Instability of Myelin Tubes under Dehydration: deswelling of layered cylindrical structures
Abstract
We report experimental observations of an undulational instability of myelin figures. Motivated by this, we examine theoretically the deformation and possible instability of concentric, cylindrical, multi-lamellar membrane structures. Under conditions of osmotic stress (swelling or dehydration), we find a stable, deformed state in which the layer deformation is given by δ R ~ rBA/(hB), where BA is the area compression modulus, B is the inter-layer compression modulus, and h is the repeat distance of layers. Also, above a finite threshold of dehydration (or osmotic stress), we find that the system becomes unstable to undulations, first with a characteristic wavelength of order xi d0, where xi is the standard smectic penetration depth and d0 is the thickness of dehydrated region.
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