HYDRODYNAMICS OF PARTICLES EMBEDDED IN A FLAT SURFACTANT LAYER OVERLYING A SUBPHASE OF FINITE DEPTH

The motion of membrane-bound objects is important in many aspects of b iology and physical chemistry. A hydrodynamic model for this Fconfigur ation was proposed by Saffman & Delbruck (1975) and here it is extende d to study the translation of a disk-shaped object in a viscous surfac e film overlying a fluid of finite depth H. A solution to the flow pro blem is obtained in the form of a system of dual integral equations th at are solved numerically. Results for the friction coefficient of the object are given for a complete range of the two dimensionless parame ters that describe the system: the ratio of the sublayer (eta) to memb rane (eta(m)) viscosities, Lambda = eta R/eta(m)h (where R and h are t he object radius and thickness of the surface film, respectively), and the sublayer thickness ratio, H/R. Scaling arguments are presented th at predict the variation of the friction coefficient based upon a comp arison of the different length scales that appear in the problem: the geometric length scales H and R, the naturally occurring length scale l(m) = eta(m)h/eta, and an intermediate length scale l(H) = (eta(m)hH/ eta)(1/2). Eight distinct asymptotic regimes are identified based upon the different possible orderings of these length scales for each of t he two limits Lambda much less than 1 and Lambda much greater than 1. Moreover, the domains of validity of available approximations are esta blished. Finally, some representative surface velocity fields are give n and the implication of these results for the characterization of hyd rodynamic interactions among membrane-bound proteins adjacent to a fin ite-depth sublayer is discussed briefly.