RESUMO
This paper studies the dynamics and fluctuations of a phospholipidic membrane in the presence of a diffusion field of foreign molecules, such as polymers, proteins, etc., which have the ability to adsorb on, and to desorb from, the membrane. We develop a model that includes, besides hydrodynamics, molecular diffusion in the surrounding fluid and lateral diffusion (i.e., diffusion along the membrane) as well as the kinetics of attachment and detachment to and from the membrane. This model is exploited here for the case of a free membrane which is globally at equilibrium while the nonequilibrium part will be presented in the future. We show that if the coupling between the membrane and the molecules is strong enough, the flat membrane can suffer a morphological instability. The numerical calculation in the nonlinear regime reveals budding, and an initial stage of spontaneous vesicle emission. When the condition of stability is satisfied we show how kinetic fluctuations lead to a rich variety of dynamical behaviors expressing the dominant dissipation mechanisms. We show that in the limit of well separated length scales related to the physical mechanisms that enter into play, the width of the membrane fluctuations exhibits various dynamical scalings with universal scaling exponents. It is shown that the usual behavior with time w approximately t(1/3) is altered in various time and length scales of interest. For example, we find that , w approximately t(1/4), w approximately t(1/2), and w approximately [t ln(t)](1/2), depending on which physical mechanism limits the membrane fluctuations on the time scale under consideration. The experimental study of the fluctuation spectrum can be viewed as a precious tool in order to have access to the underlying microscopic physical mechanisms.
