Micelles Hydrodynamics

TL;DR

This paper provides an elegant analytical proof explaining why micelles are spherical in mechanical equilibrium, based on thermodynamic principles, and suggests the formalism can be extended to other homogeneous surfaces.

Contribution

It offers the shortest analytical proof of micelle spheroidal shape in equilibrium, advancing understanding of micelle geometry in thermodynamic conditions.

Findings

Micelles are spherical in mechanical equilibrium.

The proof is concise and analytically elegant.

The formalism can be extended to vesicles and membranes.

Abstract

A micelle consists of monolayer of lipid molecules containing hydrophilic head and hydrophobic tail. These amphiphilic molecules in aqueous environment aggregate spontaneously into monomolecular layer held together due to hydrophobic effect by weak non-covalent forces. Micelles are flexible surfaces that show variety of shapes of different topology, but remarkably in mechanical equilibrium conditions they are spherical in shape. The shape and size of a micelle are functions of many variables such as lipid concentration, temperature, ionic strength, etc. Addressing the question, why the shape of micelles is sphere in mechanical equilibrium conditions, analytically proved to be a difficult problem. In the following paper we offer the shortest and elegant analytical proof of micelles spheroidal nature when they are thermodynamically equilibrated with solvent. The formalism presented in this paper can be readily extended to any homogenous surfaces, such are vesicles and membranes.