computer simulation data. The proposed simple analytical expressions can be applied to understand the stability of liquid films containing colloidal particles and the stability of suspensions, foams, and emulsions.

Towards the Interaction Between Large Solutes in a Fluid of Small Hard Spheres

“…However, since differentiation in direct (real) space is related to multiplication by s in Laplace space, a more compact expression and further generalizations can be easier obtained by using the Laplace transform formalism. In particular, the asymptotic behaviour of the force and, through the Derjaguin approximation, the decay of the interaction energy per unit area between two planar surfaces are again determined by the same zero of P (s) and both have the form of equation (2.7) but with other amplitude and phase coefficients [3,4]. In the case of two planar walls (slit-like film), the important property is the disjoining pressure which can be obtained by differentiation of the energy per unit area with respect to separation.…”

“…Recently [2][3][4], we have developed simple analytic expressions for the force and interaction potential for the same system. Our result is based on the asymptotic form of these functions, as obtained from the zeros of the Laplace transform solution of the Ornstein-Zernike equation [2,5].…”

Pinning, Retraction, and Terracing of Evaporating Droplets Containing Nanoparticles

“…This is due to particle confinement between the liquid-solid and air-liquid interfaces in the vicinity of the contact line. Decreasing the separation between the two interfaces leads to their entropically-driven attraction, which drives phase separation in colloidal dispersions [1, [3][4][5][6][7][8]. The structural component of the disjoining pressure is oscillatory in the direction normal to the interacting surfaces.…”

“…Structural forces can have a much longer range than van der Waals interactions [8,11] leading to an increase in the spreading rate of thin films [21]. These effects have been examined within the context of detergency and the promotion of oil droplet detachment from solids by surfactant solutions [8,11,[21][22][23].…”

Effect of the acrylic acid content on the permeability and water uptake of poly(styrene-co-butyl acrylate) latex films

“…In those works, the polymer colloid particles were modeled as onecomponent fluid using the hard-spheres pair potential between the colloids. This simple potential is suitable for describing different colloidal features because it takes into account the excluded volume of the colloids [17,18]; however, since colloidal particles have surface charge due to the presence of electrostatic charges, i.e. sulphate groups from the initiator and namely ionized carboxylic groups from the AA, colloidal particles start to repeal each other before they get into contact [19,20].…”