planar surface are affected by different parameters under flow A quantitative theory of kinetic-diffusive-convective adsorption conditions. The behavior of polymer adsorption and adsorpin a flow cell for polyelectrolyte and mixtures of ions in solutions tion kinetics in the adsorbed layer have been studied extenonto planar surfaces in the framework of the Nernst-Planck apsively (1-12); however, there has not been a satisfactory proach has been developed by using the new approaches: (a) The theoretical explanation to quantitatively describe the equilibeffect of the convective transport is estimated in the analytical rium adsorption and adsorption kinetics of polymer from a form. The boundary condition for the rate of adsorption at the flow solution onto a planar surface. A quantitative interpretainterface (y ร
0) is derived for the kinetic-diffusive-convectivetion of the interfacial behavior of polymers allows us to succontrolled adsorption in a flow cell, taking into account both the cessfully use them in different areas. normal and the axial fluxes in the flow cell. (b) The total electrical potential in the double layer, w(x, y, t), does not equal the electri-
We examine the analytical approaches (2-10) and the cal potential, w r ( x, y, t), due to the total electrical charge, r(x, simplifying assumptions of the earlier investigations to dey, t), in the double layer. It is shown that the total electrical scribe the adsorption kinetics in a flow cell. Despite several potential in the double layer must be found only from the integral attempts by other researchers, there is no treatment of the form of the charge-balance equation in the double layer. Equations problem which produces a general analytical approach for were derived to calculate the rate constant of the adsorption prosolving the system of nonlinear equations for polymers in cess in a flow cell for short and long times and the time needed solutions without making numerous simplifying assumpto attain the equilibrium state for the adsorption processes. It is tions. To describe the adsorption process in a flow cell, a shown that the adsorption kinetics of polyelectrolyte over a wide number of investigators (2-10) have applied the approach range of times is governed by: (I) the adsorption kinetics of polyof Leveque (13) for steady-state heat/mass transfer in a flow electrolyte on a planar surface of the bare interface for short times, cell. As shown in our paper (11), this approach cannot be (II) the adsorption kinetics at the interface as well as simultaneous diffusion in the adsorbed and double layers for intermediate times, used to describe adsorption in a flow cell since it is a nonstaand (III) the adsorption kinetics at the interface for long times. tionary process. In view of this fact, we consider this prob-แญง 1997 Academic Press lem in detail. The adsorption process in a rectangular flow Key Words: polyelectrolyte; kinetic-diffusive-convective-concell, as shown in Fig. 1, is described (9, 10) by the convectrolled adsorption; total electrical potential; flow cell. tive-diffusive mass transfer Eq. [1a], and the boundary conditions Eqs. [1b] through [1e], trial processes. Therefore, it is of importance to understand how the equilibrium state and nonequilibrium process on a y ร
0: c ร
0, [1e]