Diffuse-interface theory of active nematic interfaces: Transport mechanisms and modal structure

We develop a long-wavelength theory for the linear stability of a diffuse interface between an active nematic and an isotropic phase. The starting point is a Cahn-Hilliard-Landau-de Gennes description of the coexistence profile, coupled to Brinkman-screened Stokes hydrodynamics. Small perturbations are projected onto three interfacial degrees of freedom: the conserved height mode associated with translations of the coexistence profile, a scalar profile-distortion mode, and a transverse orientational mode corresponding to director rotations. In the screened hydrodynamic regime, activity generates a local analytic contribution, proportional to q^{2}, to the height-sector dynamics. This term competes with the passive conserved capillary relaxation, which enters at order q^{4}, and can destabilize the interface even when the homogeneous active nematic is below its bulk instability threshold. The scalar profile-distortion mode is gapped and can be eliminated at long wavelengths. The transverse orientational mode plays a different role: if its full relaxation rate is positive, it renormalizes the effective scalar height equation; if it remains soft, the long-wavelength instability is described by a coupled height-director mode. The resulting framework separates two issues that are often intertwined in active-interface problems. The first is the transport mechanism, which may be local and analytic for a screened diffuse interface or nonanalytic when long-ranged outer flow produces terms such as |q|. The second is the modal structure of the unstable branch, which may be predominantly heightlike or intrinsically coupled to director rotations.