Layer dynamics of a freely standing smectic-A film

TL;DR

This paper presents a theoretical analysis of the hydrodynamics of freely-standing smectic-A films, focusing on their dynamic properties, boundary conditions, and the importance of permeation effects near free surfaces.

Contribution

It provides a comprehensive theoretical framework for understanding the hydrodynamic modes and response functions of smectic-A films, including permeation effects and layer displacement dynamics.

Findings

Hydrodynamic mode structure differs from bulk systems.

Response functions depend on layer displacement and normal velocity.

Permeation effects are significant near free surfaces.

Abstract

We study the hydrodynamics of a freely-standing smectic-A film in the isothermal, incompressible limit theoretically by analyzing the linearized hydrodynamic equations of motion with proper boundary conditions. The dynamic properties for the system can be obtained from the response functions for the free surfaces. Permeation is included and its importance near the free surfaces is discussed. The hydrodynamic mode structure for the dynamics of the system is compared with that of bulk systems. We show that to describe the dynamic correlation functions for the system, in general, it is necessary to consider the smectic layer displacement $u$ and the velocity normal to the layers, $v_z$, together. Finally, our analysis also provides a basis for the theoretical study of the off-equilibrium dynamics of freely-standing smectic-A films.