Undulation Amplitude of a Fluid Membrane Surrounded by Near-Critical Binary Fluid Mixtures

TL;DR

This paper investigates how near-critical binary fluid mixtures influence the thermal undulation of a fluid membrane, revealing that near-criticality suppresses membrane fluctuations and can prevent large membranes from becoming floppy.

Contribution

It provides an analytic formula showing that near-criticality suppresses membrane undulation, highlighting a new mechanism affecting membrane stability in critical fluid environments.

Findings

Near-criticality suppresses membrane undulation amplitude.

Suppression can dominate over bending rigidity effects.

Large membranes are prevented from becoming floppy near criticality.

Abstract

We consider the thermal undulation, or shape fluctuation, of an almost planar fluid membrane surrounded by the same near-critical binary fluid mixtures on both sides. A weak preferential attraction is assumed between the membrane and one component of the mixture. We use the Gaussian free-energy functional to study the equilibrium average of the undulation amplitude within the linear approximation with respect to the amplitude. According to our result given by a simple analytic formula, the ambient near-criticality tends to suppress the undulation of a membrane, and this suppression effect can overwhelm that of the bending rigidity for small wave numbers. Thus, the ambient near-criticality is suggested to prevent a large membrane from becoming floppy even if the lateral tension vanishes at the equilibrium.