Fluid-magnet analogy

As model systems for scientific study, MR fluids are superior to ER fluids, because complications due to charging and conductivity in ER fluids have no counterpart in MR fluids, since magnetic monopoles, the analog of electric charges, are unknown in nature. Thus, a magnetic analog of the simple polarization model described in Section 8.2.1 for ER fluids should be even more appropriate for MR fluids. 

The problem of magnetic fields arising spontaneously in the motion of a fluid was considered by Batchelor [1], He came to the conclusion that the magnetic field increases without limit for sufficient conductivity in a given velocity field. His conclusion was based on nonrigorous considerations of the analogy between the magnetic field and a velocity vortex. 

Apropos of the analogy noted by Batchelor between vortex velocity and a magnetic field, it should be noted that for the realization of truly steady turbulence a supply of mechanical energy is necessary. The supply of energy comes about either through nonpotential volume forces or through the motion of the surfaces bounding the fluid. With these factors taken into consideration, the set of equations and boundary conditions for a vortex does... 

It is important to emphasize that these magnetic fields may be absolutely arbitrary and, in particular, it is not necessary for them to possess the symmetry of the velocity field of the fluid. In this sense the theorem proved in this paper is much stronger than an analogous theorem considered by Cowling and Phil for the axisymmetric case. They succeeded only in proving the decay of a magnetic field whose distribution, like the velocity field, is axisymmetric. 

Sum-frequency generation (SFG) at second-order and the nonlinear Raman spectroscopy BioCARS at fourth-order can also probe chiral molecules. They have no analog in linear optics. We show that both are only symmetry allowed in a fluid, if the fluid is chiral. However, in contrast to optical activity phenomena, these processes arise entirely from induced electric-dipoles (without magnetic or quadrupolar transitions) and they are not circular differential. All laser beams can be linearly polarized and no polarization modulation is required as the detection of a sum-frequency (yiz. five-wave mixing) photon is in itself a measure of the solution s chirality. Since an achiral solvent can not contribute to the signal, these techniques are sensitive, background-free probes of molecular chirality. The SFG... 

Feigenbaum went on to develop a beautiful theory that explained why a and 5 are universal (Feigenbaum 1979). He borrowed the idea of renormalization from statistical physics, and thereby found an analogy between a, 5 and the universal exponents observed in experiments on second-order phase transitions in magnets, fluids, and other physical systems (Ma 1976). In Section 10.7, we give a brief look at this renormalization theory. 

Fluid-flow switches An analog of proximity switches for fluid detection, fluid-flow sensors use a sprung or magnetic valve to detect when flow takes place in a pipe. 

Less widely appreciated is the fact that substantially the same departures from the behaviour predicted by mean-field theories occur in fluid mixtures in the region of the critical solution point. The same failures of analytic theories are found and similar critical exponents are deduced from experiment. It is the purpose of this chapter to review the thermodynamic principles underlying critical phenomena, to emphasize the analogies with pure-fluid gas-liquid equilibrium, to outline some of the difficulties encountered when one tries to determine critical exponents precisely, and to summarize the presently available experimental results from binary fluid mixtures. (For a review of the related situation in magnetism and in pure fluids, see Stanley and Levelt Sengers. )... 

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