Magnetizable fluid behaviour with effective positive, zero or negative dynamic viscosity

Abstract

<span style="font-size:11.0pt;line-height:115%; font-family:" calibri","sans-serif";mso-ascii-theme-font:minor-latin;mso-fareast-font-family:="" "times="" new="" roman";mso-fareast-theme-font:minor-fareast;mso-hansi-theme-font:="" minor-latin;mso-bidi-font-family:arial;mso-ansi-language:en-us;mso-fareast-language:="" en-us;mso-bidi-language:ar-sa"="">Analyses and measurement have shown anomalous behaviour of ferrofluids in ac magnetic fields, whereby in a rotating magnetic field the ferrofluid can be pumped but the flow direction can reverse as a function of magnetic field amplitude, frequency, and direction. This anomalous behaviour is investigated using the governing fluid mechanical linear and angular momentum conservation equations including non-symmetric viscous and Maxwell stress tensors. Here, a simple case has been examined where applied magnetic field components along and transverse to the duct axis are spatially uniform and vary sinusoidally with time. In the uniform magnetic field the magnetization characteristic depends on fluid spin velocity but does not depend on fluid flow velocity. The magnetization force density along the duct axis is zero while the magnetic torque density is non-zero as <img src='http://www.niscair.res.in/jinfo/marrow.gif' border=0> and <img src='http://www.niscair.res.in/jinfo/harrow.gif' border=0> are not collinear due to a magnetic relaxation time constant as well as due to spatially varying fluid spin velocity. The governing linear and angular momentum conservation equations then require non-symmetric fluid viscous and Maxwell stress tensors. Ferrofluid behaviour in ac magnetic fields offers an excellent experimental system to examine this unusual type of coupled electro-mechanical system. The governing equations are numerically integrated to solve for flow and spin velocity distributions for zero shear spin viscosity as a function of magnetic field strength, phase, frequency, and direction along and transverse to the duct axis; as a function of pressure gradient along the duct; vortex viscosity; dynamic viscosity; and ferrofluid magnetic susceptibility. Analytical solutions for simple limiting cases are given especially focusing on the case when the effective dynamic viscosity that depends on magnetic field strength can be made positive, zero or negative. Negative effective dynamic viscosity may explain the observed flow reversals while simple approximate theory for the transition point where the effective viscosity goes through zero predicts an infinite flow and spin velocity in response to a pressure gradient. The shear coefficient of spin viscosity, non-linear effects, and flow instabilities most likely limits the fluid mechanical response to remain large but finite. Numerical integrations show the highly non-linear and multi-valued solutions for flow and spin velocities when the shear spin viscosity coefficient is zero.</span>