Monday, November 5, 2007
23e

Force Computation Between Spheres And Flats In An Aqueous 1:1 Symmetric Electrolyte Solution Using Matlab

Xiaoting Hong, R. Eric Berson, and Gerold A. Willing. Chemical Engineering, University of Louisville, 106 Ernst Hall, Louisville, KY 40292

There is no question that discussion of the forces of attraction and repulsion between different surfaces such as flats and spherical particles are of need and importance in both the undergraduate and graduate thermodynamics courses in a chemical engineering or chemistry curriculum. It is also an important issue for students from an environmental engineering or pulp and paper background who need to understand the principles behind flocculation and coagulating during the course of waste water treatment and the paper making process. In practice, numerous products and processes depend on controlling the balance between attractive and repulsive interactions: products such as paints and inks, aerosols and gels, and rubber latexes; processes such as filtration and clarification, emulsification and demulsification. To fully explain the forces acting between different surfaces in a complex fluid, one must introduce the DLVO theory. The basic idea of the theory is that colloidal stability is dependent on the balance between two opposing contributions: a short range repulsive force and a long range attractive force. Different repulsive force equations have been derived based on the solutions of the Poisson-Boltzmann equation under different assumptions such as the Langmuir approximation, Derjaguin approximation and the Debye-Hückel approximation for both the constant surface charge and constant surface potential cases. Previously published work has theoretically demonstrated a numerical integration method for calculating the repulsive interactions when a pair of plates approaches one another to a specific surface separation. Hamaker's molecular model can then be used to calculate the van der Waals force contribution to the total force at this separation. Here we compare the total forces from approximate equations and the theoretical integration for two spheres and two flats under same conditions by using newly developed Matlab programs. Moreover, for sphere-flat systems, we can show the force curve difference by changing system parameters such as zeta potential and electrolyte concentration. These systems will be linked to specific case studies that can be implemented in the classroom to help students understand the role of colloidal scale interactions on suspension stability and discovering how varying the system parameters can influence these interactions.