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Fluid Dynamics of Viscoelastic Liquids (Hardcover, 1990 ed.)
Loot Price: R3,181
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Fluid Dynamics of Viscoelastic Liquids (Hardcover, 1990 ed.)
Series: Applied Mathematical Sciences, 84
Expected to ship within 10 - 15 working days
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This book is about two special topics in rheological fluid
mechanics: the elasticity of liquids and asymptotic theories of
constitutive models. The major emphasis of the book is on the
mathematical and physical consequences of the elasticity of
liquids; seventeen of twenty chapters are devoted to this.
Constitutive models which are instantaneously elastic can lead to
some hyperbolicity in the dynamics of flow, waves of vorticity into
rest (known as shear waves), to shock waves of vorticity or
velocity, to steady flows of transonic type or to short wave
instabilities which lead to ill-posed problems. Other kinds of
models, with small Newtonian viscosities, give rise to perturbed
instantaneous elasticity, associated with smoothing of
discontinuities as in gas dynamics. There is no doubt that liquids
will respond like elastic solids to impulses which are very rapid
compared to the time it takes for the molecular order associated
with short range forces in the liquid, to relax. After this, all
liquids look viscous with signals propagating by diffusion rather
than by waves. For small molecules this time of relaxation is
estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves
associated with such liquids move with speeds of 1 QS cm/s, or even
faster. For engineering applications the instantaneous elasticity
of these fluids is of little interest; the practical dynamics is
governed by diffusion, *say, by the Navier-Stokes equations. On the
other hand, there are other liquids which are known to have much
longer times of relaxation.
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