External Pressure Gradient Research Articles

Impact of Addition of a Newtonian Solvent to a Giesekus Fluid: Analytical Determination of Flow Rate in Plane Laminar Motion

In this study, the influence of the presence of a Newtonian solvent on the flow of a Giesekus fluid in a plane channel or fracture is investigated with a focus on the determination of the flow rate for an assigned external pressure gradient. The pressure field is nonlinear due to the presence of the normal transverse stress component. As expected, the flow rate per unit width Q′ is larger than for a Newtonian fluid and decreases as the solvent increases. It is strongly dependent on the viscosity ratio ε (0≤ε≤1), the dimensionless mobility parameter β (0≤β≤1) and the Deborah number De, the dimensionless driving pressure gradient. The degree of dependency is notably strong in the low range of ε. Furthermore, Q′ increases with De and tends to a constant asymptotic value for large De, subject to the limitation of laminar flow. When the mobility factor β is in the range 0.5÷1, there is a minimum value of ε to obtain an assigned value of De. The ratio UN/U between Newtonian and actual mean velocity depends only on the product βDe, as for other non-Newtonian fluids.

A LTNE approach on the study of transverse hydromagnetic on mixed convection in a channel.

Abstract This article reports the investigation of magneto-hydro-dynamic (MHD) fluid flow in a channel occupied within a porous medium. When the temperature of the porous surface and fluid surface are not equal, this is known as LTNE. In this paper, mixed convection in a vertical porous channel along with a transverse hydromagnetic effect is reported. The fluid in the channel is assumed electrically conducting and flow is due to the external pressure gradient and the buoyancy force. To describe the flow in a porous medium non-Darcy-Brinkman-Forchheimer extended (NDBF) model is considered here. The local thermal non-equilibrium (LTNE) model is used and the governing equations are solved numerically using the Chebyshev spectral collocation method (CSCM) and a significant agreement is found with the analytical solution in the special case. Extensive focus is given to the impact of heat transfer coefficient, Hartman number, and Darcy number on the fluid flow mechanism at fixed values of other parameters. The numerical results show that The fluid flow, as well as heat transfer, are reduced on decreasing media permeability via changing Darcy number. Both Nusselt numbers for solid and fluid reduce on reducing Darcy parameter. The velocity is reduced in the middle region of the channel on increasing Hartman number, while it is increasing near the walls. The effect of heat transfer coefficient and Hartman number on temperature is meager.

Comparison between shear-driven and pressure-driven oscillatory flows over ripples

Direct numerical simulations of oscillatory flow over a bed made of ripples have been performed. Two oscillatory flow forcing mechanisms have been compared: (i) a sinusoidal external pressure gradient (pressure-driven flow); and (ii) a sinusoidal velocity boundary conditions on the rippled bed (shear-driven flow). In the second case, the oscillations of the bed are such that when observed from a reference frame fixed with the bed, the free stream follows the same harmonic oscillation as in the pressure-driven case. While the outer layers have the same dynamics in the two cases, close to the bed differences are observed during the cycle, mostly because the large form drag across the ripples cannot be reproduced in the shear-driven case. A comparison against experimental data from an oscillating tray apparatus provides a relatively good agreement for the phase-averaged flow when the same forcing is considered (i.e. a shear-driven flow). The pressure-driven case has a comparable error to the shear-driven numerical results over the crest of the ripples, whereas the discrepancy is larger at the troughs. The discrepancies between the two cases are more limited for time-averaged flow quantities, such as the mean flow pattern and the time-averaged Reynolds stress distribution. This suggests that numerical or experimental shear-driven configurations may capture well the net effects of coastal transport processes (which occur in pressure-driven oscillatory flow), but care should be exercised in interpreting phase-dependent dynamics near the troughs. More work is needed to fully assess the sensitivity to the forcing mechanisms in different flow regimes.

Thermophysical dynamics of magnetohydrodynamic electroosmotic two phase mixed convective flow in vertical annulus: neuro computation

ABSTRACT The thermophysical dynamics of electro – magnetohydrodynamic mixed convective electrically conducting fluid flow in the vertical cylindrical annulus are explored with electric and magnetic fields. The flow and heat transfer properties are explicitly examined in viscous fluid and electroosmotic flow regions. The coupling between an external pressure gradient, electroosmosis, and an extended electromagnetic field can control fluid flow and heat transfer. The governing equations associated with the physical phenomenon are addressed with the Galerkin finite element method. Eloquently, the analysis revealed that, in the absence of a lateral electric field, the flow velocity decelerates as the Hartmann number increases, which in turn ultimately, causes the Nusselt number to rise. Since a lateral electric field is involved, the flow field, temperature field, and Nusselt number profiles are presented in two regions. The artificial neural network model discusses the thermal transport phenomenon in both regions. The artificial neural network models regression, performance plots, weights, and bias are presented. The research outcome can be utilized to design exquisite and efficacious electromagnetic devices, particularly within a particular range of thermal physical properties.

A theory of hydrogel mechanics that couples swelling and external flow.

Two aspects of hydrogel mechanics have been studied separately in the past. The first is the swelling and deswelling of gels in a quiescent solvent bath triggered by an environmental stimulus such as a change in temperature or pH, and the second is the solvent flow around and into a gel domain, driven by an external pressure gradient or moving boundary. The former neglects convection due to external flow, whereas the latter neglects solvent diffusion driven by a gradient in chemical potential. Motivated by engineering and biomedical applications where both aspects coexist and potentially interact with each other, this work presents a poroelasticity model that integrates these two aspects into a single framework, and demonstrates how the coupling between the two gives rise to novel physics in relatively simple one-dimensional and two-dimensional flows.

Interaction of micro-fluid structure in a pressure-driven duct flow with a nearby placed current-carrying wire: A numerical investigation

Abstract High population density in major cities has led to compact designs of residential multi-story buildings. Consequently, it is a natural choice of the architects to suggest the location of high-voltage wires close to the ducts with contaminated air. This observation results in the motivation for this study, i.e., the understanding of the complicated interaction of the Lorentz force (due to the current-carrying wire) with the micropolar flow in the vertical direction in the duct, with polluted air (containing dust particles) being modeled as a micropolar fluid, which is driven by some external pressure gradient. Therefore, this study focuses on an incompressible and electrically conducting micropolar fluid flow through a rectangular vertical duct, in the presence of a current-carrying wire placed outside the flow regime. The governing equations, after being translated into a dimensionless form, are solved numerically using a finite volume approach. The velocity, microrotation, and temperature fields thus obtained are examined. It has been noted that the strong magnetic force caused by the wire may distort the flow symmetry and slows down the flow. Furthermore, in the absence of wire, particles spinning in clockwise and counter-clockwise directions occupy the same amount of space in the duct, thus incorporating a sort of equilibrium in the duct. However, the imposed variable magnetic field adds to the spinning of particles in one part of the duct, while simultaneously suppressing it in the other region.

Effects of wall vibrations on channel flows

The effect of surface vibrations on the pressure-gradient-driven flows in channels has been studied. The analysis considered monochromatic waves and laminar flows. The effectiveness of the vibrations was gauged by determining the pressure gradient correction required to maintain the same flow rate as without vibrations. Waves propagating upstream always increase pressure losses. Flow response to waves propagating downstream is more complex and changes as a function of the flow Reynolds number. Such waves reduce losses if the Reynolds number $Re <\ \sim\!\!100$ , but these waves must be sufficiently fast to reduce pressure losses for larger Re values. In general, the supercritical waves, i.e. waves faster than the reference flow, reduce pressure losses with the magnitude of reduction increasing monotonically with the wave phase speed and wavenumber. The need for an external pressure gradient is eliminated if sufficiently short and fast waves are used. Generally, the subcritical waves, i.e. waves with velocities similar to the reference flow, increase pressure losses. This increase changes somewhat irregularly as a function of the wave phase speed and wavenumber forming local maxima and minima. These waves can reduce pressure losses only if the Reynolds number becomes large enough. It is shown that subcritical waves with very small amplitudes but matching the natural flow frequencies produce significant pressure losses.

Heat and mass transport in an electrically conducting nanofluid flow over two-dimensional geometries

Engineering equipment in medicine, chemical and power engineering, electronics, and other human endeavours use nanofluids. The ability to improve mass and heat transport because of the low concentration of nanoparticles is the primary driver behind the vast array of nanofluid applications. Thus, the famous problems of viscous, incompressible, Newtonian, and 2-D laminar flow are revisited to investigate the mass and heat transmission rates for water-based carbon nanotubes (CNTs) with variable magnetic fields and external pressure gradients. Flow cases considered with varying pressure gradients are the flows upon a flat plate, flow in a planar diverging and converging channel, flow over a wedge, and plane stagnation flows, which are investigated. The impressions of thermophoresis and Brownian motion parameters are examined through the Buongiorno model. Using the Görtler transformation, the leading boundary layer (BL) equations are converted into dimensionless forms of ordinary differential equations (ODEs). Runge-Kutta Fehlberg Method (RKF45) is operated to tackle the ensuing ODEs to find the mass, heat, and skin friction rates. It has been found that the rates of shear stress, mass, and heat transport slow down with an escalating magnetic field. Although mass transport rates are decreased, shear stress and heat transport (HT) rates escalate due to the solid volume portion of carbon nanotubes. Furthermore, the pressure gradient parameter facilitates faster heat and shear stress transmission rates.

Ultrafast active water pump driven by terahertz electric fields

A terahertz electric field (TEF) is employed to stimulate an active pump for water transportation by a bias applied in a nanochannel under no external pressure gradient. The excellent pumping ability is attributed to the resonance coupling between the TEF and water molecules. This proposed TEF-driven pump design will offer a guide in polar molecule transport through artificial or biological nanochannels, particularly in a controllable, noncontact, and large-scale process.

A capillary bundle model for the forced imbibition in the shale matrix with dual‐wettability

AbstractThe forced imbibition during hydraulic fracturing is one of the main mechanisms of oil production in shale oil reservoirs. However, the shale matrix has complex structures of nanopores and is rich in organic matters. The wettability of nanopores in organics matters is different from the nanopores in inorganic matters, and the characteristic of dual‐wettability leads to complex mechanisms of forced imbibition. This paper proposes a model for describing the imbibition in a dual‐wettability shale oil reservoir based on the capillary tube model. The external displacement pressure gradient is also considered to study the forced and spontaneous imbibition of hydraulic fracturing liquid into oil‐wet organic nanopores and water‐wet inorganic nanopores. The slip effect in organic nanopores and the boundary‐layer effect in inorganic nanopores are considered in this model. The analytical expressions for describing the location of the oil–water imbibition front in an oil‐wet organic nanopore and a water‐wet inorganic nanopore are derived, respectively. The semi‐analytical solution for predicting flow rate in a shale core with an external pressure gradient is given and demonstrated with a case study.

Viscoplastic effects of Newtonian fluids in nanopores: a molecular dynamics study

Understanding the influence of fluid–solid interactions on low-velocity non-Darcy flow in ultra-low permeability reservoirs is essential for enhanced oil recovery. The Poiseuille flows of C12H26 and argon under different pressure gradients in a nanopore are simulated using the molecular dynamics method. The results demonstrate that the confined fluids behave as elastic solids under lower pressure gradient but as viscous fluids under higher pressure gradient in the simulation. With increase of the external pressure gradient, the generated shear stress exceeds the yield stress related to the fluid-solid interaction and leads to a transition. This phenomenon indicates that the confined fluids in the nanopore exhibit apparent viscoplasticity. According to the viscoplastic hypothesis, the confined fluid can be divided into elastic and viscous layers, depending on the competition between the shear and yield stresses. The simulation results also indicate the yield stress increases near the wall. Assuming that the yield stress is inversely proportional to the distance from the wall, a non-Darcy flow model is proposed to calculate the flow rate by pressure gradient. The predictions of the model are consistent with the simulations for both C12H26 and argon, indicating the similarity of viscoplastic effects on the seepage of both fluid-nanopore systems.

A comparative analysis of multiple fractional solutions of generalized Couette flow of couple stress fluid in a channel

AbstractThis study provides the exact solutions of couple stress fluid (CSF) in a channel. The CSF is bounded by two plates in which the lower plate is moving with constant velocity Uo and the upper plate is fixed. The influence of the external pressure gradient is considered on the CSF fluid. To transform the classical CSF model, we have introduced three approaches to fractional derivatives, (a) Caputo (b) Caputo–Fabrizio (CF), and (c) Atangana–Baleanu (AB) fractional definitions. Exact solutions have been obtained using the Laplace and finite Fourier sine transforms jointly. Furthermore, the effect of different fractional derivatives is compared, and the results are shown in graphs. Moreover, parameters that affect the CSF motion are discussed in the graphs using the computational software MATHCAD. The most important outcome of the given study is the comparison of Caputo, CF, and AB fractional models with the classical CSF model. From the comparison, it can be noticed that AB fractional model discusses the dynamics of the CSF with a good memory effect as compared to Caputo and CF fractional operators. The CSF model can be reduced to Newtonian fluid as a limiting case and also investigated solutions in the absence of external pressure. Finally, Skin friction is evaluated for lower and upper plates, and the obtained results presented in tabular form.

Pore level foam generation in the presence of residual oil in porous media

CO2 sequestration into depleted oil and gas reservoirs is gaining traction as one of the enablers of the energy transition. Foaming the injected CO2 has the potential to increase the amount of trapped CO2 in the porous medium. In this paper, we study the effect of trapped, emulsified oil on the requirement for the geometrical criterion for Roof snap-off in a porous medium. We extend an existing hydrodynamic pore-level model to describe the wetting-liquid accumulation in an appropriately-sized pore in the presence of oil. The effect of oil on liquid flow is simulated by adjusting the pore shape to be asymmetrical as observed in microfluidic experiments with residual oil. We alter the boundary and initial conditions of the problem to test various scenarios. Specifically, four cases are presented. The liquid accumulation is presented when the amount of wetting liquid volume connected to the pore is altered through changing the boundary conditions (cases 1 and 2). Moreover, the effect of drier surrounding medium and/or drier pores is also tested by increasing either the capillary pressure surrounding the pore or the capillary pressure of the pore itself (cases 3 and 4). We find that the presence of residual oil affects the liquid accumulation times when there is no external liquid pressure gradient applied. Additionally, residual oil presence makes the Roof snap-off criterion for liquid accumulation stricter. That is, the size of pore constrictions that allow snap off, as gauged by the ratio of throat to body size, decreases. To augment our pore-level study, we use a statistical pore network to observe the effect of the microscopic changes observed in our pore-level model macroscopically. Our results indicate that a stricter Roof snap-off criterion leads to fewer germination sites for lamellae generation. Our pore network analysis computes the generation rate constant to be as much as four times larger in the absence of oil than in its presence. Results suggest that changes to the shape of pore constrictions by emulsified oil reduce the effectiveness of foam generation.

Control of Electrolyte Filtration through a Charged Porous Layer (Membrane) Using a Combination of Pressure Drop and an External Electric Field

A novel method is proposed for calculating the solvent flux density and electric current density in the process of flow of an electrolyte solution through a charged porous layer (membrane) under the simultaneous action of external pressure and electric potential gradients. The method is based on irreversible thermodynamics and the cell model of an ion-exchange membrane. It is shown that, with the increase in the electrolyte concentration, the total permeability of the porous structure also increases as a result of both barofiltration and electroosmotic transfer of the solvent when both external gradients are co-directional vectors. As for the current density, it also increases with the increasing electrolyte concentration owing to the growth of the streaming current and specific conductivity.

Numerical study of magnetic field interaction with fully developed flow in a vertical duct

Ducts are conduits or passages used to supply, return, or exhaust air, needed for heating, ventilation, or air conditioning in multistory gigantic building structures. Rapid growth in population (especially in industrially concentrated regions) has led to the culture of constructing skyscrapers of tens of storeys, in which vertical ducts are the natural choice for removing polluted air. Due to the compactness of the building design, high voltage current-carrying wires are usually located very close to exhaust ducts carrying polluted air. Consequently, a natural motivation is to study how the magnetic field produced by such a wire affects the flow, driven by an external pressure gradient (for example, exhaust fan, vacuum pump, etc.) in a vertical duct. Therefore, the paper is devoted to understanding the interaction of the developed (thermally and hydrodynamically) flow in a vertical square duct with the magnetic field produced by a nearby placed current-carrying wire. The flow is assumed to be laminar and is driven by a constant external pressure gradient. For the thermal boundary condition, we assume a uniform heat flux across the unit axial length whereas a fixed temperature is also assumed over the peripheral surface of the duct. As a result of the mathematical modeling of the problem, we come across a system of coupled Poisson-like equations which are solved numerically by following a finite volume approach. We have noted that a sufficiently higher Rayleigh number may cause a reverse flow while reducing and flattening the thermal distribution in the middle of the duct. In addition the magnetic field further reduces the flow velocity, particularly near the duct wall where the current-carrying wire (causing the magnetic field) is positioned.

Error estimates for pressure-driven Hele-Shaw flow

We consider Stokes flow past cylindrical obstacles in a generalized Hele-Shaw cell, i.e. a thin three-dimensional domain confined between two surfaces. The flow is assumed to be driven by an external pressure gradient, which is modeled as a normal stress condition on the lateral boundary of the cell. On the remaining part of the boundary we assume that the velocity is zero. We derive a divergence-free (volume preserving) approximation of the flow by studying its asymptotic behavior as the thickness of the domain tends to zero. The approximation is verified by error estimates for both the velocity and pressure in $H^1$- and $L^2$-norms, respectively.

Pressure-exerted steady laminar flow of an incompressible fluid along a porous parallel-walled channel with an impermeable wall

Abstract This paper is devoted to the pressure-exerted steady laminar flow of an incompressible Newtonian fluid along a parallel-walled horizontal channel with a porous upper wall and an impermeable lower wall. The fluid is sucked or blown through the porous wall, at constant and uniform velocity, orthogonally to the wall. At the same time, an external pressure gradient constant in time is applied between the two ends of the channel. The aim of this work is to determine and analyze the effects of the external pressure gradient on the flow, the suction/blowing velocity being kept constant. The two-dimensional configuration of the flow with zero-divergence velocity field allows the existence of the stream function given by a single nonlinear partial differential equation which replaces the Navier–Stokes equations and is called the vorticity equation. This latter equation is demonstrated by applying an unusual approach which uses the vector momentum equation in its general form. From the similarity-solutions assumption, it is shown that the vorticity equation leads to a two-point boundary value problem whose solutions are computed by means of a numerical shooting technique including the Newton–Raphson optimization algorithm. Physical understandings of the flow under consideration are derived from the results obtained.

Effects of an external constant pressure gradient on a steady incompressible laminar flow through a semi-porous annular pipe

Abstract In this paper, we examine a steady laminar flow for an incompressible fluid located in a semi porous annular pipe and subjected to a favorable constant pressure gradient applied between the two borders of the pipe. The inner wall is impermeable and the fluid is sucked or injected at the outer wall at constant and uniform velocity, orthogonally to the wall. The problem under study depends on three parameters: the pipe gap ratio, the dimensionless external pressure gradient, and the Reynolds number defined from the sum of the suction or injection velocity and the maximum Hagen–Poiseuille velocity. The conservation of mass induces the zero-divergence velocity field which allows replacing the steady-flow Navier–Stokes equations with a single equation satisfied by the stream function and called the vorticity equation. Assuming the similarity-solution hypothesis, the problem under consideration is reduced to a fourth-order nonlinear ordinary differential equation with two boundary conditions at each wall. The numerical shooting technique including the Runge–Kutta algorithm and the Newton–Raphson optimization method is applied to obtain the solution for the steady flow. For various values of the dimensionless external pressure gradient, the profiles of the velocity components are found and investigations on the wall shear stress for both walls are performed. The results obtained are discussed and physical understandings for the problem studied are derived.

Novel electroosmotic micromixer configuration based on ion‐selective microsphere

In this paper, a micromixer of a new configuration is presented, consisting of a spherical chamber in the center of which an ion-selective microsphere is placed. Stratified liquid is introduced through the chamber via inlet and outlet holes under an external pressure gradient and an external electric field is directed in such a way that the resulting electroosmotic flow is directed against the pressure-driven flow, resulting in mixing. The investigation is carried out by direct numerical simulation on a super-computer. Optimal values of the applied electric field are determined to yield strong mixing. Above this optimal mixing regime, a number of instabilities and bifurcations are realized, which qualitatively coincide with those occurring during electrophoresis of an ion-selective microgranule. As shown by our calculation, these instabilities do not lead to an enhanced mixing. The resulting electroconvective vortices remain confined near the surface of the microgranule, and do not sufficiently perturb the stratified fluid flow further from the granule. On the other hand, another type of instability caused by the salt concentration gradient can generate sufficiently strong oscillations to enhance mixing. However, this only occurs when the external electric field is sufficiently high that the electroosmotic flow is comparable to the pressure-driven flow. This ultimately leads to creation of reverse flows of the liquid and cessation of the device operation. Thus, it was shown that the best mixing occurs in the absence of electrokinetic instability. Based on the data obtained, it is possible to select the necessary geometric characteristics of the micromixer to achieve the optimal mixing mode for a given set of liquids, which may be ten times more effective than passive mixers at the same flow rates. A comparison with the experimental data of the other authors confirms the effectiveness of this device and its other capabilities. Furthermore, the basic device design can be operated in other modes, for example, an electrohydrodynamic pump, a streaming current generator, or even a micro-reactor, depending on the system parameters and choice of an ion-selective granule.

Instabilities during convection–diffusion of binary mixtures in a non-isothermal flow: A linear stability analysis

This paper reports a fully developed thermo–solutal mixed convection flow of the binary mixture of some important chemical species and its linear stability characteristics in a vertical channel. The flow is jointly driven by an external pressure gradient as well as simultaneous buoyancy effects of thermal and chemical species diffusion. A spectral collocation method is adopted to solve the governing equations numerically. The numerical calculation is performed for a wide range of the governing flow parameters. The main emphasis is given to examine the effect of the buoyancy ratio, which is defined as N, on basic flow characteristics and the instability mechanism for chemical species diffusion of interest in the air (Pr = 0.7) over a Schmidt number (Sc) range 0.2–2.01. A comprehensive investigation shows that when N≥−1, the heat and mass transfer rates increase monotonically on increasing the thermal buoyant force, whereas for N<−1 they are in a sinusoidal form. The velocity profiles contain the point of inflection for N>−1; however, both the point of inflection and flow separation are present when N<−1. The stability of the flow decreases on increasing the value of Sc, when the buoyant force from species diffusion acts in the same direction as the thermal buoyant force. The flow is also unstable under mild heating conditions for a relatively large magnitude of N. The disturbance kinetic energy analysis at the linear stability critical point shows that more contribution of the shear term in the production of disturbance kinetic energy effectively stabilizes the flow.