Kinetics of Langmuirian adsorption onto planar, spherical, and cylindricalsurfaces

The kinetics of adsorption processes in solution onto adsorbents having dif ferent geometric shapes have been explored theoretically. The basic assumpt ions were (i) the diffusion of adsorbate in quiescent homogeneous solution with no convection, (ii) simple Langmuir-type adsorption kinetics and isoth erm, (iii) the bulk concentration of the adsorbate in solution being suffic iently high to stay constant during the adsorption process, and (iv) the ge ometric shape of the adsorption surface being planar, spherical, or cylindr ical. The diffusion equation with the time-dependent boundary conditions im plied by the adsorption process was shown to lead to a nonlinear Volterra-t ype integral equation which is common for the three adsorbent geometries wi th a single definitive parameter, geometric factor, varying between 0 and 1 . A numerical method was developed far solving this equation, and approxima te analytical solutions were derived for the very beginning and the very en d of the adsorption process. Implications of the results for the analytical methods based on the use of microparticles, such as various immunoassays, are discussed.