Small equatorial deformation of homogeneous spherical fluid vesicles

Area of Science:

• Fluid dynamics
• Membrane mechanics
• Biophysics

Background:

• Spherical fluid vesicles are fundamental structures in biology and soft matter physics.
• Understanding their mechanical response to external forces is crucial for various applications.
• Previous studies have explored vesicle deformation, but specific interactions with localized constraints require further investigation.

Purpose of the Study:

• To analytically investigate the deformation of a spherical fluid vesicle subjected to a rigid circular ring at its equator.
• To determine the critical force initiating membrane deformation and analyze the resulting changes in curvature.

Main Methods:

• Analytical solution of the linearized Euler-Lagrange equation for a vesicle.
• Incorporation of global constraints (fixed area and volume) and a local constraint from the ring.
• Calculation of first-order perturbations to the membrane's generating curve.

Main Results:

• The vesicle's deformation is characterized by the radius difference between the membrane and the ring, and a physical parameter.
• A critical force is identified that initiates membrane deformation.
• The deformation results in a discontinuity in membrane curvature at the ring's location.

Conclusions:

• The study provides an analytical framework for understanding vesicle response to localized external forces.
• The findings offer insights into the mechanics of membrane-ring interactions and critical deformation thresholds.
• This work contributes to the fundamental understanding of fluid vesicle mechanics under constraint.