Analytical Study of Forces on a Glass Sphere under the Effects of Fluid's Viscosity, pH, and Ionic Strength for Flow-Induced Particle Mobilization

This paper presents an analytical study on the roles of fluid viscosity, pH, and ionic strength in the variations of the interparticle forces and the force equilibrium of a spherical particle resting on a particle bed. The purpose of this analytical study is to provide a theoretical explanation of the observed trends of the effects of viscosity, pH, and ionic strength on the particle mobilization under laminar flow conditions in an experimental program. Viscosity affects the mobilizing hydraulic shear force, while pH and ionic strength affect the interparticle surface forces (i.e., van der Waals force and electrostatic force) between a particle and the particle bed. In this paper, the experimental program and the observations on particle mobilization under the effects of viscosity, pH, and ionic strength are first overviewed; then, the hydraulic dynamic force and interparticle surface forces in terms of van der Waals force and electrostatic force are computed. The study investigates the variations of the van der Waals force and electrostatic force with particle separation distance, pH, ionic strength, and temperature and how the variations affect the critical flow velocity, i.e., the flow velocity that induces particle mobilization. The following major conclusions are drawn from this analytical study. (1) As the pH increases and zeta potential decreases, the electrostatic force (repulsion) between a test particle and a bed of particles increases, and the test particle is more likely to mobilize; thus, the critical flow velocity decreases. (2) As the ionic strength increases, the repulsive electrostatic force generally decreases and could cause the net surface force on the test particle to change from repulsion to attraction; consequently, the test particle becomes less likely to mobilize; thus, the critical flow velocity increases. (3) The trend of electrostatic force variation with ionic strength remains the same when the fluid's zeta potential changes from -10 to -40 mV. As the zeta potential decreases from -10 to -40 mV and the pH increases, the electrostatic force can increase by one order of magnitude and becomes more significant when compared with the van der Waals force. (4) When the fluid temperature increases from 5°C to 50°C, the variation of the electrostatic force is not significant and is within one order of magnitude at various ionic strengths. However, the hydraulic shear force decreases significantly due to the significant decrease of viscosity when the fluid temperature increases from 5°C to 50°C; thus, it significantly increases the magnitude of critical velocity.