Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
Ferrofluid droplets under external magnetic field and shear flow in non-equilibrium magnetization regime
Submission Author:
Arthur Guilherme , PB
Co-Authors:
Arthur Guilherme, Taygoara Oliveira
Presenter: Arthur Guilherme
doi://10.26678/ABCM.ENCIT2022.CIT22-0480
Abstract
Ferrofluid droplets immersed in a non-magnetizable carrier fluid subjected to the combined action of a simple shear flow and external magnetic fields are studied in this work. This problem has potential applications in areas such as microfluidics, biomedicine, and microrheology and has been subject of research recently. Nevertheless, up to our knowledge all theoretical and numerical studies consider superparamagnetic ferrofluids, i.e. the local magnetization is linearly proportional to the local magnetic field. In the present work, we consider the regime of non-equilibrium magnetization, in which the local magnetization is influenced by the vorticity, brownian magnetic relaxation and precessional magnetic torque, as described by the Shliomis (1971) model. The non-dimensional parameters governing the problem are the Péclet number ($Pe$), accounting for the ratio between brownian relaxation time and a characteristic time of the shear flow; the capillary number (Ca), which is the ratio between shear stress and surface tension; and a magnetic capillary number (Ca_{mag}), that measures the ratio between magnetic stress and surface tension. The three-dimensional problem has a full set of fifteen well-coupled equations. They are the incompressible Navier-Stokes with interface and magnetic forces source terms, Maxwell's equations at magnetostatic limit, the magnetization evolution equation, the equilibrium magnetization equation and the interface capturing equation. The classical projection method is used to solve the pressure-velocity coupling. The finite-difference in a staggered grid is used to discretize space. The time integration is made through a Crank-Nicolson scheme for the momentum equations and the explicit Euler method for the magnetization evolution. The interface capturing problem is treated using a level-set method with conservative high-order time and space discretization. We present results comparing the bulk and local magnetization, droplet deformation, and susceptibility behavior for different Pe at distinct flow conditions, i.e., distinct Ca and Ca_{mag} and distinct magnetization regimes. It was observed that vorticity could change the monotonicity of the bulk magnetization and deformation with respect to Pe_m.
Keywords
Magnetization, Magnetic relaxation, Ferrofluid droplet, Level Set method
