Mixed initial-boundary value problems describing motions of Maxwell fluids with linear dependence of viscosity on the pressure
12 Oct 2021-Zeitschrift für Naturforschung A (Walter de Gruyter GmbH)-Vol. 76, Iss: 12, pp 1107-1124
About: This article is published in Zeitschrift für Naturforschung A.The article was published on 2021-10-12. It has received None citations till now. The article focuses on the topics: Viscosity & Boundary value problem.
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01 Jan 1966
555 citations
TL;DR: In this paper, a preliminary account of the isothermals, the isopiestics, and the isometrics with respect to viscosity is given, and it is shown that the marine glue can be changed permanently by cautiously heating it for different lengths of time.
Abstract: 1. Hist01\"ical.-In the following paragraphs, I endeavor to give a preliminary account of what may be called the isothermals, the isopiestics, and the isometrics with respect to viscosity. Notwithstanding the great geological importancet of tbese relat.ions, nobody has as yet attempted to represent them systematical1y. 2. The Material cho.sen.-In order to obtain pronounced results for the effect of pressure on viscosity, substances mnst be selected on which temperature has a similarly obvious effect. For, in addition to the di,'ect accees to the molbcule which is beyond the reach of pressure, tempe\"atnre has the same marked iufluence on the expansion mechanism per unit of volume increment as the other agency. Hence liquids like marine glue, pitch, etc., which change continuously from solid to liquid, and in which this change takes place at an enormously rapid rate and is complete within relatively few degrees, are especially available for the present investigation. The following data refer to marine glue. Viscosity is considered as a physical qnality, and apart from such chemical considerations as are introdnced in passing from one body to another. I mnst state, however, that the marine glue can be made to change its viscosity permanently, by cautiously heating it for different lengths of time. Thus I obtained charges
532 citations
01 Jan 2007
TL;DR: In this paper, it was shown that the theory of D'Alembert's principle of equality of pressure in all directions is a necessary consequence of the absence of tangential action.
Abstract: T he equations of Fluid Motion commonly employed depend upon the fundamental hypothesis that the mutual action of two adjacent elements of the fluid is normal to the surface which separates them. From this assumption the equality of pressure in all directions is easily deduced, and then the equations of motion are formed according to D'Alembert's principle. This appears to me the most natural light in which to view the subject; for the two principles of the absence of tangential action, and of the equality of pressure in all directions ought not to be assumed as independent hypotheses, as is sometimes done, inasmuch as the latter is a necessary consequence of the former The equations of motion so formed are very complicated, but yet they admit of solution in some instances, especially in the case of small oscillations. The results of the theory agree on the whole with observation, so far as the time of oscillation is concerned. But there is a whole class of motions of which the common theory takes no cognizance whatever, namely, those which depend on the tangential action called into play by the sliding of one portion of a fluid along another, or of a fluid along the surface of a solid, or of a different fluid, that action in fact which performs the same part with fluids that friction does with solids. Thus, when a ball pendulum oscillates in an indefinitely extended fluid, the common theory gives the arc of oscillation constant.
494 citations
TL;DR: In this article, a simple constitutive equation is proposed for the isothermal shear of lubricant films in rolling/sliding contacts. But the model may be described as nonlinear Maxwell, since it comprises nonlinear viscous flow superimposed on linear elastic strain.
Abstract: A simple constitutive equation is proposed for the isothermal shear of lubricant films in rolling/sliding contacts. The model may be described as nonlinear Maxwell, since it comprises nonlinear viscous flow superimposed on linear elastic strain. The nonlinear viscous function can take any convenient form. It has been found that an Eyring 'sinh law' fits the measurements on five different fluids, although the higher viscosity fluids at high pressure are well described by the elastic/perfectly plastic equations of Prandtl-Reuss. The proposed equation covers the complete range of isothermal behaviour: linear and nonlinear viscous, linear viscoelastic, nonlinear viscoelastic and elastic/plastic under any strain history. Experiments in support of the equations are described. The nonlinear Maxwell constitutive equation is expressed in terms of three independent fluid parameters: the shear modulus $G$, the zero-rate viscosity $\eta $ and a reference stress $\tau _{0}$. The variations of these parameters with pressure and temperature, deduced from the experiments, are found to be in broad agreement with the Eyring theory of fluid flow.
476 citations