Creeping motion of a solid particle inside a spherical elastic cavity^⋆

Area of Science:

• Fluid dynamics
• Biophysics
• Soft matter physics

Background:

• Understanding particle dynamics within elastic cavities is crucial for modeling biological systems like fluid vesicles.
• Low-Reynolds-number hydrodynamics governs the motion of small particles in viscous fluids.

Purpose of the Study:

• To develop an analytical theory for the motion of a solid particle inside a spherical elastic cavity.
• To model fluid vesicles using a solid particle within a larger spherical elastic cavity.
• To investigate the role of membrane properties on particle hydrodynamics.

Main Methods:

• Linear hydrodynamic equations
• Stream function technique for concentric particle motion
• Image solution technique for arbitrary particle positions
• Boundary integral simulations for validation

Main Results:

• For concentric particles, motion is determined solely by membrane shear properties; bending is irrelevant.
• Analytical expressions for particle-cavity hydrodynamic interactions were derived.
• Particle self-mobility is higher in elastic cavities than rigid ones.
• Pair-mobility is solely dependent on membrane shear properties.

Conclusions:

• The analytical theory accurately predicts particle motion within elastic cavities.
• Membrane shear properties are key determinants of hydrodynamic interactions.
• The model provides insights into fluid vesicle dynamics.