Nonisothermal retardation of elastic fluids

1982 ◽  
Vol 43 (1) ◽  
pp. 756-757
Author(s):  
A. N. Prokunin ◽  
V. D. Sevruk
Keyword(s):  
Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 432
Author(s):  
Silvia C. Hirata ◽  
Mohamed Najib Ouarzazi

The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions.


1990 ◽  
Vol 34 (7) ◽  
pp. 993-1010 ◽  
Author(s):  
Christopher J. Matice ◽  
William E. VanArsdale
Keyword(s):  

1997 ◽  
Vol 32 (6) ◽  
pp. 761-771 ◽  
Author(s):  
V. M. Entov ◽  
Kh. S. Kestenboim ◽  
S. V. Pokrovsky ◽  
G. A. Shugay

1956 ◽  
Vol 6 (2-3) ◽  
pp. 226-236 ◽  
Author(s):  
L. J. F. Broer
Keyword(s):  

Author(s):  
Yu.G. NAZMEEV ◽  
O.F. MOOSSIN ◽  
T.N. VEZIROGLU
Keyword(s):  

1795 ◽  
Vol 85 ◽  
pp. 24-45

However satisfactory the general principles of motion may be, when applied to the action of bodies upon each other, in all those circumstances which are usually included in that branch of natural philosophy called mechanics, yet the application of the same principles in the investigation of the motions of fluids, and their actions upon other bodies, is subject to great uncertainty. That the different kinds of airs are constituted of particles endued with repulsive powers, is manifest from their expansion when the force with which they are compressed is removed. The particles being kept at a distance by their mutual repulsion, it is easy to conceive that they may move very freely amongst each other, and that this motion may take place in all directions, each particle exerting its repulsive power equally on all sides. Thus far we are acquainted with the constitution of these fluids; but with what absolute degree of facility the particles move, and how this may be affected under different degrees of compression, are circumstances of which we are totally ignorant. In respect to those fluids which are denominated liquids, we are still less acquainted with their nature. If we suppose their particles to be in contact, it is extremely difficult to conceive how they can move amongst each other with such extreme facility, and produce effects in directions opposite to the impressed force without any sensible loss of motion. To account for this, the particles are supposed to be perfectly smooth and spherical. If we were to admit this supposition, it would yet remain to be proved how this would solve all the phænomena, for it is by no means self-evident that it would. If the particles be not in contact, they must be kept at a distance by some repulsive power. But it is manifest that these particles attract each other, from the drops of all perfect liquids affecting to form themselves into spheres. We must therefore admit in this case both powers, and that where one power ends the other begins, agreeable to Sir Isaac Newton's idea of what takes place not only in respect to the constituent particles of bodies, but to the bodies themselves. The incompressibility of liquids (for I know no decisive experiments which have proved them to be compressible) seems most to favour the former supposition, unless we admit, in the latter hypothesis, that the repulsive force is greater than any human power which can be applied. The expansion of water by heat, and the possibility of actually converting it into two permanently elastic fluids, according to some late experiments, seem to prove that a repulsive power exists between the particles; for it is hard to conceive that heat can actually create any such new powers, or that it can of itself produce any such effects. All these uncertainties respecting the constitution of fluids must render the conclusions deduced from any theory subject to considerable errors, except that which is founded upon such experiments as include in them the consequences of all those principles which are liable to any degree of uncertainty.


According to Dalton, the particles of one gas possess no repulsive or attractive power with regard to the particles of another gas; and accordingly, if m measures of a gas A be mixed with n measures of another gas B, each will occupy m + n measures of space. The density of A in such a mixture will be m / m + n' and of B, n / m + n' , the pressure upon any one particle of such a gaseous mixture arising solely from particles of its own kind. “It is scarcely necessary,” Dalton remarks, “to insist upon the application of this hypothesis to the solution of all our difficulties respecting the constitution of mixed gases where no chemical union ensues. The moment we admit it every difficulty vanishes. The atmosphere, or, to speak more properly, the compound of atmospheres, may exist together in the most intimate mixture without any regard to their specific gravities, and without any pressure upon one another. Oxygen gas, azotic gas, hydrogenous gas, carbonic acid gas, aqueous vapour, and probably several other elastic fluids, may exist in company under any pressure, and at any temperature, without any regard to their specific gravities, and without any pressure upon one another, while each of them, however paradoxical it may appear, occupies the whole space allotted to them all.” In conformity with this law, Gay Lussac found that the vapours of alcohol and water mix like two gases which have no action upon one another. The density of the mixed vapours agreed closely with the density calculated according to Dalton’s law. In 1836 Magnus published an important memoir on the same subject. He found that, if two liquids which do not mix with one another are introduced into a barometer tube, the tension of the mixed vapours at any temperature is equal to the sum of the tensions of the vapours of the two liquids. But when the liquids have the property of mixing with one another the behaviour of their vapours he found to be altogether different. The tension of the mixed vapours was no longer equal to the sum of the tensions of each vapour separately. This statement appears at first view to contradict the experiments of Gay Lussac, but, as Magnus himself has pointed out, the conditions under which the observations of the two eminent physicists were made were essentially different. In the experiments of Gay Lussac the mixed liquids were wholly converted into vapour, and therefore the mixed vapours formed were not in contact with any liquid, while in those of Magnus an excess of the mixed liquids was always present, and in contact with the vapour,


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