[Paper Review] Vesicles in magnetic fields

David Salač|arXiv (Cornell University)|Aug 19, 2016

Electrohydrodynamics and Fluid Dynamics25 references3 citations

TL;DR

This paper presents a theoretical model of liposome vesicles in magnetic fields, deriving hydrodynamic forces from magnetic energy to simulate vesicle dynamics. It demonstrates that magnetic field-induced lipid anisotropy generates a torque aligning vesicles with the field, validated through numerical simulations showing stable alignment and deformation under field exposure.

ABSTRACT

Liposome vesicles tend to align with an applied magnetic field. This is due to the directional magnetic susceptibility difference of the lipids which form the membrane of these vesicles. In this work a model of liposome vesicles exposed to magnetic field is presented. Starting from the base energy of a lipid membrane in a magnetic field, the force applied to the surrounding fluids is derived. This force is then used to investigate the dynamics of vesicle in the presence of magnetic fields.

Motivation & Objective

• To develop a comprehensive model of vesicle dynamics under externally applied magnetic fields, addressing a gap in theoretical studies of magnetohydrodynamics in soft matter.
• To derive the hydrodynamic force on the fluid surrounding a vesicle from the magnetic energy of the lipid membrane, accounting for field-induced anisotropy.
• To simulate the time-evolving behavior of vesicles, including alignment, stretching, and shape deformation, under static magnetic fields.
• To establish a framework for predicting vesicle response in magnetic fields, supporting applications in targeted drug delivery and cell sorting.
• To validate the model using numerical simulations that capture key physical behaviors such as rotational alignment and surface tension effects.

Proposed method

• Formulates the magnetic energy of the lipid membrane based on its directional magnetic susceptibility anisotropy, leading to a force density on the surrounding fluid.
• Applies the leaky-dielectric model to assume no free charges in bulk fluids, eliminating Lorentz forces and focusing on field-induced interfacial forces.
• Uses surface vector calculus to derive surface gradients, divergences, and tensor operations on the vesicle membrane, enabling force computation on the interface.
• Derives the force balance on the membrane using the surface divergence of the stress tensor, incorporating curvature and normal vector dynamics.
• Implements a numerical scheme to solve the coupled fluid-membrane system, enforcing inextensibility, constant volume, and surface area incompressibility.
• Simulates vesicle evolution under magnetic fields using a finite-difference or finite-element approach, tracking orientation, shape, and deformation over time.

Experimental results

Research questions

• RQ1 How does the magnetic field induce a force on a liposome vesicle due to anisotropic magnetic susceptibility of its lipid membrane?
• RQ2 What are the hydrodynamic forces generated on the surrounding fluid by the magnetic energy of the vesicle membrane?
• RQ3 How do the vesicle’s shape and orientation evolve over time under a static magnetic field?
• RQ4 What role does membrane inextensibility and surface area incompressibility play in balancing magnetic stretching forces?
• RQ5 How does the model predict the alignment and deformation of vesicles compared to experimental observations?

Key findings

• The magnetic field induces a torque on the vesicle due to the anisotropic diamagnetic susceptibility of lipids, causing the vesicle to align with the field direction.
• The derived force density on the fluid arises from the surface gradient of the magnetic energy, leading to fluid motion that drives vesicle deformation.
• Numerical simulations show that vesicles align with the magnetic field and undergo stretching, with shape changes balanced by increased bending and surface tension energy.
• The model successfully captures the experimentally observed alignment of liposomes in magnetic fields, particularly for DPPC-based vesicles.
• The absence of free charges in the fluid allows the use of the leaky-dielectric model, simplifying the force derivation and enabling accurate simulation of vesicle dynamics.
• The surface divergence and projection operator formalism enables consistent computation of forces on the curved vesicle membrane, ensuring geometric accuracy.