Analytic Solutions and Numerical Simulation of Self-Assemble Magnetic Colloidal Structures

Self-assembled magnetic colloidal structures that lie at a fluid-air interface can have a wide range of behavior, from localized axisymmetric star-like objects to linear, snake-like ones. Modeling these structures requires both the extensive use of the Navier-Stokes Equations from an analytic standpoint as well as the ability to numerically solve and simulate them alongside Newton's Equations. Analytically, these equations are approximated by an asymptotic expansion with a small viscosity. Using those expressions, simulations are run on GPU's to utilize their parallel capability. The result is a remarkable, qualitative recapturing of the experimentally observed behavior, namely, the formation of both snakes and stars from a randomized initial condition.