No-slip Wall Research Articles

Universal image systems for non-periodic and periodic Stokes flows above a no-slip wall

It is well-known that by placing judiciously chosen image point forces and doublets to the Stokeslet above a flat wall, the no-slip boundary condition can be conveniently imposed on the wall Blake (1971) [8]. However, to further impose periodic boundary conditions on directions parallel to the wall usually involves tedious derivations because single or double periodicity in Stokes flow may require the periodic unit to have no net force, which is not satisfied by the well-known image system. In this work we present a force-neutral image system. This neutrality allows us to represent the Stokes image system in a universal formulation for non-periodic, singly periodic and doubly periodic geometries. This formulation enables the black-box style usage of fast kernel summation methods. We demonstrate the efficiency and accuracy of this new image method with the periodic kernel independent fast multipole method in both non-periodic and periodic geometries. We then extend this new image system to other widely used Stokes fundamental solutions, including the Laplacian of the Stokeslet and the Rotne–Prager–Yamakawa tensor.

Premixed flame stability and transition to detonation in a supersonic combustor

Simulations of a supersonic, reacting, premixed flow in a channel were performed to investigate the effect of flow speed on ignition, flame stability, and transition to detonation. The configuration studied was a rectangular channel with a supersonic inflow of stoichiometric ethylene–oxygen, a transmissive outflow boundary, and no-slip adiabatic walls. The compressible reactive Navier–Stokes equations were solved by a high-order numerical algorithm on an adapting mesh for inflow Mach numbers, M∞, of 3 to 10. For M∞= 3, the fuel-oxidizer mixture does not reach a sufficient temperature for autoignition. Boundary layers that form on the top and bottom walls deflect the incoming flow, resulting in the formation of an oblique shock train. For M∞ ≥ 5, the fuel-oxidizer mixture ignites in the boundary layers and the flame front expands into the channel. The flame front becomes unstable and turbulent with time due to a Rayleigh–Taylor (RT) instability at the interface between the low-density burned gas and high-density unburned gas. Detonation is initiated in several locations at the flame front and in the unburned gas through an energy-focusing mechanism. As M∞ increases, the time scales for growth of the RT instability at the flame front and eventual detonation increase significantly. Despite the difference in time scales, the flame evolution process is qualitatively independent of M∞: ignition in the boundary layer, laminar flame expansion, growth of an RT instability at the flame front, turbulent flame expansion, and deflagration-to-detonation transition.

Hydrodynamic coupling and rotational mobilities near planar elastic membranes.

We study theoretically and numerically, the coupling and rotational hydrodynamic interactions between spherical particles near a planar elastic membrane that exhibits resistance toward shear and bending. Using a combination of the multipole expansion and Faxén's theorems, we express the frequency-dependent hydrodynamic mobility functions as a power series of the ratio of the particle radius to the distance from the membrane for the self mobilities and as a power series of the ratio of the radius to the interparticle distance for the pair mobilities. In the quasi-steady limit of zero frequency, we find that the shear- and bending-related contributions to the particle mobilities may have additive or suppressive effects depending on the membrane properties in addition to the geometric configuration of the interacting particles relative to the confining membrane. To elucidate the effect and role of the change of sign observed in the particle self mobilities and pair mobilities, we consider an example involving a torque-free doublet of counterrotating particles near an elastic membrane. We find that the induced rotation rate of the doublet around its center of mass may differ in magnitude and direction depending on the membrane shear and bending properties. Near a membrane of only energetic resistance toward shear deformation, such as that of a certain type of elastic capsules, the doublet undergoes rotation of the same sense as observed near a no-slip wall. Near a membrane of only energetic resistance toward bending, such as that of a fluid vesicle, we find a reversed sense of rotation. Our analytical predictions are supplemented and compared with fully resolved boundary integral simulations where very good agreement is obtained over the whole range of applied frequencies.

The dynamics of a healthy and infected red blood cell in flow through constricted channels: A DPD simulation.

Understanding the dynamics of red blood cell (RBC) motion under in silico conditions is central to the development of cost-effective diagnostic tools. Specifically, unraveling the relationship between the rheological properties and the nature of shape change in the RBC (healthy or infected) can be extremely useful. In case of malarial infection, RBC progressively loses its deformability and tends to occlude the microvessel. In the present study, detailed mesoscopic simulations are performed to investigate the deformation dynamics of an RBC in flow through a constricted channel. Specifically, the manifestation of viscous forces (through flow rates) on the passage and blockage characteristics of a healthy red blood cell (hRBC) vis-á-vis an infected red blood cell (iRBC) are investigated. A finite-sized dissipative particle dynamics framework is used to model plasma in conjunction with a discrete model for the RBC. Instantaneous wall boundary method was used to model no-slip wall boundary conditions with a good control on the near-wall density fluctuations and compressibility effects. To investigate the microvascular occlusion, the RBC motion through 2 types of constricted channels, viz, (1) a tapered microchannel and (2) a stenosed-type microchannel, were simulated. It was observed that the deformation of an infected cell was much less compared with a healthy cell, with an attendant increase in the passage time. Apart from the qualitative features, deformation indices were obtained. The deformation of hRBC was sudden, while the iRBC deformed slowly as it traversed through the constriction. For higher flow rates, both hRBC and iRBC were found to undergo severe deformation. Even under low flow rates, hRBC could easily traverse past the constricted channel. However, for sufficiently slow flow rates (eg, capillary flows), the microchannel was found to be completely blocked by the iRBC.

A Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows

The present paper proposes a Lagrangian criterion of unsteady flow separation for two-dimensional periodic flows based on the principle of weighted averaging zero skin-friction given by Haller (HALLER, G. Exact theory of unsteady separation for two-dimensional flows. Journal of Fluid Mechanics, 512, 257–311 (2004)). By analyzing the distribution of the finite-time Lyapunov exponent (FTLE) along the no-slip wall, it can be found that the periodic separation takes place at the point of the zero FTLE. This new criterion is verified with an analytical solution of the separation bubble and a numerical simulation of lid-driven cavity flows.

Flow-induced phase separation of active particles is controlled by boundary conditions

Active particles, including swimming microorganisms, autophoretic colloids, and droplets, are known to self-organize into ordered structures at fluid-solid boundaries. The entrainment of particles in the attractive parts of their spontaneous flows has been postulated as a possible mechanism underlying this phenomenon. Here, combining experiments, theory, and numerical simulations, we demonstrate the validity of this flow-induced ordering mechanism in a suspension of active emulsion droplets. We show that the mechanism can be controlled, with a variety of resultant ordered structures, by simply altering hydrodynamic boundary conditions. Thus, for flow in Hele-Shaw cells, metastable lines or stable traveling bands can be obtained by varying the cell height. Similarly, for flow bounded by a plane, dynamic crystallites are formed. At a no-slip wall, the crystallites are characterized by a continuous out-of-plane flux of particles that circulate and re-enter at the crystallite edges, thereby stabilizing them. At an interface where the tangential stress vanishes, the crystallites are strictly 2D, with no out-of-plane flux. We rationalize these experimental results by calculating, in each case, the slow viscous flow produced by the droplets and the long-ranged, many-body active forces and torques between them. The results of numerical simulations of motion under the action of the active forces and torques are in excellent agreement with experiments. Our work elucidates the mechanism of flow-induced phase separation in active fluids, particularly active colloidal suspensions, and demonstrates its control by boundaries, suggesting routes to geometric and topological phenomena in an active matter.

CFD modeling of filmwise steam condensation with noncondensable gas with modified boundary condition

Filmwise condensation plays an important role in many industrial applications. With the presence of noncondensable gas, the condensation process can be complicated and an appropriate modeling of the phenomena is necessary. This study takes the approach of modeling condensation with Computational Fluid Dynamics (CFD) based on species diffusion, with only the gas mixture modeled as the entire computational domain. The condensation rate is modeled as a sink term for the conservation equations. In addition, we suggest the use of free surface boundary condition, that is, a shear free boundary, as opposed to traditional approaches where the condensation is modeled to occur on a dry, no-slip wall. The free surface assumption provides better representation of the physical condensing interface without having to include both liquid and gas phases in the computational domain, which can bring great increase in computational cost with limited benefit. The free surface assumption is validated via case studies considering reasonable range of interfacial conditions, showing that the error from the free surface assumption can be quantified and is reasonably low for the considered range of conditions. Then, the developed condensation model and the free surface assumption for the condensing interface are implemented into the CFD codes and validated against a set of experimental data. The performance of the condensation model and the free surface assumption are assessed based on the prediction of the condensation heat transfer coefficient. The results show that the predictions are improved with applying the free surface boundary condition for the condensing interface compared to the results with the traditional no-slip boundary conditions.

Water Transport and Removal in PEMFC Gas Flow Channel with Various Water Droplet Locations and Channel Surface Wettability

Water transport and removal in the proton exchange membrane fuel cell (PEMFC) is critically important to fuel cell performance, stability, and durability. Water emerging locations on the membrane-electrode assembly (MEA) surface and the channel surface wettability significantly influence the water transport and removal in PEMFC. In most simulations of water transport and removal in the PEMFC flow channel, liquid water is usually introduced at the center of the MEA surface, which is fortuitous, since water droplet can emerge randomly on the MEA surface in PEMFC. In addition, the commonly used no-slip wall boundary condition greatly confines the water sliding features on hydrophobic MEA/channel surfaces, degrading the simulation accuracy. In this study, water droplet is introduced with various locations along the channel width direction on the MEA surface, and water transport and removal is investigated numerically using an improved model incorporating the sliding flow property by using the shear wall boundary condition. It is found that the water droplet can be driven to the channel sidewall by aerodynamics when the initial water location deviates from the MEA center to a certain amount, forming the water corner flow in the flow channel. The channel surface wettability on the water transport is also studied and is shown to have a significant impact on the water corner flow in the flow channel.

Swimming trajectories of a three-sphere microswimmer near a wall.

The hydrodynamic flow field generated by self-propelled active particles and swimming microorganisms is strongly altered by the presence of nearby boundaries in a viscous flow. Using a simple model three-linked sphere swimmer, we show that the swimming trajectories near a no-slip wall reveal various scenarios of motion depending on the initial orientation and the distance separating the swimmer from the wall. We find that the swimmer can either be trapped by the wall, completely escape, or perform an oscillatory gliding motion at a constant mean height above the wall. Using a far-field approximation, we find that, at leading order, the wall-induced correction has a source-dipolar or quadrupolar flow structure where the translational and angular velocities of the swimmer decay as inverse third and fourth powers with distance from the wall, respectively. The resulting equations of motion for the trajectories and the relevant order parameters fully characterize the transition between the states and allow for an accurate description of the swimming behavior near a wall. We demonstrate that the transition between the trapping and oscillatory gliding states is first order discontinuous, whereas the transition between the trapping and escaping states is continuous, characterized by non-trivial scaling exponents of the order parameters. In order to model the circular motion of flagellated bacteria near solid interfaces, we further assume that the spheres can undergo rotational motion around the swimming axis. We show that the general three-dimensional motion can be mapped onto a quasi-two-dimensional representational model by an appropriate redefinition of the order parameters governing the transition between the swimming states.

Hydrodynamic interaction of a self-propelling particle with a wall : Comparison between an active Janus particle and a squirmer model.

Using lattice Boltzmann simulations we study the hydrodynamics of an active spherical particle near a no-slip wall. We develop a computational model for an active Janus particle, by considering different and independent mobilities on the two hemispheres and compare the behaviour to a standard squirmer model. We show that the topology of the far-field hydrodynamic nature of the active Janus particle is similar to the standard squirmer model, but in the near-field the hydrodynamics differ. In order to study how the near-field effects affect the interaction between the particle and a flat wall, we compare the behaviour of a Janus swimmer and a squirmer near a no-slip surface via extensive numerical simulations. Our results show generally a good agreement between these two models, but they reveal some key differences especially with low magnitudes of the squirming parameter [Formula: see text]. Notably the affinity of the particles to be trapped at a surface is increased for the active Janus particles when compared to standard squirmers. Finally, we find that when the particle is trapped on the surface, the velocity parallel to the surface exceeds the bulk swimming speed and scales linearly with [Formula: see text].

Unsteady Stokes flow near boundaries: the point-particle approximation and the method of reflections

Problems of particle dynamics involving unsteady Stokes flows in confined geometries are typically harder to solve than their steady counterparts. Approximation techniques are often the only resort. Felderhof (see e.g. J. Phys. Chem. B, vol. 109 (45), 2005, pp. 21406–21412; J. Fluid Mech., vol. 637, 2009, pp. 285–303) has developed a point-particle approximation framework to solve such problems, especially in the context of Brownian motion. Despite excellent agreement with past experiments, this framework produces unsteady drag coefficients that depend on particle density. This is inconsistent, since the problem can be formulated mathematically without any reference to the particle’s density. We address this inconsistency in our work. Upon implementing our modifications, the framework passes consistency checks that it previously failed. Further, it is not obvious that such an approximation should work for short-time-scale motion. We investigate its validity by deriving it from a general formalism based on integral equations through a series of systematic approximations. We also compare results from the point-particle framework against a calculation performed using the method of reflections, for the specific case of a sphere near a full-slip plane boundary. We find from our analysis that the reasons for the success of the point-particle approximation are subtle and have to do with the nature of the unsteady Oseen tensor. Finally, we provide numerical predictions for Brownian motion near a full-slip and a no-slip plane wall based on the point-particle approximation as used by Felderhof, our modified point-particle approximation and the method of reflections. We show that our modifications to Felderhof’s framework would become significant for systems of metallic nanoparticles in liquids.

Brownian motion near an elastic cell membrane: A theoretical study.

Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this paper, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of nearby particles. In the steady limit, the diffusional behavior approaches that near a no-slip hard wall. The analytical predictions are validated and supplemented with boundary-integral simulations.

A Computational Analysis of Blood Flow through Portal Vein under Normal and Extrahepatic Obstructions

Portal hypertension is an alarming disease globally whereas Extrahepatic portal vein obstruction (EHPVO) is an important cause of portal hypertension among children in most of the Asian countries. The frequent occurrence of this disease is due to the formation of thrombosis in the portal vein. To acquire insights into the behaviour of hemodynamics, EHPVO case is studied by the technique of computational fluid dynamics (CFD) by considering partial block formation with different sizes inside the main portal vein. On the basis of block sizes, three cases namely normal portal vein (without block in the portal vein) case, 40% block in the portal vein case and 85% block in the portal vein case are simulated by assuming a 2D steady, laminar and fully developed flow with no-slip wall condition using AnsysTM Fluent. Our study reveals that the flow distribution between the left and right branches of the portal vein is significantly influenced by the formation of the block in the main portal vein. It is concluded that Extrahepatic portal vein obstruction leads to the possibility of Hypertrophy and Atrophy complex to the liver and could heighten the risk of liver diseases. Our numerical examination will play a great role to the Liver Specialist for understanding the flow behavior with obstructed flow path as well as the diagnosis of associated liver disease and their treatments.Journal of Bangladesh Academy of Sciences, Vol. 41, No. 2, 183-199, 2017

The common mechanism of turbulent skin-friction drag reduction with superhydrophobic longitudinal microgrooves and riblets

Turbulent skin-friction drag reduction with superhydrophobic (SH) longitudinal microgrooves and riblets is investigated by direct numerical simulation (DNS), using lattice Boltzmann methods, in channel flow. The liquid/gas interfaces in the SH longitudinal microgrooves were modelled as stationary, curved, shear-free boundaries, with the meniscus shape determined from the solution of the Young–Laplace equation. Interface protrusion angles of$\unicode[STIX]{x1D703}=0^{\circ },-30^{\circ },-60^{\circ },-90^{\circ }$were investigated. For comparison, the same geometries as those formed by the SH interfaces were also studied as riblets. Drag reductions of up to 61 % and up to 5 % were realized in DNS with SH longitudinal microgrooves and riblets, respectively, in turbulent channel flows at bulk Reynolds numbers of$Re_{b}=3600$($Re_{\unicode[STIX]{x1D70F}_{0}}\approx 222$) and$Re_{b}=7860$($Re_{\unicode[STIX]{x1D70F}_{0}}\approx 442$), with arrays of SH longitudinal microgrooves or riblets of size$14\lesssim g^{+0}\lesssim 56$and$g^{+0}/w^{+0}=7$on both walls, where$g^{+0}$and$w^{+0}$denote the widths and spacings of the microgrooves in base flow wall units, respectively. An exact analytical expression is derived which allows the net drag reduction in laminar or turbulent channel flow with any SH or no-slip wall micro-texture to be decomposed into contributions from: (i) the effective slip velocity at the wall, (ii) modifications to the normalized structure of turbulent Reynolds shear stresses due to the presence of this effective slip velocity at the wall, (iii) other modifications to the normalized structure of turbulent Reynolds shear stresses due to the presence of the wall micro-texture, (iv) modifications to the normalized structure of mean flow shear stresses due to the presence of the wall micro-texture and (v) the fraction of the flow rate through the wall micro-texture. Comparison to DNS results shows that SH longitudinal microgrooves and riblets share a common mechanism of drag reduction in which$100\,\%$of the drag reduction arises from effects (i) and (ii). The contributions from (iii)–(v) were always drag enhancing, and followed a common scaling with SH longitudinal microgrooves and riblets when expressed as a function of the square root of the microgroove cross-sectional area in wall units. Extrapolation of drag reduction data from DNS to high Reynolds number flows of practical interest is discussed. It is shown that, for a given geometry and size of the surface micro-texture in wall units, the drag reduction performance of micro-textured surfaces degrades with increasing bulk Reynolds number of the flow. Curved SH interfaces at low protrusion angle ($\unicode[STIX]{x1D703}=-30^{\circ }$) were found to enhance the drag reduction by up to 3.6 % compared to flat interfaces, while reducing the instantaneous pressure fluctuations on the SH interfaces by up to a factor of two. This suggests that the longevity of SH interfaces in turbulent flow may be improved by embedding the SH surface within the microgrooves of shallow, scalloped riblets.

Entropy Stability and the No-Slip Wall Boundary Condition

We present an entropy stable numerical scheme subject to no-slip wall boundary conditions. To enforce entropy stability only the no-penetration boundary condition and a temperature condition are needed at a wall, and this leads to an $L^2$ bound on the conservative variables. In this article, we take the next step and design a finite difference scheme that also bounds the velocity gradients. This necessitates the use of the full no-slip conditions.

Fluctuating hydrodynamic methods for fluid-structure interactions in confined channel geometries

We develop computational methods for the study of fluid-structure interactions subject to thermal fluctuations when confined within channels with slit-like geometry. The methods take into account the hydrodynamic coupling and diffusivity of microstructures when influenced by their proximity to no-slip walls. We develop stochastic numerical methods subject to no-slip boundary conditions using a staggered finite volume discretization. We introduce techniques for discretizing stochastic systems in a manner that ensures results consistent with statistical mechanics. We show how an exact fluctuation-dissipation condition can be used for this purpose to discretize the stochastic driving fields and combined with an exact projection method to enforce incompressibility. We demonstrate our computational methods by investigating how the proximity of ellipsoidal colloids to the channel wall affects their active hydrodynamic responses and passive diffusivity. We also study for a large number of interacting particles collective drift-diffusion dynamics and associated correlation functions. We expect the introduced stochastic computational methods to be broadly applicable to applications in which confinement effects play an important role in the dynamics of microstructures subject to hydrodynamic coupling and thermal fluctuations.

Focusing of active particles in a converging flow

We consider active particles swimming in a convergent fluid flow in a trapezoid nozzle with no-slip walls. We use mathematical modeling to analyze trajectories of these particles inside the nozzle. By extensive Monte Carlo simulations, we show that trajectories are strongly affected by the background fluid flow and geometry of the nozzle leading to wall accumulation and upstream motion (rheotaxis). In particular, we describe the non-trivial focusing of active rods depending on physical and geometrical parameters. It is also established that the convergent component of the background flow leads to stability of both downstream and upstream swimming at the centerline. The stability of downstream swimming enhances focusing, and the stability of upstream swimming enables rheotaxis in the bulk.

Guidance of microswimmers by wall and flow: Thigmotaxis and rheotaxis of unsteady squirmers in two and three dimensions.

The motions of an unsteady circular-disk squirmer and a spherical squirmer have been investigated in the presence of a no-slip infinite wall and a background shear flow in order to clarify the similarities and differences between two- and three-dimensional motions. Despite the similar bifurcation structure of the dynamical system, the stability of the fixed points differs due to the Hamiltonian structure of the disk squirmer. Once the unsteady oscillating surface velocity profile is considered, the disk squirmer can behave in a chaotic manner and cease to be confined in a near-wall region. In contrast, in an unsteady spherical squirmer, the dynamics is well attracted by a stable fixed point. Additional wall contact interactions lead to stable fixed points for the disk squirmer, and, in turn, the surface entrapment of the disk squirmer can be stabilized, regardless of the existence of the background flow. Finally, we consider spherical motion under a background flow. The separated time scales of the surface entrapment (thigmotaxis) and the turning toward the flow direction (rheotaxis) enable us to reduce the dynamics to two-dimensional phase space, and simple weather-vane mechanics can predict squirmer rheotaxis. The analogous structure of the phase plane with the wall contact in two and three dimensions implies that the two-dimensional disk swimmer successfully captures the nonlinear interactions, and thus two-dimensional approximation could be useful in designing microfluidic devices for the guidance of microswimmers and for clarifying the locomotions in a complex geometry.

Quantitative analysis of effects of hemodynamic stress on temporal variations of cardiac phases in models of human carotid bulbs.

In this study, we evaluated the hemodynamics of carotid artery models with carotid bulbs of various sizes using computational fluid dynamics (CFD) and the Fluent CFD software. The oscillatory shear index (OSI) and flow velocity distribution were evaluated in carotid models without a carotid bulb and with carotid bulbs of known geometry (major axis of 10, 11, 12, 13, and 14mm; carotid bifurcation angle of 50°). Furthermore, the diameters of the common carotid artery, the external carotid artery, and the internal carotid artery were defined as 7.2, 4.0, and 4.5mm, respectively. The accuracy of the CFD analysis in this study was verified using a flow phantom and measuring velocities with phase-contrast cine magnetic resonance imaging. The CFD parameters were defined as follows: rigid and no-slip walls, pulsatile flow, and 0Pa of peripheral pressure. The OSI in the carotid bulb tended to show a high value during the expansion of the carotid bulb (maximum and minimum OSI: 0.11±0.08 at d bulb: 14mm; 0.0013±0.0011 at no bulb), and the region of high OSI expanded with the expansion of the carotid bulb. The flow separated near the carotid bulb, and the flow deceleration expanded downstream as the size of the bulb increased. These findings suggest that the size of the carotid bulbs contributed to the OSI because the larger bulbs exhibited higher OSI values. The relation between the OSI and the carotid bulb size could serve as a risk indicator for atherosclerosis.

Implementation of D3Q19 Lattice Boltzmann Method with a Curved Wall Boundary Condition for Simulation of Practical Flow Problems

In this paper, implementation of an extended form of a no-slip wall boundary condition is presented for the three-dimensional (3-D) lattice Boltzmann method (LBM) for solving the incompressible fluid flows with complex geometries. The boundary condition is based on the off-lattice scheme with a polynomial interpolation which is used to reconstruct the curved or irregular wall boundary on the neighboring lattice nodes. This treatment improves the computational efficiency of the solution algorithm to handle complex geometries and provides much better accuracy comparing with the staircase approximation of bounce-back method. The efficiency and accuracy of the numerical approach presented are examined by computing the fluid flows around the geometries with curved or irregular walls. Three test cases considered herein for validating the present computations are the flow calculation around the NACA0012 wing section and through the two different porous media in various flow conditions. The study shows the present computational technique based on the implementation of the three-dimensional Lattice Boltzmann method with the employed curved wall boundary condition is robust and efficient for solving laminar flows with practical geometries and also accurate enough to predict the flow properties used for engineering designs.