Interfacial interactions of rough spherical surfaces with random topographies

Abstract

A mathematical model was created based on surface element integral (SEI) and XDLVO theory for assessing the interfacial interaction between rough spherical surfaces with random topographies, which were generated following a modified two-variable Weierstrass-Mandelbrot (WM) function. The surface construction and interfacial interaction equations used in this study facilitated the generation of randomly rough spherical surfaces, which assisted in improving the prediction accuracy of particle interactions for natural colloidal particles. This modeling study presented discussions on the interaction of rough surfaces having different asperity heights, asperity positions, random landscape, and roughness in colloidal systems. We observed that the asperity number and ratio were primary parameters for influencing the interfacial interaction between spherical surfaces. The arrangement and randomness in the position of asperities on the surface had negligible effects on the interfacial interaction. The elevated asperity height, as a result of increased fractal roughness or relative fractal roughness on spherical surfaces, could hamper the interfacial energy between surfaces. However, increasing the fractal dimension and relative fractal dimension generated smoother surfaces and thus elevated the interfacial energy developed between surfaces. The most impactful parameter of surface morphologies in altering interfacial energy was fractal dimension as it could control the asperity height and asperity number simultaneously. The largest primary maximum was predicted (216 kT) when the fractal dimension was 2.43, which represented the strongest stability of particles in a suspension.