Theory of nematic and polar active fluid surfaces

Abstract

We derive a fully covariant theory of the hydrodynamics of nematic and polar active surfaces, subjected to internal and external forces and torques. We study the symmetries of polar and nematic surfaces and find that in addition to 5 different types of in-plane isotropic surfaces, polar and nematic surfaces can be classified into 5 polar, 2 pseudopolar, 5 nematic and 2 pseudonematic types of surfaces. We give examples of physical realisations of the different types of surfaces we have identified. We obtain expressions for the equilibrium tensions, moments, and external forces and torques acting on a passive polar or nematic surface. We calculate the entropy production rate using the framework of thermodynamics close to equilibrium and find constitutive equations for polar and nematic active surfaces with different symmetries. We study the instabilities of a confined flat planar-chiral polar active layer and of a confined deformable polar active surface with broken up-down symmetry.

References in corpus (4)

• Topology and Dynamics of Active Nematic Vesicles
• Quantifying material properties of cell monolayers by analyzing integer topological defects
• Integer topological defects of cell monolayers -- mechanics and flows
• Hydrodynamic theory for nematic shells: the interplay among curvature, flow and alignment

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• Passive defect driven morphogenesis in nematic membranes
• Defect binding-unbinding transition in active nematic membranes
• A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces