Membrane compression in tumbling and vacillating-breathing regimes for quasispherical vesicles

Area of Science:

• Fluid dynamics
• Biophysics
• Soft matter physics

Background:

• Quasispherical vesicles are model systems for biological cells and microcapsules.
• Understanding vesicle behavior in flow is crucial for applications in drug delivery and microfluidics.
• Previous studies have focused on qualitative descriptions of vesicle dynamics.

Purpose of the Study:

• To derive analytical results for quasispherical vesicles in linear shear flow at low deformability.
• To investigate the oscillatory regimes: tumbling (TB) and vacillating-breathing (VB) modes.
• To analyze the transition between VB and TB modes and associated membrane dynamics.

Main Methods:

• Analytical derivation based on a well-established vesicle model.
• Focus on low deformability regimes in linear shear flow.
• Analysis of control parameter Γ and its effect on vesicle dynamics.

Main Results:

• Detailed characterization of the tumbling (TB) and vacillating-breathing (VB) modes.
• Identification of the VB-to-TB transition at Γ=1, marked by maximal extension in the vorticity direction.
• Derivation of an analytical expression for effective membrane tension.
• Discovery of a critical bending number leading to membrane compression.
• Observation of fourth-order membrane deformation during the VB-to-TB transition.

Conclusions:

• The study provides precise analytical insights into vesicle dynamics in shear flow.
• The VB-to-TB transition exhibits unique characteristics, including specific vesicle profiles and deformations.
• The findings contribute to a deeper understanding of membrane mechanics and fluid-structure interactions.