# Algorithms for accurately calculating forces between dipolar particles

Thursday, March 15, 2018 - 11:30am - 12:20pm

Lind 305

Sibani Biswal (Rice University)

Typically, forces between dipolar particles are calculated using dipole-based models such as the dipolar model (DM). These models allow for simple force calculations between paramagnetic spheres in an external magnetic field, but are typically inaccurate for systems where particles are in close proximity due to multipolar effects. Additionally, the dipolar model cannot be used for anisotropic magnetic particles and new models are needed.

To address this challenge, I will describe how to solve for the force between dipolar colloids by solving Laplace’s equation for magnetostatics with multiple boundary conditions at the interfaces and integrating the Maxwell stress tensor over the particle volume. Typically a singularity arises from a discontinuity in the boundary conditions. However, a numerical solution to the Laplace’s equation can be obtained by using a smoothed representation of susceptibility to replace the boundary conditions. Additionally, by considering the position of the dipole moment that is offset from the center of the particles, a superposition method can be used to calculate the forces between anisotropic dipolar particles.

To address this challenge, I will describe how to solve for the force between dipolar colloids by solving Laplace’s equation for magnetostatics with multiple boundary conditions at the interfaces and integrating the Maxwell stress tensor over the particle volume. Typically a singularity arises from a discontinuity in the boundary conditions. However, a numerical solution to the Laplace’s equation can be obtained by using a smoothed representation of susceptibility to replace the boundary conditions. Additionally, by considering the position of the dipole moment that is offset from the center of the particles, a superposition method can be used to calculate the forces between anisotropic dipolar particles.

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