On the problem of transient hydrodynamic instability of nematics in magnetic field: I. Instability at splay deformation

Abstract

A dependence of the square of dimensionless magnetic-field (MF) strength on the square of dimensionless wave vector of the domain structure, $h^2 \left( {\tilde q^2 } \right)$, is analytically derived for the transient hydrodynamic instability arising at splay deformation under a MF. The domain formation is related to the fold catastrophe; the square of the critical field of domain formation, h ² _D , is determined from the condition ${{\partial \left[ {h^2 \left( {\tilde q^2 } \right)} \right]} \mathord{\left/ {\vphantom {{\partial \left[ {h^2 \left( {\tilde q^2 } \right)} \right]} \partial }} \right. \kern-\nulldelimiterspace} \partial }\left( {\tilde q^2 } \right) = 0$. In the general case, the function $h^2 \left( {\tilde q^2 } \right)$ is a ratio of two polynomials whose coefficients for calamitics are determined by combinations of four dimensionless viscosities ν₂/ν₁, ν₆/ν₁, ν₇/ν₁, and ν₈/ν₁. Under some assumptions, the quotient of the polynomials at large $\tilde q^2$ is a quadratic function which allows one to experimentally determine the dimensionless viscosities ν₂/ν₁, ν₆/ν₁, ν₇/ν₁, and α₂/ν₁.