Particle interactions immobile liquids

Hence, the overall resistance to the mass transfer predicted by this variant of the BAMcomb model is the sum of the resistance in the liquid film and the resistance in the pore fluid. The value of the liquid film mass transfer coefficient Kf can be calculated from literature correlations,400,407,408 while the method for the estimation of the apparent pore liquid mass transfer coefficient Kp can be derived from Eq. (163). The surface interaction between the protein and the immobilized ligand at the internal particle surface can be treated in the same way as for nonporous particles, i.e.,... 

The repulsive forces arise from the electromagnetic interactions of the charged layer surrounding the particles, the so-called electrical double layer. On the surface of the particles, a charged layer may be formed due to selective adsorption of ions. This part of the double layer is immobile and consists of tightly adsorbed ions in direct contact with the particle surface. In the solution adjacent to the particle, a second layer, in which the ions are more diffusely distributed, penetrates into the liquid. This part of the double layer is termed the diffusion layer. The extent of this diffusion layer depends on the electrolyte concentration increasing electrolyte concentration causes this diffuse double layer to shrink closer in to the particle, so that the electrostatic potential falls off more quickly with distance. The process by which the particles are stabilized by the repulsive forces of the electrical double layers is known as electrostatic stabilization. 

Another important problem that has attracted the attention of a host of investigators (Ruckenstein and Prieve, 1973 Saville, 1977 Spielman, 1977 Tien and Payatakes, 1979) is particle collection. In the deep bed filtration of colloidal particles, one seeks to describe the interaction and the collision between one colloidal particle and one grain of the packing material that forms the bed. The latter, called the collector, is immobile. The liquid containing the suspended colloidal particles flows past the collectors and flocculation of the colloid particles with the grains of the packing material is called particle capture. The particles are brought to the collector surface both by convection and diffusion. 

Maxey and Riley [47] derived an equation of motion for a small rigid sphere of radius R in a nonuniform flow. If one considers small bubbles moving in a polar liquid, this equation might be appropriate because surfactants would tend to immobilize the surface of a bubble and make it behave like a rigid sphere. Maxey and Riley assumed that the Reynolds number based on the difference between the sphere velocity and the undisturbed fluid velocity was small compared to unity. In addition, they assumed that the spatial nonuni-formity of the undisturbed flow was sufficiently small that the modified drag due to particle rotation and the Saffman [48] lift force could be neglected. Finally, they ignored interactions between particles. 

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