Mobile phase material balance equation

On the above basis the mobile phase material balance equation cein be written as ... 

Thus, two mass balance equations are written in the lumped pore diffusion model for the two different fractions of the mobile phase, the one that percolates through the network of macropores between the particles of the packing material and the one that is stagnant inside the pores of the particles ... 

Equilibrium The physical process (reaction) of adsorption or ion exchange is considered to be so fast relative to diffusion steps that in and near the solid particles, a local equilibrium exists. Then, the so-called adsorption isotherm of the form q = f(Ce) relates the stationary and mobile-phase concentrations at equilibrium. The surface equilibrium relationship between the solute in solution and on the solid surface can be described by simple analytical equations (see Section 4.1.4). The material balance, rate, and equilibrium equations should be solved simultaneously using the appropriate initial and boundary conditions. This system consists of four equations and four unknown parameters (C, q, q, and Ce). 

Model. A difference equation for the material balance was obtained from a discrete reactor model which was devised by dividing the annulus into a two dimensional array of cells, each taken to be a well stirred batch reactor. The model supposes that axial motion of the mobile phase and bed rotation occur by instantaneous discontinuous jumps, between cells. Reaction occurs only on the solid surface, and for the reaction type A B + C used in this work, -dn /dt = K n - n n. Linear isotherms, n = BiC, were used, and while dispersion was not explicitly included, it could be simulated by adjusting the number of cells. The balance is given by Eq. 2, where subscript n is the cell index in the axial direction, and subscript m is the index in the circumferential direction. 

The basic material balance of the mobile phase for all lumped rate models is based on Equations 6.3, 6.4 and 6.13-6.17 and can be derived in the same marmer as the equilibrium-dispersive model (Equation 6.58) ... 

When the material of solid surface is to a significant extent soluble in the wetting liquid, one also observes the hysteresis phenomena. In this case changes in the profile of the solid surface occur due to a contact with the liquid phase. To understand this, let us recall Fig. III-19, from which one can see that the vertical component of the oLG vector can not be fully balanced by the surface tensions of the two other surfaces. If a liquid is in contact with a solid phase that is insoluble, this vertical component, oLG, is balanced by the elastic resistance of the solid surface. The situation is entirely different when a drop of liquid (L,) is placed onto the surface of another liquid (L2) in this case all phases are highly mobile, and the state of equilibrium is described by the vector Neuman equation ... 

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