Surfactant monolayers and lipid bilayers are intrinsically two- dimensional structures with viscoelastic mechanical properties. Monolayers display a plethora of complex broken symmetry phases, each with its own rheological signature, while bilayers are of fundamental biological importance in forming the cell membrane and the principal internal partitions of the cell. Understanding the low energy excitations and mechanical response of these materials is thus an important probe of novel two-dimensional phases and essential to biomechanics at the cellular level, cell cell recognition, and trans- port across membranes; as such, a number of macroscopic and microscopic techniques have been developed to explore the rheological properties of mono- layers and membranes. In this chapter we review the fundamental physics and rheology of molecularly thin membranes, paying particular attention to the fact that these systems are necessarily bounded on one or both sides by an aqueous fluid. We develop the basic theory of both the in- and out-of-plane viscoelastic response of membranes and monolayers, and apply this theory to the study of particle transport in the surface. Such transport measurements form the basis of typical rheological experiments. We also report on more recent investigations regarding the role of nontrivial membrane geometry on particle transport, and examine a novel approach to monolayer and mem- brane microrheology using the thermal fluctuations of particles submerged beneath the membrane. We conclude with a discussion of open questions in the field and some speculations on future research directions.
A. A. Evans and A. J. Levine, Membrane Rheology, forthcoming in “Complex Fluids in Biological Systems” (Springer)