Viscous fingering in a yield stress fluid

A new Monte Carlo method for calculating ground-state properties of liquid 4He is described. It is shown that Bose-Einstein condensation (BEC) implies delocalization of the wave function. It is shown that there is no general connection between the static structure factor and BEC. It is suggested that the observed connection in liquid 4He is due to the creation of spaces in the liquid structure, which are required so that the wave function can delocalize, in the presence of the hard-core interactions. It is shown that this suggestion is quantitatively consistent with observations on liquid 4He.     

The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model

The stability of a couple stress fluid saturated horizontal porous layer heated from below and cooled from above when the fluid and solid phases are not in local thermal equilibrium is investigated. The Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the solid and fluid phases separately. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of thermal non-equilibrium on the onset of convection is discussed. It is shown that the results of the thermal non-equilibrium Darcy model for the Newtonian fluid case can be recovered in the limit as couple stress parameter C→0. We also present asymptotic analysis for both small and large values of the inter phase heat transfer coefficient H. We found an excellent agreement between the exact solutions and asymptotic solutions when H is very small.     

Mechanical stress tensor for a fluid in a magnetostatic field

Summary Two constraints on the form of the mechanical stress tensor for an uncharged and linear dielectric fluid at rest in a magnetostatic field are determined. Moreover, it is shown that the stress tensor proposed by Helmholtz, that proposed by Einstein-Laub and that proposed by Liu-Müller are unacceptable as mechanical stress tensors for a dielectric fluid in the conditions stated above.     

Maxwell stress in fluid mixtures

We examine the structure of Maxwell stress in binary fluid mixtures under an external electric field and discuss its consequence. In particular, we show that, in immiscible blends, it is intimately related to the statistics of domain structure. This leads to a compact formula, which may be useful in the investigation of electrorheological effects in such systems. The stress tensor calculated in a phase separated fluid under a steady electric field is in a good agreement with recent experiments.     

Entropy of a two-component fluid in a square-well model

An analytical expression valid for two approximations, notably, the random phase approximation (RPA) and the mean spherical approximation (MSA), is derived for entropy of a two-component system with the pair potential of a square well (SW). This expression is applied to calculate the excess entropy of mixing of the Na-K and Na-Cs equiatomic compositions. It is shown that the use of the SW model leads to better results than the application of the hard-sphere model. The MSA gives better convergence with the experiment compared with the RPA.     

Mathematical model of a fluid flowmeter

A mathematical model of operation of a fluid (jet) device measuring the liquid or gas flow rate is suggested. The model takes into account the effect of deep negative feedback produced by connecting the control channels of the bistable jet element.     

A dynamic deformation model of an elastoplastic porous medium

A closed system of equations is obtained for dynamic deformation of an elastoplastic Prandtl-Reiss porous medium. The heterogeneous approach makes it possible to describe the properties of such media in a wide range of loading rates within the theory of plastic flow with the kinematic simplification. The hydrodynamic deformation theory of porous media [1, 2] has been first correctly generalized to the case of including the deviator components of the stress tensor of the medium. The well-known functions of the model are determined from analyzing the fundamental deformations of the corresponding spherical cells.Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–53, July, 1992.     

Internal motion of a small element of fluid in an inviscid flow

We look at the internal motion of a small element of fluid in inviscid and incompressible flows by neglecting the actions of the other elements which constitutes the whole fluid. This free motion of the elements leads, in a finite time, to the divergence of the velocity field in the element and to its flattening in a plane.     

Spinor model of a perfect fluid

Different characteristics of matter influencing the evolution of the uUniverse haves been simulated by means of a nonlinear spinor field. We have considered two cases where the spinor field nonlinearity occurs either as a result of self-action or due to the interaction with a scalar field.     

Stochastic model of a one-dimensional fluid

A one-dimensional point process with correlations constructed via a geometrical rule is shown to behave like a fluid at equilibrium. The equation of state is calculated and the “inverse problem” of finding an interaction potential underlying the system is considered. The effective potential is found to be dependent on macroscopic parameters via a dependence on the density of the system.     

Collective modes in a one-dimensional nonuniform fluid model

A one-dimensional fluid with short-range repulsive interaction and one period of cosinusoidal attraction in a periodic container is transformed to a two-mode format. The system has both high-temperature single-phase regions and lowtemperature two-phase regions with a very broad spatial interface that can be stabilized by a weak external field. The case of vanishing external field brings out properties of the mode amplitude dependence which one expects to extend to more complex systems.     

Evaporation of an emulsion trapped in a yield stress fluid

The present work deals with emulsions of volatile alkanes in an aqueous clay suspension, Laponite, which forms a yield stress fluid. For a large enough yield stress (i.e. Laponite concentration), the oil droplets are prevented from creaming and the emulsions are thus mechanically stabilized. We have studied the evaporation kinetics of the oil phase of those emulsions in contact with the atmosphere. We show that the evaporation process is characterized by the formation of a sharp front separating the emulsion from a droplet-free Laponite phase, and that the displacement of the front vs. time follows a diffusion law. Experimental data are confronted to a diffusion-controlled model, in the case where the limiting step is the diffusion of the dissolved oil through the aqueous phase. The nature of the alkane, as well as its volume fraction in the emulsion, has been varied. Quantitative agreement with the model is achieved without any adjustable parameter and we describe the mechanism leading to the formation of a front.     

Generalized model of a fluid with spin

A generalized variational theory of a classical ideal fluid with spin is developed. Compared with the Weyssenhoff-Raabe model, the new theory takes into account interaction of the spin of the elements of the fluid with one another and with external fields.Translated from Izvestiya Vysshikh Uchebnykh, Zavedenii, Fizika, No. 2, pp. 98–101, February, 1991.     

Mathematical model of elastoplastic deformation of a mesovolume of material with a finite number of slip systems

Institute of Physics of Strength and Materials Science, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 26–57, November, 1995.     

Internal stress and heterogeneous dislocation structure in creep

The present work deals with the problem of microstructural interpretation of internal stress measured in high-temperature creep by the strain-transient dip-test technique. The development of microstructure in the course of creep is considered a transition from uniformly distributed dislocations to a well-developed substructure. The substructure is supposed to have a composite character that consists of cell or subgrain boundaries with few dislocations in cell or subgrain interiors. Model equations for the relation of internal stress to the parameters of the dislocation structure are discussed and examined with reference to experimental data. The evolution of internal stress in creep, evaluated using different formulae, is compared with the evolution of macroscopically measured internal stress. The use of applied-stress dependences of microstructure parameters permits quite realistic estimates of the values of internal stress in steady-state creep.     

Internal waves in a compressible two-layer model atmosphere: Hamiltonian description

We consider slow, compared to the speed of sound, motions of an ideal compressible fluid (gas) in a gravitational field in the presence of two isentropic layers with a small specific-entropy difference between them. Assuming the flow to be potential in each of the layers (v _{1, 2} = ▿ϕ_{1, 2}) and neglecting the acoustic degrees of freedom (div($ \bar \rho $ \bar \rho (z)▿ϕ_{1, 2}) ≈ 0, where $ \bar \rho $ \bar \rho (z) is the average equilibrium density), we derive the equations of motion for the boundary in terms of the shape of the surface z = η(x, y, t) itself and the difference between the boundary values of the two velocity field potentials: ψ(x, y, t) = ψ₁ − ψ₂. We prove the Hamilto nian structure of the derived equations specified by a Lagrangian of the form ℒ = ∫$ \bar \rho $ \bar \rho (η)η _t ψdxdy − ℋ{η, ψ}. The system under consideration is the simplest theoretical model for studying internal waves in a sharply stratified atmosphere in which the decrease in equilibrium gas density due to gas compressibility with increasing height is essentially taken into account. For plane flows, we make a generalization to the case where each of the layers has its own constant potential vorticity. We investigate a system with a model dependence $ \bar \rho $ \bar \rho (z) ∝ e ^−2αz with which the Hamiltonian ℋ{η, ψ} can be represented explicitly. We consider a long-wavelength dynamic regime with dispersion corrections and derive an approximate nonlinear equation of the form u _t + auu _x − b[−$ \hat \partial _x^2 $ \hat \partial _x^2 + α²]^1/2 u _x = 0 (Smith’s equation) for the slow evolution of a traveling wave.