Anatoli Stulov, Magneto-optical tomography of Cosserat flows
Magneto-optical tomography is a nondestructive method for the three-dimensional stress analysis in transparent specimens. It is based on the measurement of the change in the polarization of light passed through a birefringent medium. The sample under study is placed in a strong constant magnetic field and illuminated in the direction parallel to this field. The plane of polarization of a light beam transmitted through the sample acquires an additional rotation, caused by the Faraday effect. The flow birefringence phenomenon in liquid is caused by presence of oblong molecules (polymers) or extended colloidal particles. The particles at rest have both an isotropic and homogeneous distribution, and therefore the liquid is also optically isotropic. The flow causes orientation of particles along the current lines, and this fact creates the induced birefringence. In case of the solution that contains polymeric chains, the flow besides orientation of molecules causes their extension and untwisting along the current lines. The reconstruction algorithm is based on the nonlinear effect of the magnetic field and flow birefringence on the parameters of polarized light, and uses the exponential Radon transform of an imaginary parameter. The theories of flow birefringence consist of three groups, which are applied to different classes of Cosserat fluids, namely plastic flows (Neiman’s law, Filon–Jessop law, Doyle law), polymeric flows (Waylands’s theory for non- Newtonian fluids), and colloidal suspensions. Numerous nonlinear constitutive models (Giesekus, Phan-Thien-Tanner) may be identified for simulation of generalized continua flow. Different types of microstructure give different types of the stress-optical rules, rheological characteristics, and constitutive equations. It is shown that the magneto-optical methods permit, in principle, to apply tomographic techniques for reconstruction of the strain and stress tensor fields of Cosserat flow.
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