Brownian motion (diffusion) of particles in membranes occurs in a highly anisotropic environment. For such particles a translational mobility (independent of velocity) can be defined if the viscosity of the liquid embedding the membrane is taken into account. The results of a model calculation are presented. They suggest that for a realistic situation translational diffusion should be about four times faster in relation to rotational diffusion than in the isotropic case.
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Saffman et al. (1975) studied this question.