A ferrofluid is a stable suspension of magnetic nano-particles. It behaves like an ordinary Newtonian fluid in the absence of a magnetic field, but displays a variety of novel behavior in a field. In the past decades, thorough knowledge on a single droplet under the influence of a rotating field has been obtained. In this project, we study the detailed dynamics of droplets in a magnetic field by a full numerical solution of the free interface problem and by means of lubrication approximation. The open source finite volume software package Gerris will be used for this project. It features adaptive mesh refinement on a structured quad-/oct-tree grid, a volume-of-fluid formulation of the interface between the ferrofluid and the surrounding liquid, and an accurate computation of the surface tension.

We also study the magneto wetting phenomena: the application of a uniform magnetic field to induce dewetting of a thin ferrofluid film. Here we present the study, where thin film equations are derived using the long wave approximation of the coupled static Maxwell and Stokes equations and the contact angle is imposed via a disjoining/conjoining pressure model.

External Collaborators:

James J. Feng, U. of British Columbia (Website)
Ian Griffiths, Oxford (Website)
Pengtao Yue, Virgina Tech (Website)
Ching-Yao Chen, National Chiao Tung University (Website)

Recent Publications

I. Rukshin, J. Mohrenweiser, P. Yue, and S. Afkhami, Modeling Superparamagnetic Particles in Blood Flow for Applications in Magnetic Drug Targeting, Fluids, 2, 29, (2017)

Magnetic drug targeting is a technique that involves the binding of medicine to magnetizable particles to allow for more specific transport to the target location. This has recently come to light as a method of drug delivery that reduces the disadvantages of conventional, systemic treatments. This study developed a mathematical model for tracking individual superparamagnetic nanoparticles in blood flow in the presence of an externally applied magnetic field. The model considers the magnetic attraction between the particles and the external magnet, influence of power law flow, diffusive interaction between the particles and blood, and random collisions with red blood cells. A stochastic system of differential equations is presented and solved numerically to simulate the paths taken by particles in a blood vessel. This study specifically focused on localized cancer treatment, in which a surface tumor is accessed through smaller blood vessels, which are more conducive to this delivery method due to slower flow velocities and smaller diameters. The probability of the particles reaching the tumor location is found to be directly dependent on ambient factors; thus, diffusion through Brownian motion and red blood cell collisions, different magnetic field and force models, blood viscosities, and release points are considered.

S. Afkhami, L.J. Cummings, and I. Griffiths, Interfacial deformation and jetting of a magnetic fluid, Computers & Fluids, 124, 149-156, (2016)

An attractive technique for forming and collecting aggregates of magnetic material at a liquid–air interface by an applied magnetic field gradient was recently proposed, and its underlying principle was studied theoretically and experimentally (Tsai et al., 2013): when the magnetic field is weak, the deflection of the liquid–air interface has a steady shape, while for sufficiently strong fields, the interface destabilizes and forms a jet that extracts magnetic material. Motivated by this work, we develop a numerical model for the closely related problem of solving two-phase Navier–Stokes equations coupled with the static Maxwell equations. We computationally model the forces generated by a magnetic field gradient produced by a permanent magnet and so determine the interfacial deflection of a magnetic fluid (a pure ferrofluid system) and the transition into a jet. We analyze the shape of the liquid–air interface during the deformation stage and the critical magnet distance for which the static interface transitions into a jet. We draw conclusions on the ability of our numerical model to predict the large interfacial deformation and the consequent jetting, free of fitting parameters.

I. Seric, S. Afkhami, and L. Kondic, Interfacial instability of thin ferrofluid films under a magnetic field, Journal of Fluid Mechanics, 755, R1, (2014)

We study magnetically induced interfacial instability of a thin ferrofluid film subjected to an applied uniform magnetic field and covered by a non-magnetizable passive gas. Governing equations are derived using the long-wave approximation of the coupled static Maxwell and Stokes equations. The contact angle is imposed via a disjoining/conjoining pressure model. Numerical simulations show the patterning resulting from unstable perturbations and dewetting of the ferrofluid film. We find that the subtle competition between the applied field and the van der Waals induced dewetting determines the appearance of satellite droplets. The results suggest a new route for generating self-assembled ferrofluid droplets from a thin film using an external magnetic field. An axisymmetric droplet on a surface is also studied, and we demonstrate the deformation of the droplet into a spiked cone, in agreement with experimental findings.