Pressure-driven Flow Research Articles

Kinetics and morphology of multi-core compound drops in pressure-driven flows

Compound drops or, double emulsions, find important applications in cosmetics and food industry, biomedical devices, petroleum industry, and many others. Most naturally occurring compound drops in these applications tend to contain multiple smaller cores inside an outer shell and their interactions are expected to have significant impact on the shape and kinetics of the entire drop. Yet, the existing literature focuses heavily on probing the mechanics of only single-core compound drops. As such, in this article, we numerically explore the dynamics and the morphology of multi-core compound drops suspended in pressure-driven background flows in narrow confinements, using the phase field formalism. To this end, we specifically consider dual and triple-core compound drops in a variety of configurations. Our findings reveal that multi-core compound drops may be inherently unstable as their kinetics is largely dominated by pinch-off and merger of the cores. Such events are, in turn, strongly influenced by several factors, such as the distribution of the cores within the shell, the starting position of the drop, core eccentricity, to underline a few. It is observed that the insight gained from the behavior of single-core drops helps us understand the kinetics of dual-core drops and likewise, those of dual-core ones are crucial toward understanding the intricacies of triple-core drops. Despite such hierarchy, the complexities in the motion and deformation of the cores and the shell in the presence of background flows increase very rapidly as the number of cores increase beyond three.

Stabilizing Pipe Flow by Flattening the Velocity Profile

It is important to control turbulence in industrial processes. Past experimental and numerical researches have shown that a turbulent puff in pipe flow can be removed or delayed by flattening the profile of the upstream velocity because a flattened velocity profile causes the point of inflection on it to collapse. The energy gradient theory has been developed to study turbulent transition, and the relevant studies have shown that turbulence arises due to the generation of singularities in the flow field. In pressure-driven flows like the pipe flow, the point of inflection on the velocity profile leads to the appearance of a singular point in the unsteady Navier–Stokes equation. In this study, the energy gradient theory is used to demonstrate why the point of inflection on the profile of velocity of pipe flow is the critical point for generating turbulence. Then, it is shown how flattening the velocity profile leads to the elimination of the point of inflection on the velocity profile of pipe flows to delay turbulent transition. It is also clarified why this technique is not effective at higher Reynolds number because the flattened velocity profile violates the criterion for flow stability relating to transition to turbulence.

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.

Turbulent mixed convection in vertical and horizontal channels

Turbulent shear flows driven by a combination of a pressure gradient and buoyancy forcing are investigated using direct numerical simulations. Specifically, we consider the set-up of a differentially heated vertical channel subject to a Poiseuille-like horizontal pressure gradient. We explore the response of the system to its three control parameters: the Grashof number $Gr$ , the Prandtl number $Pr$ , and the Reynolds number $Re$ of the pressure-driven flow. From these input parameters, the relative strength of buoyancy driving to the pressure gradient can be quantified by the Richardson number $Ri=Gr/Re^2$ . We compare the response of the mixed vertical convection configuration to that of mixed Rayleigh–Bénard convection, and find a nearly identical behaviour, including an increase in wall friction at higher $Gr$ , and a drop in the heat flux relative to natural convection for $Ri=O(1)$ . This closely matched response is despite vastly different flow structures in the systems. No large-scale organisation is visible in visualisations of mixed vertical convection – an observation that is confirmed quantitatively by spectral analysis. This analysis, combined with a statistical description of the wall heat flux, highlights how moderate shear suppresses the growth of small-scale plumes and reduces the likelihood of extreme events in the local wall heat flux. Vice versa, starting from a pure shear flow, the addition of thermal driving enhances the drag due to the emission of thermal plumes.

Enhanced three-dimensional particle detection in microcirculation experiments with defocus particle tracking and ghost red blood cells

AbstractExperimental investigations on the motion of rigid particles in microcirculation environments are still scarce owing to the three-dimensional (3D) motion of the particles and to the particle image masking due to the presence of the red blood cells (RBCs). Despite the recent progress on the 3D tracking of rigid particles in RBC flows with defocus particle tracking (DPT) methods, the problem of particle image masking remains to be solved. Here, we propose, test, and evaluate the use hemoglobin-free RBCs, also known as ghost RBCs, as a replacement for normal RBCs in experiments with rigid particles in microcirculation environments. We performed DPT measurements of a pressure-driven flow of normal and ghost RBC suspensions seeded with rigid particles at three different flow rates. We show that the quasi-transparent appearance of ghost RBCs, as a result of the lack of hemoglobin, eliminates the RBC-induced masking of the defocused particle images and allows to achieve the particle matching standards found in cell-free experiments. In fact, ghost RBC suspensions enable the tracking of the rigid particles across the entire height of the microchannel, which was not possible in normal RBC flows. On a fluid dynamic level, we show that ghost RBC suspensions provide similar conditions to normal RBCs in terms of the velocity of the rigid particles and the rigid particles exhibit similar lateral dynamics in both types of cell suspensions. In essence, the findings from this work demonstrate that ghost RBCs are a well-suited replacement for normal RBCs in experiments aiming at deciphering the motion of rigid particles in microcirculation environments. Graphical abstract

Mass and momentum balance during particle migration in the pressure-driven flow of frictional non-Brownian suspensions

The transient shear-induced particle migration of frictional non-Brownian suspensions is studied using particle-resolved simulations. The numerical method – the fictitious domain method – is well suited to heterogeneous flows thanks to a frame-invariant formulation of the subgrid (lubrication) corrections that does not involve the ambient flow (Orsi et al., J. Comput. Phys., vol. 474, 2023, 111823). The paper aims to give an accurate quantitative picture of the mass and momentum balance during the flow. The various assumptions and local constitutive laws that together form the suspension balance model (SBM) are thoroughly examined. To this purpose, the various quantities of interest are locally averaged in space and time, and their profile across the channel is extensively studied, with specific attention to the time evolution of the different contributions, either hydrodynamic in nature or from contact interactions, to the shear and normal stresses. The latter, together with the velocity gradient in the wall-normal direction and the volume fraction profile, yield the local constitutive laws, which are compared with their counterpart obtained in homogeneous shear flow. A fair agreement is observed except in a layering area at the boundaries and at the very centre of the channel. In addition, the main assumption of the SBM, i.e. the local relation between the hydrodynamic force on the particles and the particle flux, is meticulously investigated. The hydrodynamic force is found to be mainly a drag, except in the lower range of the probed volume fractions, where a non-drag contribution is observed.

Mechanism of instability in non-uniform dusty channel flow

Particles in pressure-driven channel flow are often inhomogeneously distributed. Two modes of low-Reynolds-number instability, absent in Poiseuille flow of clean fluid, are created by inhomogeneous particle loading, and their mechanism is worked out here. Two distinct classes of behaviour are seen: when the critical layer of the dominant perturbation overlaps with variations in particle concentration, the new instabilities arise, which we term overlap modes. But when the layers are distinct, only the traditional Tollmien–Schlichting mode of instability occurs. We derive the dominant critical-layer balance equations in this flow along the lines done classically for clean fluid. These reveal how concentration variations within the critical layer cause the two particle-driven instabilities. As a result of these variations, disturbance kinetic energy production is qualitatively and majorly altered. Surprisingly, the two overlap modes, although completely different in the symmetry of the eigenstructure and regime of exponential growth, show practically identical energy budgets, highlighting the relevance of variations within the critical layer. The wall layer is shown to be unimportant. We derive a minimal composite theory comprising all terms in the complete equation which are dominant somewhere in the flow, and show that it contains the essential physics. When particles are infinitely dense relative to the fluid, the volume fraction is negligible. But for finite density ratios, the volume fraction of particles causes a profile of effective viscosity. This is shown to be uniformly stabilizing in the present flow. Gravity is neglected here, and will be important to study in the future. So will the transient growth of perturbations due to non-normality of the stability operator, in a quest for the mechanism of transition to turbulence.

Heat and mass transfer analysis of s-PTT nanofluid in microchannels under combined electroosmotic and pressure-driven flows with wall slip using the homotopy perturbation method

The heat and mass transfer of the electroosmotic flow in microchannel transporting viscoelastic nanofluid is investigated considering Brownian motion of nanoparticles and slip boundary conditions. The simplified Phan-Thien-Tanner model is employed to describe the rheological behavior of fluid and the nonlinear Navier model with non-zero slip critical shear stress is considered at walls. The governing nonlinear momentum, mass, and heat transfer equations are solved using the Homotopy Perturbation Method. The study reveals that increasing the fluid elasticity, nanoparticle concentration, and size significantly enhances the flow rate, heat and mass transfer. Additionally, elasticity and Reynolds number decrease the friction factor. Reducing the double-layer thickness and increasing the Reynolds number lead to higher flow rates and fluid velocities. Notably, the findings emphasize the critical role of the slip conditions on the Sherwood and Nusselt numbers.

General synthetic iterative scheme for non-equilibrium dense gas flows

The recently-developed general synthetic iterative scheme (GSIS), which is tailored for non-equilibrium dilute gas, has been extended to find the steady-state solutions of the non-equilibrium dense gas flows based on the Shakhov-Enskog model, resolving the problems of slow convergence and requirement of ultra-fine grids in near-continuum flows that exist in the conventional iterative scheme. The key ingredient of GSIS is the tight coupling of the mesoscopic kinetic equation and the macroscopic synthetic equations that are exactly derived from the kinetic equation. On the one hand, high-order terms computed from the velocity distribution function provide the higher-order constitutive relations describing the non-equilibrium effects for the macroscopic synthetic equations. On the other hand, the macroscopic quantities obtained from the macroscopic synthetic equations are used to guide the evolution of the velocity distribution function in the kinetic equation. The efficiency and accuracy of GSIS are demonstrated in several test cases, including the shock wave passing through a cylinder and the pressure-driven dense gas flows passing through parallel plates and porous media. The effects of denseness are analyzed in a wide range of gas rarefaction.

Boundary Element Method for Viscous Flow through Out-phase Slip-patterned Microchannel under the Influence of Inclined Magnetic Field

Abstract In this paper, we investigate the impact of an inclined magnetic field of uniform intensity on viscous, incompressible pressure-driven Stokes flow through a slip-patterned, rectangular microchannel using the boundary element method based on the stream function-vorticity variables approach. The present investigation focuses only on the out-phase slip patterning of the microchannel walls. We address two scenarios of slip patterning, specifically large and fine slip patterning, which are determined by the periodicity of the patterning. We utilized the no-slip and Navier’s slip boundary conditions in an alternative manner on the walls. The Stokes equations govern the viscous flow through a microchannel. We assume a very small magnetic Reynold’s number to eliminate the equation of induced magnetic field in the present study. We analyzed the impact of considered dimensionless hydrodynamic parameters, including the Hartman number (Ha), inclination angle (θ) of the magnetic field, and the slip length (ls ) on fluid dynamics. In the case of fine slip, we observed significant variations in both velocity and pressure gradient, in contrast to large slip patterning. Fine slip patterning significantly increases the shear stress at slip regimes, while large slip periodicity significantly reduces it at no-slip regimes. The present investigation has several notable implications, such as regulation and advancement of mixing and heat transmission within microfluidic systems.

Master curves for unidirectional flows of FENE-P fluids in rectilinear and curvilinear geometries

We demonstrate that velocity profiles for steady, unidirectional shear flows of the FENE-P (Finitely-Extensible Nonlinear Elastic, with Peterlin closure) fluid, undergoing canonical rectilinear (pressure-driven flow in a rectangular channel or a circular pipe) or curvilinear (in Taylor–Couette or Dean configurations) flows, obey universal master curves that are a function only of the ratio Wi/L , for a fixed solvent to solution viscosity parameter β. Here, Wi is the Weissenberg number defined as the product of the dumbbell relaxation time and an appropriate shear rate, while L is the ratio of the maximum extension of the polymer to its equilibrium root-mean-square end-to-end distance. The data collapse and the resulting master curves for the velocity profile is a generalization of the recent demonstration of master curves for polymer viscosity and first normal stress coefficient for a FENE-P fluid under steady simple shear flow (Yamani and McKinley, 2023). For pressure-driven channel and pipe flows, we derive simple analytical expressions for the velocity profiles, in the high shear-rate regime of Wi/L≫1, that readily elucidate the role of finite extensibility of the polymer on the velocity profiles. In the Wi/L≫1 regime, for all the flows considered, the limit of zero solvent (β=0) is shown to be singular, owing to the absence of a high-shear plateau in the total solution viscosity, resulting in very different velocity profiles for β=0 and β→0.

Transient behavior and steady-state rheology of dense frictional suspensions in pressure-driven channel flow

AbstractResults from particle-resolved Direct numerical simulations are presented for dense suspensions of frictional non-colloidal spheres in viscous pressure-driven channel flow. The bulk solid volume fraction varies between $$\phi _b=0.2$$ ϕ b = 0.2 and 0.6, and the Coulomb friction coefficient is either $$\mu _c = 0$$ μ c = 0 or 0.5. The main objectives are to unravel the influence of (1) $$\phi _b$$ ϕ b and $$\mu _c$$ μ c on the flow development time and of (2) heterogeneous shear on the steady-state suspension rheology. Starting from an initially homogeneous distribution, the particles show shear-induced migration toward the core until equilibrium is reached. The flow development time decays exponentially with increasing $$\phi _b/\Phi _R$$ ϕ b / Φ R , where $$\Phi _R$$ Φ R is a friction-dependent reference bulk concentration beyond which particle contacts cause a rapid increase in the particle stress. The steady-state rheology is studied by means of the ‘viscous’ and ‘frictional’ rheology frameworks. Excluding the central core and wall regions, the data for the local relative suspension viscosity collapse onto a single curve as function of the normalized local concentration $${\bar{\phi }}/\phi _m$$ ϕ ¯ / ϕ m , where $$\phi _m$$ ϕ m is the friction-dependent maximum flowable packing fraction. The frictional rheology shows ‘subyielding’ at low viscous number $$I_v$$ I v in the core region, where the macroscopic friction coefficient $$\mu $$ μ drops below the minimal value found for homogeneous shear flows. A modified frictional rheology model is presented that captures subyielding. Finally, a model is presented for $${\bar{\phi }}/\phi _{mp}$$ ϕ ¯ / ϕ mp as function of $$I_v$$ I v , where $$\phi _{mp}$$ ϕ mp is a modified maximum flowable packing fraction. It captures both ‘overcompaction’ in the core beyond $$\phi _{m}$$ ϕ m at high $$\phi _b$$ ϕ b and maximum core concentrations below $$\phi _m$$ ϕ m at lower $$\phi _b$$ ϕ b .

Lateral migration of a deformable fluid particle in a square channel flow of viscoelastic fluid

Cross-stream migration of a deformable fluid particle is investigated computationally in a pressure-driven channel flow of a viscoelastic fluid via interface-resolved simulations. Flow equations are solved fully coupled with the Giesekus model equations using an Eulerian–Lagrangian method and extensive simulations are performed for a wide range of flow parameters to reveal the effects of particle deformability, fluid elasticity, shear thinning and fluid inertia on the particle migration dynamics. Migration rate of a deformable particle is found to be much higher than that of a solid particle under similar flow conditions mainly due to the free-slip condition on its surface. It is observed that the direction of particle migration can be altered by varying shear thinning of the ambient fluid. With a strong shear thinning, the particle migrates towards the wall while it migrates towards the channel centre in a purely elastic fluid without shear thinning. An onset of elastic flow instability is observed beyond a critical Weissenberg number, which in turn causes a path instability even for a nearly spherical particle. An inertial path instability is also observed once particle deformation exceeds a critical value. Shear thinning is found to be suppressing the path instability in a viscoelastic fluid with a high polymer concentration whereas it reverses its role and promotes path instability in a dilute polymer solution. It is found that migration of a deformable particle towards the wall induces a secondary flow with a velocity that is approximately an order of magnitude higher than the one induced by a solid particle under similar flow conditions.

DC Electric Fields Promote Biodegradation of Waterborne Naphthalene in Biofilter Systems.

Biofiltration is a simple and low-cost method for the cleanup of contaminated water. However, the reduced availability of dissolved chemicals to surface-attached degrader bacteria may limit its efficient use at certain hydraulic loadings. When a direct current (DC) electric field is applied to an immersed packed bed, it invokes electrokinetic processes, such as electroosmotic water flow (EOF). EOF is a surface-charge-induced plug-flow-shaped movement of pore fluids. It acts at a nanometer distance above surfaces and allows the change of microscale pressure-driven flow profiles and, hence, the availability of dissolved contaminants to microbial degraders. In laboratory percolation columns, we assessed the effects of a weak DC electric field (E = 0.5 V·cm-1) on the biodegradation of waterborne naphthalene (NAH) by surface-attached Pseudomonas fluorescens LP6a. To vary NAH bioavailability, we used different NAH concentrations (C0 = 2.7, 5.1, or 7.8 × 10-5 mol·L-1) and Darcy velocities typical for biofiltration ( = 0.2-1.2 × 10-4 m·s-1). In DC-free controls, we observed higher specific degradation rates (qc) at higher NAH concentrations. The qc depended on , suggesting bioavailability restrictions depending on the hydraulic residence times. DC fields consistently increased qc and resulted in linearly increasing benefits up to 55% with rising hydraulic loadings relative to controls. We explain these biodegradation benefits by EOF-altered microscale flow profiles allowing for better NAH provision to bacteria attached to the collectors even though the EOF was calculated to be 100-800 times smaller than bulk water flow. Our data suggest that electrokinetic approaches may give rise to future technical applications that allow regulating biodegradation, for example, in response to fluctuating hydraulic loadings.

Scale dependence and non-isochoric effects on the thermohydrodynamics of rarefied Poiseuille flow

The plane Poiseuille flow of a rarefied gas in a finite length channel, driven by an axial pressure gradient, is analysed numerically to probe (i) the role of ‘dilatation’ ( $\varDelta ={\boldsymbol \nabla }\boldsymbol {\cdot }{\boldsymbol u}\neq 0$ ) on its thermohydrodynamics as well as to clarify (ii) the possible equivalence with its well-studied ‘dilatation-free’ or ‘isochoric’ ( ${\rm D}\rho /{\rm D}t=0$ ) counterpart driven by a constant acceleration. Focussing on the mass flow rate ${\mathcal {M}}({Kn})$ , which is an invariant quantity for both pressure-driven and acceleration-driven Poiseuille flows, it is shown that while ${\mathcal {M}}\sim \log {{Kn}}$ at ${Kn}\gg 1$ in the acceleration-driven case, the mass flow saturates to a constant value ${\mathcal {M}}\sim {{Kn}}^0$ at ${Kn}\gg 1$ in the pressure-driven case due to the finite length ( $L_x<\infty$ ) of the channel. The latter result agrees with prior theory and recent experiments, and holds irrespective of the magnitude of the axial pressure gradient ( $G_p$ ). The pressure-dilatation cooling ( $\varPhi _p=-p\varDelta <0$ ) is shown to be responsible for the absence of the bimodal shape of the temperature profile in the pressure-driven Poiseuille flow. The dilatation-driven reduction of the shear viscosity and the odd signs of two normal stress differences ( ${\mathcal {N}}_1$ and ${\mathcal {N}}_2$ ) in the pressure-driven flow in comparison with those in its acceleration-driven counterpart are explained from the Burnett-order constitutive relations for the stress tensor. While both ${\mathcal {N}}_1$ and ${\mathcal {N}}_2$ appear at the Burnett order $O({{Kn}}^2)$ in the acceleration-driven flow, the leading term in ${\mathcal N}_1$ scales as $(\mu/p)\varDelta$ due to the non-zero dilatation in the pressure-driven Poiseuille flow which confirms that the two flows are not equivalent even at the Navier–Stokes–Fourier order $O({{Kn}})$ . The heat-flow rate ( ${{\mathcal {Q}}_q}_x=\int q_x(x,y) \,{{\rm d} y}$ ) of the tangential heat flux is found to be negative (i.e. directed against the axial pressure gradient), in contrast to its positive asymptotic value (at ${Kn}\gg 1$ ) in the acceleration-driven flow. Similar to the scale-dependence of the mass flow rate, ${{\mathcal {Q}}_q}_x({{Kn}}, L_x)$ is found to saturate to a constant value at ${Kn}\gg 1$ in finite length channels. The double-well shape of the $q_x(y)$ -profile in the near-continuum limit agrees well with predictions from a generalized Fourier law. On the whole, the dilatation-driven signatures (such as the pressure-dilatation work and the ‘normal’ shear-rate differences) are shown to be the progenitor for the observed differences between the two flows with regard to (i) the hydrodynamic fields, (ii) the rheology and (iii) the flow-induced heat transfer.

Molecular dynamics study of the thermal radiatively pressure-driven flow of two immiscible hybrid nanofluids through a curved pipe with viscous dissipation

Hybrid nanomaterials significantly enhance thermal systems through improved thermal conductivity, efficient energy storage, and customized thermomechanical properties. Due to their superior thermophysical characteristics, hybrid nanofluids are crucial in fields such as industry, biomedicine, transportation, and pharmaceuticals. Therefore, the current article scrutinizes the characteristics of heat transfer on the thermally radiative flow of two immiscible hybrid nanofluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is divided into two distinct regions: namely, (i) Region 1 (core) is filled with base fluid kerosene oil containing copper (Cu) and carbon nanotube (CNT) nanoparticles, while (ii) Region 2 (peripheral) is filled with base fluid water containing zinc oxide (ZnO) and aluminum oxide (Al2O3) nanoparticles. The complex curvilinear coordinates called toroidal coordinates are used to form a mathematical model for the present problem. The fluid in the core region is assumed to be more viscous than that of the peripheral region as such types of flows are observed in real life (viz. blood flow through arteries). Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric, and regularity conditions while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Reynolds number, viscosity ratio, and density ratio on the axial velocity and temperature is studied through 2-dimensional graphs, contour plots, and streamlines. The results show that the axial velocity of immiscible fluids flow decreases with an increase in the concentration of nanomaterials. Heat transport characteristics of nanofluid are increased by the addition of nanomaterials.

Streaming electric field, electroviscous effect, and electrokinetic liquid flows in the induced pressure-driven transport of active liquids in narrow capillaries.

In this paper, we develop a theory for studying the electrokinetic effects in a charged nanocapillary filled with active liquid. The active particles present within the active liquid are self-driven, demonstrate vortex defects, and enforce a circumferentially arranged polarization field. Under such circumstances, there is the development of an induced pressure-gradient-driven transport dictated (similar to diffusioosmotic transport) by the presence of an axial gradient in the activity (or the concentration of the active particles). This pressure-driven transport has a profile different from the standard Hagen-Poiseuille flow in a nanocapillary. Also, this induced pressure-driven flow drives electrokinetic effects, which are characterized by the generation of a streaming electric field, associated electroosmotic (EOS) transport opposing pressure-driven flow, and electroviscous effect. We quantify these effects as functions of dimensionless parameters that vary inversely as the strength of the activity-induced pressure-driven flow and salt concentrations. Overall, we anticipate that this paper will draw immense attention toward a new type of activity-induced pressure-driven flow and associated electrokinetic phenomena in charged nanoconfinements.

High-Pressure CO2 and CH4 Transport in Smooth Crystalline Silica Mesopores: A Molecular Dynamics Study.

In this study, we use molecular dynamics (MD) simulation to study pressure-driven CO2 and CH4 flows and their slippage behaviors in β-cristobalite mesopores. The result illustrates that both CO2 and CH4 have an apparent adsorption layer on pore surface. However, significant differences in gas slippage are observed: CH4 flow shows considerable slippage, while it is negligible for CO2 flow. This disparity is attributed to the collective effect of gas molecular configurations and surface structure. The linear molecular structure of CO2 allows it to align perpendicular to the surface, even penetrating into the surface. Notably, the perpendicular orientation of CO2 molecules is energetically favored near the center of the equilateral triangle formed by adjacent oxygen atoms on β-cristobalite surface. Conversely, the symmetric molecular structure of CH4, coupled with its larger size, prevents its penetration into pore surfaces. Therefore, despite smooth crystalline surfaces, CO2 topological accessible plane is much more curved than that of CH4. Consequently, CO2 displays hesitating motions undergoing rotational movements, which significantly hinders its slippage. This study highlights the collective influences of gas molecular characteristics and surface structure on gas slippage, affording important insights into gas sequestration and the development of functional materials for gas separation.

Comparisons between full molecular dynamics simulation and Zhang's multiscale scheme for nanochannel flows.

In a very small surface separation, the fluid flow is actually multiscale consisting of both the molecular scale non-continuum adsorbed layer flow and the intermediate macroscopic continuum fluid flow. Classical simulation of this flow often takes over large computational source and is not affordable owing to using molecular dynamics simulation (MDS) to model the adsorbed layer flow, if the flow field size is on the engineering size scale such as of 0.01-10mm or even bigger like occurring in micro or macro hydrodynamic bearings. The present paper uses full MDS to validate Zhang's multiscale flow model, which yields the closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate continuum fluid flow. Here, full MDS was carried out for the pressure-driven flow of methane in the nano slit pore made of silicon respectively with the channel heights 5.79nm, 11.57nm, and 17.36nm. According to the number density distribution, the flow areas were respectively discriminated as the adsorbed layer zone and the intermediate fluid zone. The values of the characteristic parameters for Zhang's multiscale scheme were extracted from full MDS and input to Zhang's multiscale flow equations respectively for calculating the flow velocity profile and the volume flow rates of the adsorbed layers and the intermediate fluid. It was found that for these three channel heights, the flow velocity profiles calculated from Zhang's model approximate those calculated from full MDS, while the total flow rates through the channel calculated from Zhang's model are close to those calculated from full MDS. The accuracy of Zhang's multiscale flow model is improved with the increase of the channel height. The recent modification of the optimized potential for liquid simulation (MOPLS) model was used to calculate the interaction force between two methane molecules. In order to calculate the interaction force between the wall atoms and the methane molecules accurately, our previous non-equilibrium multiscale MDS was used. The interaction forces between the methane molecule and the wall atom were obtained from the coupled potential function by the L-B mixing rule when the fluid molecules arrived at near wall. The methane molecule diameter was obtained from the radial distribution function by using equilibrium MDS under the same initial conditions. The local viscosities across the adsorbed layer were obtained from the local velocity profile by using the Poiseuille flow method. The motion equation of the methane molecule was solved by the leapfrog method. The temperature of the simulation system was checked by Bhadauria's method, i.e., the system temperature was rectified by the velocities in the y- and z-directions. The flow velocity distributions across the channel height and the volume flow rates through the channel were also calculated from Zhang's closed-form explicit flow equations respectively for the adsorbed layer flow and the intermediate fluid flow. The results respectively obtained from full MDS and Zhang's multiscale flow equations were then compared.

Rheological analysis of pressure-driven Jeffrey fluid flow between corrugated porous curved walls with slip constraints

Pressure-driven movement is a fundamental concept with numerous applications in various industries, scientific disciplines, and fields of engineering. Its proper execution is vital for promoting revolutionary innovations and providing solutions in numerous sectors. Therefore, this article scrutinizes the pressure-driven flow of a magnetized Jeffrey fluid between two curved corrugated walls. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity and temperature taking the corrugation amplitude as the perturbation parameter. Furthermore, the volumetric flow rate, skin friction coefficient, and local Nusselt numbers are precisely calculated numerically for a variety of parameters, with the results presented comprehensively in tabular form. The impact of dissimilar parameters, such as the curvature parameter, wave number, magnetic parameter, Darcy number, thermal radiation, heat source/sink parameter, Jeffery fluid parameter, and amplitude parameter, on the flow fields is analyzed through graphical and tabular forms and discussed in detail. The results show that the velocity profile increases due to the curvature parameter and the Jeffrey fluid parameter. However, it decreases due to the magnetic parameter. The temperature distribution rises with the thermal slip and heat source/sink parameters. Meanwhile, it declined for the radiation parameter and the curvature parameter. The model can be used to simulate blood flow in arteries with varying geometries and magnetic fields, aiding in the study of cardiovascular diseases and the design of medical devices such as stents.