A simple model of a vesicle drop in a confined geometry

TL;DR

This paper provides an exact solution for a 2D directed walk model of a confined vesicle-like drop, analyzing how wall interactions and pressure influence its behavior, with implications for polymer stabilization.

Contribution

It introduces an exact analytical model of a confined vesicle with wall interactions and pressure effects, extending previous polymer models.

Findings

Negative pressure prevents confinement effects at large wall separations.

The model captures the competition between wall adhesion and pressure.

Exact solutions reveal phase behavior of the vesicle system.

Abstract

We present the exact solution of a two-dimensional directed walk model of a drop, or half vesicle, confined between two walls, and attached to one wall. This model is also a generalisation of a polymer model of steric stabilisation recently investigated. We explore the competition between a sticky potential on the two walls and the effect of a pressure-like term in the system. We show that a negative pressure ensures the drop/polymer is unaffected by confinement when the walls are a macroscopic distance apart.