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.
Anderson D.M., Cermelli P., Fried E., Gurtin M.E., McFadden G.B. (2007) General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids. J. Fluid Mech. 581:323–370zbMATHCrossRefADSMathSciNetGoogle Scholar
Cermelli P., Fried E., Gurtin M.E. (2005) Transport relations for surface integrals arising in the formulation of balance laws for evolving fluid interfaces. J. Fluid Mech. 544:339–351zbMATHCrossRefADSMathSciNetGoogle Scholar