By G. Böhme
This quantity is to be used in technical universities, and for practicing engineers who're concerned with circulation difficulties of non-Newtonian fluids. The therapy of the topic relies all through on continuum mechanics version thoughts and techniques. simply because in Non-Newtonian fluids the fabric homes working count seriously at the kinematics of the stream, designated awareness is paid to the derivation and rationalization of the sufficient constitutive equations used. The e-book will be learn regardless of different resources. It starts by way of contemplating a few common rules of continuum mechanics, reviews easy motions (steady and unsteady shear flows) and proceeds by way of levels to kinematically extra advanced motions. difficulties of assorted levels of trouble on the finish of every bankruptcy invite lively participation through the reader. a number of stimulating themes from the literature are thought of within the booklet
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Additional resources for Non-Newtonian Fluid Mechanics
73) Hence this yields the following expressions for the history of the relative right-Cauchy-Green tensor (according to equation ( 1 . 74) It is noteworthy that besides the constant velocity component V normal to the wall and the local velocity component u(y) parallel to the wall, only the velocity component u(y + Vs) enters, which a material point possessed at the time in the past s. One can easily satisfy oneself from this fact that in the present case the determinant of the tensor Because the determinant always has the value unity.
Before that we shall look at applications of the important class of steady shear flows in detail. If the plane shear flow sketched in Fig. 1 is steady, then the velocity field and hence the rate of strain of each layer is constant with time. Therefore every fluid particle experiences, apart from a rotation, at all times a constant shear rate y(y). Hence it looks back to a peculiar monotonous deformation history, in which there were no variations at all, so that the memory of the past only contains one bit of information, namely the quantity for the particle concerned.
By the introduction If one puts = curiae satisfied. 1103 > ), then the continuity equation According to these relations the field with two components is reduced to a single Furthermore the stream function ψ has an obvious meaning. The curves Ψ (x,y,t) = constant at a certain time are of course the stream lines, because if one proceeds along such a curve 0 = d * = ^ dx + ^ dy = - vdx + udy 3x 3y applies. 104) The relationship dy/dx = v/u which follows from that is the differen tial equation of the stream lines (equation ( 1 .