Ferrohydrodynamics: Retrospective and Issues

Field-induced motion of ferrofluids through immiscible viscous media: Testbed for restorative treatment of retinal detachment

“…The droplet volume must also be considered, as it will likely affect the size of the hole that can be sealed, as well as the overall motion of the droplet. Mathematical models for the motion of ferrofluids were described by Shliomis [6][7][8][9][10][11] and Felderhof [12][13][14]. Others investigated the use of gradient fields for positioning ferrofluids in microfluidic [15], capillary [16], and controlled rheological systems [17][18][19].…”

Nonlinear energy dissipation of magnetic nanoparticles in oscillating magnetic fields

“…However, Eq. (21) itself is an approximate magnetization relaxation equation, quantitatively accurate only at low applied magnetic field amplitude and frequency [34][35][36]. For moderate to high alternating magnetic field amplitude and frequency a more exact magnetization relaxation equation to describe the time rate of change of the magnetization of a suspension of magnetic nanoparticles was derived by Martsenyuk, Raikher, and Shliomis [28] (31)…”

Global weak solutions to a ferrofluid flow model

“…To our knowledge the existence of solutions (strong or weak) to system (1), (2) has not yet been considered in the literature. As first step in the study of the existence of solutions to system (1), (2), we consider in this paper a regularized system where the magnetization Equation (1c), which is a Bloch-type equation, is replaced by the following:…”

“…where U is the fluid velocity, and the parameters , , 0 , 0 , , and are positive and their physical meaning can be found in for example, [1,2,5]. The magnetic field H satisfies the magnetostatic equations…”

“…This paper deals with the question of global solvability of the equations proposed by Shliomis [1,2] to describe the flow of an incompressible ferrofluid submitted to an external magnetic field. Ferrofluids (also called magnetic fluids) are suspensions of ferromagnetic nanoparticles in carrier liquids.…”