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The Quarterly Journal of Mechanics and Applied Mathematics 1952 5(1):42-53; doi:10.1093/qjmam/5.1.42
© 1952 by Oxford University Press
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PROBLEMS OF CROSS-VISCOSITY

I. BRAUN and M. REINER

( Rheological Laboralory, Institute of Technology Haifa )

Reiner's (1) equation of a general viscous liquid, which differs from Stokes's equation by a quadratic term defining a ‘coefficient of cross-viscosity’, is integrated for the cases of (i) a cylindrical rod rotating in a liquid, (ii) the rotating coaxial cylinder viscometer, (iii) the tube viscometer, (iv) the parallel plate-torsional viscometer, thus providing criteria for crucial experiments to decide whether the ‘centripetal effect’ in certain liquids is totally or partially due to cross-viscosity. Provided the liquid climbs up the rod in instrument (i), there should be radial tension upon the internal cylinder of instrument (ii). In instrument (iii) the wall pressure should be greater than the Newtonian hydrodynamic pressure by a term involving the ordinary shear viscosity. Finally there should be in instrument (iv) a parabolically distributed pressure upon the plate which vanishes at a distance from the axis of rotation which is 1/{surd}3 times the radius of the plate.


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