Modeling non-Darcian flow and solute transport in porous media with the Caputo–Fabrizio derivative

In this study, the non-Darcian flow and solute transport in porous media are modeled with a revised Caputo derivative called the Caputo–Fabrizio fractional derivative. The fractional Swartzendruber model is proposed for the non-Darcian flow in porous media. Furthermore, the normal diffusion equation is converted into a fractional diffusion equation in order to describe the diffusive transport in porous media. The proposed Caputo–Fabrizio fractional derivative models are addressed analytically by applying the Laplace transform method. Sensitivity analyses were performed for the proposed models according to the fractional derivative order. The fractional Swartzendruber model was validated based on experimental data for water flows in soil–rock mixtures. In addition , the fractional diffusion model was illustrated by fitting experimental data obtained for fluid flows and chloride transport in porous media. Both of the proposed fractional derivative models were highly consistent with the experimental results.     

On a fully nonlinear degenerate parabolic system modeling immiscible gas–water displacement in porous media

In this paper, we are interested in the simultaneous flow of two immiscible fluid phases within a porous medium. We consider a two-phase flow model where the fluids are immiscible and there is no mass transfer between the phases. The medium is saturated by compressible/incompressible phase flows. We study the gas–water displacement without simplified assumptions on the state law of gas density. We establish an existence result for the nonlinear degenerate parabolic system based on new energy estimate on pressures.     

Predictions of the gas–liquid flow in wet electrostatic precipitators

Based on Computational Fluid Dynamics (CFD), the present paper aims to simulate several important phenomena in a wet type ESP from the liquid spray generation to gas-droplet flow in electric field. A single passage between the adjacent plates is considered for the simulation domain. Firstly, the electric field intensity and ion charge density are solved locally around a corona emitter of a barbed wire electrode, which are applied to the entire ESP using periodic conditions. Next, the Euler–Lagrange method is used to simulate the gas-droplet flow. Water droplets are tracked statistically along their trajectories, together with evaporation and particle charging. Finally, the deposition density on the plate is taken as the input for the liquid film model. The liquid film is simulated separately using the homogenous Eulerian approach in ANSYS-CFX. In the current case, since the free surface of the thin water film is difficult to resolve, a special method is devised to determine the film thickness.As parametric study, the variables considered include the nozzle pressure, initial spray spreading patterns (solid versus hollow spray) and plate wettability. The droplet emission rate and film thickness distribution are the results of interest. Main findings: electric field has strong effect on the droplet trajectories. Hollow spray is preferred to solid spray for its lower droplet emission. The liquid film uniformity is sensitive to the plate wettability.     

Chaotic analysis of pressure fluctuation signal in the gas–liquid–solid slurry column

The pressure signal of a slurry column is easily obtained by using a pressure sensor, and a chaotic analysis method is used to analyze these signals in order to indicate the flow pattern of the slurry column. The slopes of the correlation integral curve indicate the flow pattern of the slurry column in various operating conditions. The flow pattern is dispersed bubble regime when the superficial velocity is low and the correlation integral curve has two slopes. The flow pattern changes into transition regime with increase in the superficial velocity, the correlation integral curve has only one slope. In the case of the flow pattern becoming a slugging regime, there are several slopes to the correlation integral curve. So it is convenient to find out the flow pattern in the slurry column by solving the slopes of the correlation integral of the pressure signal. The maximum Lyapunov exponent represents the chaos in a slurry column with various solid holdups. The maximum Lyapunov exponent is nearly similar at different heights when the flow patterns are dispersed bubble regime and slugging regime, but the maximum Lyapunov exponent at the axial height is quite different when the flow pattern is transition regime.     

Energy criterion of nonlinear stability of a flow of the Rivlin–Ericksen fluid in porous medium

Nonlinear stability of the motionless state of the thermosolutal Rivlin–Ericksen fluid in porous medium for the case of stress-free boundaries is studied by generalized energy method. By means of introducing an energy functional we will prove a sufficient condition for unconditional nonlinear stability of the motionless state. The nonlinearly stabilizing effect of concentration on the system is proved. Furthermore, for certain range of system parameters our sufficient condition for stability is also necessary.     

Solution of double nonlinear problems in porous media by a combined finite volume–finite element algorithm

The combined finite volume–finite element scheme for a double nonlinear parabolic convection-dominated diffusion equation which models the variably saturated flow and contaminant transport problems in porous media is extended. Whereas the convection is approximated by a finite volume method (Multi-Point Flux Approximation), the diffusion is approximated by a finite element method. The scheme is fully implicit and involves a relaxation-regularized algorithm. Due to monotonicity and conservation properties of the approximated scheme and in view of the compactness theorem we show the convergence of the numerical scheme to the weak solution. Our scheme is applied for computing two dimensional examples with different degrees of complexity. The numerical results demonstrate that the proposed scheme gives good performance in convergence and accuracy.     

Mathematical simulation of gas–liquid mixture flow in a reservoir and a wellbore with allowance for the dynamical interactions in the reservoir–well system

Fluid dynamic processes related to mature oil field development are simulated by applying a numerical algorithm based on the gas–liquid mixture flow equations in a reservoir and a wellbore with allowance for the dynamical interaction in the reservoir–well system. Numerical experiments are performed in which well production characteristics are determined from wellhead parameters.     

Eigenvalue bounds for the Schur complement with a pressure convection–diffusion preconditioner in incompressible flow computations

If the stationary Navier–Stokes system or an implicit time discretization of the evolutionary Navier–Stokes system is linearized by a Picard iteration and discretized in space by a mixed finite element method, there arises a saddle point system which may be solved by a Krylov subspace method or an Uzawa type approach. For each of these resolution methods, it is necessary to precondition the Schur complement associated to the saddle point problem in question. In the work at hand, we give upper and lower bounds of the eigenvalues of this Schur complement under the assumption that it is preconditioned by a pressure convection–diffusion matrix.     

Analysis of electroosmotic flow with periodic electric and pressure fields via the lattice Poisson–Boltzmann method

This paper analyzes the electroosmotic flow fields in heterogeneous microchannels by applying the lattice Poisson–Boltzmann equation. The influences of surface potential, ionic molar concentration, channel height, and driving force fields on fluid velocity are discussed in detail. A scheme for producing vortexes in a straight channel by adjusting the heterogeneous surface potentials and phase angles of the periodic driving force fields is introduced. By distributing the heterogeneous surface potentials at particular positions, we can create vortexes near walls or in the center of the channel. The size, strength, and rotational direction of vortexes are further variable by introducing appropriate phase angles for a single driving force field or for the phase differences between combined driving force fields, such as electric/pressure fields. These obstacle-like vortexes perturb fluids and hinder flow, and thus, may be useful for enhancing micromixer performance.     

Prediction of the bed-load transport by gas–liquid stratified flows in horizontal ducts

Solid particles can be transported as a mobile granular bed, known as bed-load, by pressure-driven flows. A common case in industry is the presence of bed-load in stratified gas–liquid flows in horizontal ducts. In this case, an initially flat granular bed may be unstable, generating ripples and dunes. This three-phase flow, although complex, can be modeled under some simplifying assumptions. This paper presents a model for the estimation of some bed-load characteristics. Based on parameters easily measurable in industry, the model can predict the local bed-load flow rates and the celerity and the wavelength of instabilities appearing on the granular bed.     

CFD simulation of gas–solid flow with a cluster structure-dependent drag coefficient model in circulating fluidized beds

To model the effect of clusters on hydrodynamics of gas and particles phases in risers, the interfacial drag coefficient is taken into account in computational fluid dynamic simulations by means of a two-fluid model. The momentum and energy balances that characterize the clusters in the dense phase and dispersed particles in the dilute phase are described by the multi-scale resolution approach. The model of cluster structure-dependent (CSD) drag coefficient is proposed on the basis of the minimization of energy dissipation by heterogeneous drag (MEDHD) in the full range of Reynolds number. The model of CSD drag coefficient is then incorporated into the two-fluid model to simulate flow behavior of gas and particles in a riser. The distributions of volume fraction and velocity of particles are predicted. Simulated results are in agreement with experimental data published in the literature.     

Euler–Lagrange equations governing the flow of solids by extended slip with applications to plane torsion

The paper presents a variational principle based on a new physical law governing the rotationally continuous flow of a solid that flows by means of the recently identified mechanism of extended slip. The Euler–Lagrange equations derived from this principle are applied to the plane torsion problem. Theoretical results so obtained are compared to experimental measurements made using discs of cold-worked aluminium, and excellent agreement between experiment and theory is obtained. Interesting properties of plane torsion are revealed by this investigation. It is shown, for instance, that within the shear annulus in the disc, at each stage of its expansion, the rotation rate is independent of position. Moreover, if we consider the disc centre to be rotating relative to its edge, the rotation rate in the shear annulus is opposite to that in the rigid centre of the disc. At each stage, not only are the senses of rotation of the disc centre and the shear annulus opposite but the products of rotation rate and area for the two domains remain equal.     

Effect of a measuring instrument in the “Bose condensate” of a classical gas in a phase transition and in experiments with negative pressure

We systematically present a new approach to classical thermodynamics using asymptotic distributions from number theory that generalize the Bose-Einstein distribution. We justify the transition to the liquid state, the thermodynamics of fluids, and also the behavior of liquids in the region of negative pressures We present a comparison with experimental data.     

Global strong solutions to the viscous liquid–gas two-phase flow model with slip boundary conditions in 3D exterior domains

This paper is concerned with the viscous liquid–gas two-phase flow model in a three-dimensional exterior domain with the slip boundary conditions. We are able to prove the existence of a global strong solution when the initial total energy is suitably small. The initial masses of liquid and gas are allowed to contain a vacuum, with no extra restriction between the initial masses of liquid and gas. It should be noted here that we consider the slip boundary condition in a three dimensional (3D) exterior domain which is in sharp contrast to result of Yu (2021) where they consider the Cauchy problem.     

A Hamilton–Jacobi method to describe the evolutionary equilibria in heterogeneous environments and with non-vanishing effects of mutations

In this note, we characterize the solution to a system of elliptic integro-differential equations describing a phenotypically structured population subject to mutation, selection, and migration. Generalizing an approach based on the Hamilton–Jacobi equations, we identify the dominant terms of the solution when the mutation term is small (but nonzero). This method was initially used, for different problems arisen from evolutionary biology, to identify the asymptotic solutions, while the mutations vanish, as a sum of Dirac masses. A key point is a uniqueness property related to the weak KAM theory. This method allows us to go further than the Gaussian approximation commonly used by biologists, and is an attempt to fill the gap between the theories of adaptive dynamics and quantitative genetics.     

Y spaces and global smooth solution of fractional Navier–Stokes equations with initial value in the critical oscillation spaces

For fractional Navier–Stokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in $C({\mathbb{R}}_{+},X)$. In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces $Y^{m,\beta }$ where $Y^{m,\beta }$ is not contained in $C({\mathbb{R}}_{+},{\dot{B}}_{\infty }^{1?2\beta ,\infty })$. Consequently, for $\frac{1}{2}<\beta <1$, we establish the global well-posedness of fractional Navier–Stokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any Besov–Morrey spaces ${({\dot{B}}_{p,q}^{{\gamma }_1,{\gamma }_2}({\mathbb{R}}^n))}^n$ or any Triebel–Lizorkin–Morrey spaces ${({\dot{F}}_{p,q}^{{\gamma }_1,{\gamma }_2}({\mathbb{R}}^n))}^n$ where $1\le p,q\le \infty ,0\le {\gamma }_2\le \frac{n}{p},{\gamma }_1?{\gamma }_2=1?2\beta$. These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel–Lizorkin spaces etc.