Immiscible Newtonian Fluids Research Articles

Displacement of a Newtonian fluid by a non-Newtonian fluid in a porous medium

This paper presents an analytical Buckley-Leverett-type solution for one-dimensibnal immiscible displacement of a Newtonian fluid by a non-Newtonian fluid in porous media. The non-Newtonian fluid viscosity is assumed to be a function of the flow potential gradient and the non-Newtonian phase saturation. To apply this method to field problems a practical procedure has been developed which is based on the analytical solution and is similar to the graphic technique of Welge. Our solution can be regarded as an extension of the Buckley-Leverett method to Non-Newtonian fluids. The analytical result reveals how the saturation profile and the displacement efficiency are controlled not only by the relative permeabilities, as in the Buckley-Leverett solution, but also by the inherent complexities of the non-Newtonian fluid. Two examples of the application of the solution are given. One application is the verification of a numerical model, which has been developed for simulation of flow of immiscible non-Newtonian and Newtonian fluids in porous media. Excellent agreement between the numerical and analytical results has been obtained using a power-law non-Newtonian fluid. Another application is to examine the effects of non-Newtonian behavior on immiscible displacement of a Newtonian fluid by a power-law non-Newtonian fluid.

Analysis of superposed fluids by the finite element method: Linear stability and flow development

AbstractA Galerkin finite element method is described for studying the stability of two superposed immiscible Newtonian fluids in plane Poiseuille flow. The formulation results in an algebraic eigenvalue problem of the form Aλ2 + Bλ + C = 0 which, after transforming to a standard generalized eigenvalue problem, is solved by the QR algorithm. The numerical results are in good agreement with previous asymptotic results. Additional results show that the finite element method is ideally suited for studying linear stability of superposed fluids when parameters characterizing the flow fall outside the range amenable to perturbation methods. The applicability of the finite element method to similar eigenvalue problems is demonstrated by analysing the steady‐state spatial development of two superposed fluids in a channel.

Effect of geometry on advancing contact angles in fine capillaries

Experiments performed in fine capillaries (radius between 15 and 50 μm) show that the laminar flow of two immiscible newtonian fluids is well described by the Washburn equation. The apparent contact angle is nearly a constant in drainage, and is an increasing function of the capillary number in imbibition; this function depends on the radius of the capillary tube. The apparent contact angle decreases as the radius decreases. A simple model of surface heterogeneity provides a semiquantitative interpretation of this phenomenon.

ONE- AND TWO-PHASE FLOW IN NETWORK MODELS OF POROUS MEDIA

Abstract We discuss the low Reynolds number flow of one or two immiscible Newtonian fluids in network models of microscopically random porous media. For the case of a single fluid, we reduce the flow problem to an analog random electrical resistor problem and use an 'effective medium theory' to express the permeability of such networks in terms of the pore space geometry. For the flow of two fluids we use the Washburn approximation to incorporate capillary pressure differences, and show that this problem may also be formulated as a random electrical network. In this case, the capillary menisci correspond to moving batteries, and we follow the motion of the fluid-fluid interface (the ensemble of analog batteries) by a time-step procedure. We study the time evolution of the interface and the dynamics of blobs of one fluid contained in the other, as a function of the network geometry.’

Stability of low-tension interfaces and propagation of longitudinal waves: Role of the electrical double layers

A linear hydrodynamic analysis isdeveoped in order to study the mechanical stability and the surface wave properties of a charged interface between two immiscible Newtonian fluids. The Boltzmann ionic distribution is instantaneously restored in the diffuse layers and the adsorption—desorption steps are assumed to be the determinant process for the mass transport between bulk and interface. Surface tension gradients and longitudinal electrical stresses are considered. The surface potential may be higher than the value corresponding to the considered thermal energy (⋍25 mV at 300°K). The negative electrical contribution to the total interfacial tension is responsible for the onset of surface motion while the influence of the viscosity on low-tension interfaces has a stabilizing effect. Finally the role of the surface charge and of the adsorption—desorption process on the dynamic surface elasticity is discussed.

The Newtonian Two‐Fluid Model and Stationary Flow in Cylindrical Tubes of Varying Radius

AbstractThe stationary and laminar flow of two immiscible Newtonian fluids with equal density and different viscosities in cylindrical tubes with varying radius is considered. The expressions of the wall shearing stress and the flow resistance are calculated. The results are applied to flow through locally constricted tubes, for example to the flow of blood in blood vessel with stenosis.

Hydrodynamic and chemical stability of fluid—fluid reacting interfaces: I. General theory for aperiodic regimes

Under nonequilibrium conditions, the coupling between surface chemical reactions and hydrodynamics can induce the onset of convection at an interface between two immiscible Newtonian fluids. A linear analysis of interfacial stability is performed for any number of fluctuating species. The uniform reference steady state is at rest. A nonequilibrium surface elasticity coefficient is defined in terms of the surface relaxation processes. The study is restricted to aperiodic regimes. It is qualitatively and quantitatively shown that unstable and marginal aperiodic regimes can occur only for negative values of the surface elasticity. The instability is due to the self-amplification of the fluctuations of the surface tension. The chemical kinetic conditions necessary for the occurrence of this phenomenon are discussed. Intrinsically (i.e., without convection) unstable—aperiodic regimes with respect to time—surface chemical reactions always induce nonoscillatory unstable mechanochemical regimes, for the same values of the chemical parameters, when these processes are coupled with hydrodynamics. The chemical positive feedback which is responsible for the intrinsic chemical instability is then the fundamental destabilizing factor for the interfacial instability. In the absence of feedback loops in the chemical scheme, unstable mechanochemical regimes are also possible owing to the competition between interfacial chemical and convective processes. The qualitative behavior of the solutions of the dispersion equation is discussed, as well as the roles of the viscosities in the bulk phases and in the surface. New and general stability conditions are obtained.