Exponential filtration of a liquid in the presence of sources

A study is made of the plane exponential filtration of an incompressible liquid under the action of two sources (sinks). The solution is based on an S. A. Chaplygin transformation, the possibility of whose use in the investigation of nonlinear filtration was first noted in [1]. In [2–5] this transformation was used in a consideration of filtration with a limiting gradient. In the present article, another nonlinear law of resistance, an exponential law, is used to construct an exact solution. The use of S. A. Chaplygin variables makes it possible to transform the starting system of equations to a Helmholtz equation, which then reduces to a functional relation which is solvable by the Wiener-Hopf method. The results obtained point to the possibility of using the proposed method to solve other problems of plane exponential filtration, generated by sources or sinks, particularly when they are arranged symmetrically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 91–96, September–October, 1973.     

Oil emulsion separation with fluidic oscillator generated microbubbles

Surfactants stabilise oil droplets in water, forming a dispersed oil–water emulsion. Treatment of oily effluents is a serious challenge owing to the high stability and colloidal nature of the oil droplets. In many applications, microbubbles are employed for separation purposes due to their buoyancy and increased surface area to volume ratio. This property has been exploited in the water treatment industry for separation in a process known as dissolved air flotation (DAF). Though practically efficient, the process is energy intensive operating at >5 bars and consequently consuming ∼90% of the total energy required in water purification plants. In this study microbubbles were produced by fluidic oscillation via a no-moving part diverter valve to cut down the energy consumption considerably. Microbubbles are applied for the separation of emulsified oil in a process known as microflotation. The mean bubble size generated by fluidic oscillation from the 50 μm pore diffuser was ∼100 μm, otherwise coarse bubbles were produced under steady flow. The effect of surfactant concentration on oil droplet size was investigated. It was found that oil droplet size varied inversely proportional to surfactant concentration. In addition, it was found that the oil removal efficiency also depends on the surfactant concentration. The maximum oil removal efficiency by Microflotation was found to be 91% under lowest surfactant concentration tested (0.3 wt%) whilst at highest surfactant concentration used (10 wt%); lowest recovery efficiency (19.4%) was recorded.     

Integrodifferential equations for plane filtration in the presence of cracks

A system of singular integr Differential equations is derived for the plane problem of steady-state filtration in a plate cut by a system of cracks. We consider an arbitrary set of cracks, and also monoperiodic and biperiodic systems of cracks, in an infinite plane. In the case of a system of infinite parallel rectilinear cracks, the general solution is obtained in explicit form-in quadratures. As an example, we find the complex potential and the formula for the output from a borehole for a linear system of tiered, flooded plates, cut by a system of rectilinear parallel cracks.     

Dispersion of a filtration flow

In this paper we shall consider the transport of a dynamically neutral impurity in a porous medium containing random inhomogeneities. The original versions of the equations for the mean impurity concentration [1, 2] were based on the hyphothesis that the random motions obeyed the Markov principle, use being made of the diffusion equations of A. N. Kolmogorov. Later [3, 4] the method of perturbations was used to study the complete system of equations for the impurity concentration and random filtration velocity in the case of a constant, nonrandom porosity; after an averaging process this yields a generalized equation for the average concentration. In the limiting cases of small- and large-scale inhomogeneities in the permeability of the medium, the basic integrodifferential equation may be, respectively, reduced to parabolic and hyperbolic equations of the second order. In the present analysis we shall use the perturbation method to study the transport of an impurity by a flow when the filtration velocity of the latter fluctuates around inhomogeneities in the permeability field, the porosity of the medium in which the flow is taking place also constituting a random field, correlating with the field of permeability. We shall derive equations for the average concentration and should formulate the corresponding boundary-value problems for these equations; we shall also calculate the components of the dispersion tensor and shall consider the equilibrium sorption of an impurity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 65–69, July–August, 1976.The author is grateful to A. I. Shnirel'man for useful discussions.     

Plane filtration in a laminar medium in the presence of imperfect reservoirs

Exact and approximate solutions were obtained describing filtration flow in a plane region in sectors corresponding to imperfect reservoirs and suction gaps. These equations make it possible to obtain an approximate solution to the three-dimensional problem of the filtration of ground waters by solution of the two-dimensional problem; imperfect reservoirs are permitted in the filtration region.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 76–83, May–June, 1973.     

MHD Asymmetric flow in the presence of diffusion

The present work is made to study the MHD flow in the presence of diffusion, for asymmetric flow past a semi-infinite unmoving plate. We consider the flow of an incompressible, viscous and electrically conducting fluid under the influence of a transversely applied magnetic field.

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Asymmetrische MHD-Strömung in Gegenwart von Diffusion

Zusammenfassung Diese Arbeit ist ein Versuch, MHD-Strömungen in Gegenwart von Diffusion zu untersuchen. Dabei wurde für die asymmetrische Strömung hinter einer halbunendlichen festen Platte ein inkompressibles, viskoses und elektrisch leitendes Fluid angenommen. Senkrecht zur Platte wirkt ein magnetisches Feld, das Einfluß auf die Strömung nimmt.

     

The presence of slug flow in horizontal two-phase flow

One of the flow regimes occurring in horizontal two-phase flows is characterized by periodic large waves “surging” along the tube. This flow, called “slug” flow, has been frequently observed in low and high pressure gas liquid systems, but it has been noticed that slugging is absent in certain liquid-liquid two-phase systems. A method is developed giving the necessary conditions for the presence of slug flow. This method quantitatively explains the observed absence of slugging in certain liquid-liquid flows.     

Effects of inhomogeneity of flow in nonlinear nonstationary filtration

A method of numerical solution of two-dimensional nonstationary problems of the theory of elastic regime in nonlinear filtration is developed. The nonstationary processes in an element of five-point grid of wells and in the neighborhood of a well, which occur in the external flow, are investigated. The effects of anisotropy of propagation of perturbations related to the nonlinearity of the problem is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 74–78, November–December, 1977.The authors are grateful to L. A. Chudov for advice and constant attention to the work.     

Towards a theory of nonequilibrium multiphase filtration flow

A new theoretical model of joint filtration flow of immiscible incompressible fluids is presented. This model takes into account relaxation processes due to the exchange of the fluids between pores of different sizes, and these relaxation processes are driven by capillary forces. The fluids occupy connected regions in the four-dimensional space formed by three coordinates and the pore length scale. When fluid exchange between pores of given sizes is effected by way of successive flow through pores of all intermediate sizes, the fluid pressure within each region is governed by a hyperbolic equation, the role of time being played by the pore linear scale. Pressure jumps across hypersurfaces separating these regions are equal to corresponding values of capillary pressure. A supplementary condition at any such hypersurface requires the speed of its displacement in the four-dimensional space to coincide with the normal velocity components of both the adjoining fluids. As a result, a new formulation of multiphase filtration flow problems is gained with allowance made for capillary relaxation in the porous space.     

Modeling radial filtration in squeeze flow of highly concentrated suspensions

Liquid-phase migration in highly concentrated suspensions undergoing constant-force squeeze flow is modeled numerically by taking into account the time and position dependence of the rheological properties due to changes in the volume fraction of solids. This is done by coupling the equation of motion for a non-Newtonian material that behaves approximately as a Bingham plastic with a continuity equation that includes diffusive flux. The developed model was first tested with experimental data and then used to study the effect of various parameters on liquid-phase migration.     

Wavy flow of a liquid film in the presence of a cocurrent turbulent gas flow

Wavy downflow of viscous liquid films in the presence of a cocurrent turbulent gas flow is analyzed theoretically. The parameters of two-dimensional steady-state traveling waves are calculated for wide ranges of liquid Reynolds number and gas flow velocity. The hydrodynamic characteristics of the liquid flow are computed using the full Navier-Stokes equations. The wavy interface is regarded as a small perturbation, and the equations for the gas are linearized in the vicinity of the main turbulent flow. Various optimal film flow regimes are obtained for the calculated nonlinear waves branching from the plane-parallel flow. It is shown that for high velocities of the cocurrent gas flow, the calculated wave characteristics correspond to those of ripple waves observed in experiments.     

Stability of fluid flow in the presence of a compliant surface

This paper is concerned with the dynamic behaviour of a thin elastic plate in the presence of flow. The plate is excited by a time varying force applied on a line which is at right angles to the direction of flow. Causality is invoked to make the solution unique. It is found that the system responds differently for flow speeds above and below a critical value. Above this value, a temporal instability occurs and the amplitude of the motion grows with time at each point on the plate. Below this value there are travelling waves upstream of the driver, whilst downstream the behaviour is dominated by a disturbance which does not grow with time at any one position, but nevertheless grows as it is convected downstream. This type of instability is less severe than the temperal one and is of the type generally referred to as convective.     

Radial filtration during constant-force squeeze flow of soft solids

Various soft solid suspensions were squeezed at constant force between polished and roughened circular glass plates and the time-dependence of the interplate separation was measured. The filterability of suspensions was quantified by their desorptivity S obtained from measurements of capillary suction time. The squeeze flow (SF) of suspensions for which S < 2 μm s^−1/2 was largely consistent with rheological theory, which neglected radial filtration: the relative motion between the liquid and solid phases of the suspension in the radial pressure gradient. Suspensions having S > 2 μm s^−1/2 showed SF behavior that was consistent with the presence of radial filtration.     

Oil low to a lateral well in the presence of bottom water

Exact solutions are obtained for a number of two-dimensional problems of steady-state fluid flow to a lateral hole in a reservoir with a quiescent bottom fluid of higher density or with a fluid of lower density at the reservoir top __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 114–126, September–October, 2008.