Sharp-Interface Nematic-Isotropic Phase Transformations With Flow |
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Authors: | Eliot Fried |
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Institution: | (1) Department of Mechanical, Aerospace and Structural Engineering, Washington University in St Louis, St Louis, MO 63130-4899, USA |
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Abstract: | We develop a sharp-interface theory for phase transformations between the isotropic and uniaxial nematic phases of a flowing
liquid crystal. Aside from conventional evolution equations for the bulk phases and corresponding interface conditions, the
theory includes a supplemental interface condition expressing the balance of configurational momentum. As an idealized illustrative
application of the theory, we consider the problem of an evolving spherical droplet of the isotropic phase surrounded by the
nematic phase in a radially-oriented state. For this problem, the bulk and interfacial equations collapse to a single nonlinear
second-order ordinary differential equation for the radius of the droplet—an equation which, in essence, expresses the balance
of configurational momentum on the interface. This droplet evolution equation, which closely resembles a previously derived
and extensively studied equation for the expansion of contraction of a spherical gas bubble in an incompressible viscous liquid,
includes terms accounting for the curvature elasticity and viscosity of the nematic phase, interfacial energy, interfacial
viscosity, and the ordering kinetics of the phase transformation. We determine the equilibria of this equation and study their
stability. Additionally, we find that motion of the interface generates a backflow, without director reorientation, in the
nematic phase. Our analysis indicates that a backflow measurement has the potential to provide an independent means to determine
the density difference between the isotropic and uniaxial nematic phases. |
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