Yield stress in thin layers of ferrofluids

We present results of theoretical study of quasielastic behavior of ferrofluid filling a thin flat gap, placed into perpendicular magnetic field. When the field exceeds a certain critical magnitude, magnetic particles form dense discrete domains, elongated along the field, and linking the gap boundaries. Due to these bridges between the gap boundaries, the ferrofluid exhibits quasielastic properties with respect to shear strain in the plane of the gap. We estimated the elastic modules as well as the yield stress of the system, depending on magnetic field and concentration of magnetic particles in the ferrofluid. Analysis shows that there are at least two microscopical mechanisms of transition from the elastic to fluid behavior of the ferrofluid. The first one is connected with the loss of the mechanical equilibrium of the domains, slopped, under the shear stress, with respect to applied magnetic field. The second mechanism is connected with breakup of the “bridge” into two separate drops, when the shear strain exceeds some critical magnitude. Estimates show that for real ferrofluids the second mechanism is more probable.