No-slip Flow Research Articles

Tunable hydrodynamic characteristics in microchannels with biomimetic superhydrophobic (lotus leaf replica) walls

The present work comprehensively addresses the hydrodynamic characteristics through microchannels with lotus leaf replica (exhibiting low adhesion and superhydrophobic properties) walls. The lotus leaf replica is fabricated following an efficient, two-step, soft-molding process and is then integrated with rectangular microchannels. The inherent biomimetic, superhydrophobic surface-liquid interfacial hydrodynamics, and the consequential bulk flow characteristics, are critically analyzed by the micro-particle image velocimetry technique. It is observed that the lotus leaf replica mediated microscale hydrodynamics comprise of two distinct flow regimes even within the low Reynolds number paradigm, unlike the commonly perceived solely apparent slip-stick dominated flows over superhydrophobic surfaces. While the first flow regime is characterized by an apparent slip-stick flow culminating in an enhanced bulk throughput rate, the second flow regime exhibits a complete breakdown of the aforementioned laminar and uni-axial flow model, leading to a predominantly no-slip flow. Interestingly, the critical flow condition dictating the transition between the two hydrodynamic regimes is intrinsically dependent on the micro-confinement effect. In this regard, an energetically consistent theoretical model is also proposed to predict the alterations in the critical flow condition with varying microchannel configurations, by addressing the underlying biomimetic surface-liquid interfacial conditions. Hence, the present research endeavour provides a new design-guiding paradigm for developing multi-functional microfluidic devices involving biomimetic, superhydrophobic surfaces, by judicious exploitation of the tunable hydrodynamic characteristics in the two regimes.

Slip yield stress effects in start-up Newtonian Poiseuille flows

Analytical solutions are derived for various start-up Newtonian Poiseuille flows assuming that slip at the wall occurs when the wall shear stress exceeds a critical value, known as the slip yield stress. Two distinct regimes characterise the steady axisymmetric and planar flows, which are defined by a critical value of the pressure gradient. If the imposed pressure gradient is below this critical value, the classical no-slip, start-up solution holds. Otherwise, no-slip flow occurs only initially, for a finite time interval determined by a critical time, after which slip does occur. For the annular case, there is an additional intermediate (steady) flow regime where slip occurs only at the inner wall, and hence, there exist two critical values of the pressure gradient. If the applied pressure gradient exceeds both critical values, the velocity evolves initially with no-slip at both walls up to the first critical time, then with slip only along the inner wall up to the second critical time and finally with slip at both walls.

Numerical study of aerosol particle deposition in simple and converging–diverging micro-channels with a slip boundary condition at the wall

The design of micro-devices involving aerosol transport requires the study of the deposition of aerosols in micro-channels. In this study, the slip and no-slip boundary conditions for the gas flow regime were applied to the Navier–Stokes equations to obtain the particle deposition in simple and converging–diverging micro-channels. The equation of particle motion included inertial, viscous, Brownian, and gravity terms. It was found that the ratio of gravity to inertial effects controls the deposition of particles with diameters of 0.1–1μm, and the ratio of diffusion to inertial effects controls the deposition of particles with diameters of 0.01–0.001μm. Comparison between the no-slip and slip flow regimes showed that the deposition of 0.1- to 1-μm-diameter particles was less and the deposition of 0.01- to 0.001-μm-diameter particles was greater for the slip flow regime. There was no significant difference between slip and no-slip flow regimes for the deposition of 0.01- to 0.1-μm-diameter particles. Finally, it was shown that the stagnated gas in the corners of the converging–diverging micro-channel produced similar gas velocity profiles under the slip and no-slip flow regimes.

Numerical investigation into the effects of ordered particle packing and slip flow on the performance of chromatography

The pressure drop and the plate height of chromatography columns packed with particles in the face-centered cubic, the body-centered cubic and the simple cubic configurations are calculated by a volume averaging method model. It is found that the Kozeny-Carman equation provides a reasonable prediction of the pressure drop when particles are in the face-centered cubic configuration, but overestimates the pressure drop when particles are in the body-centered cubic and the simple cubic configurations. The face-centered cubic configuration has the advantage to provide a smaller longitudinal dispersion coefficient than the body-centered cubic, the simple cubic, and the random configurations. The pressure drop and the plate height for slip flow through particles in the face-centered cubic configuration are lower than that for no-slip flow. The values of the smallest reduced plate height of columns packed with particles in the face-centered cubic configuration for no-slip flow and slip flow are about 0.084 and 0.059, respectively. The plate height of the ordered particle packing structures is smaller and the effect of slip flow on the plate height is less remarkable than results reported in literature.

Influence of Knudsen number on fluid viscosity for analysis of divergence in fluid conveying nano-tubes

In this paper, the effects of Knudsen number (Kn) and slip boundary condition have been addressed on the viscosity of a nano-flow passing through a nano-tube. The dimensionless parameter, Kn, as a small size parameter, influences the stability behavior and critical flow velocity of a nano-tube conveying gas fluid considerably, as compared to a purely continuum and size-free formulation. Consequently, a Kn-dependent viscosity affects both directly on viscosity values and indirectly on a dimensionless parameter, velocity correction factor, VCF, defined as a ratio of no-slip boundary flow velocity to slip boundary flow velocity. The effect of viscosity on critical flow velocity is so large that for a numerical study reaches one-fourth of that velocity, ignoring viscosity effect on slip boundary condition. These variations in critical flow velocity of a nano-pipe conveying fluid may affect structural design of nano-devices remarkably specifically, targeted drug delivery systems.

Friction Factor Correlations for Compressible Gaseous Flow in a Concentric Micro Annular Tube

Compressible momentum and energy equations were solved numerically for concentric micro annular tubes with slip velocity and temperature jump wall boundary conditions. The results were expressed in the form of the product of friction factor and Reynolds number (f · Re) for a quasi-fully developed condition and for the ranges of Re < 1000 and Ma < 1. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The outer tube radius ranged from 5 to 40 µm with radius ratios of 0.2, 0.5, and 0.8. The length to hydraulic diameter ratio was more than 100. The stagnation pressure was chosen in such a way that the exit Mach number ranged from 0.1 to 1.0, and the outlet pressure was fixed at the atmospheric pressure. For the case of incompressible slip flow, f · Re is calculated as a function of radius ratio and Knudsen number. For high speed flows, the values of f · Re for compressible slip flow were higher than those for incompressible slip flow due to compressibility effects. Also, f · Re correlation for compressible slip flow was obtained from compressible no-slip flow and incompressible slip flow as a function of Mach and Knudsen numbers and radius ratio. In addition, a correlation for microchannel, microtube, and micro annular tube was obtained from the authors' previous work.

Vortex‐in‐cell method combined with a boundary element method for incompressible viscous flow analysis

SUMMARYIn this study, an immersed boundary vortex‐in‐cell (VIC) method for simulating the incompressible flow external to two‐dimensional and three‐dimensional bodies is presented. The vorticity transport equation, which is the governing equation of the VIC method, is represented in a Lagrangian form and solved by the vortex blob representation of the flow field. In the present scheme, the treatment of convection and diffusion is based on the classical fractional step algorithm. The rotational component of the velocity is obtained by solving Poisson's equation using an FFT method on a regular Cartesian grid, and the solenoidal component is determined from solving an integral equation using the panel method for the convection term, and the diffusion term is implemented by a particle strength exchange scheme. Both the no‐slip and no‐through flow conditions associated with the surface boundary condition are satisfied by diffusing vortex sheet and distributing singularities on the body, respectively. The present method is distinguished from other methods by the use of the panel method for the enforcement of the no‐through flow condition. The panel method completes making use of the immersed boundary nature inherent in the VIC method and can be also adopted for the calculation of the pressure field. The overall process is parallelized using message passing interface to manage the extensive computational load in the three‐dimensional flow simulations. Copyright © 2011 John Wiley &amp; Sons, Ltd.

On the importance of fibers' cross-sectional shape for air filters operating in the slip flow regime

In this paper, we investigate the effects of fibers' cross-sectional shape on the performance of a fibrous filter in the slip and no-slip flow regimes. The slip flow regime is expected to prevail when fiber diameter is comparable in size to the mean free path of the gas molecules (about 65 nm at normal temperatures and pressures), whereas the no-slip flow regime describes the aerodynamic condition of flow through media with large fibers. Our numerical simulations conducted for flow around single fibers with different geometries indicate that, while the collection efficiency is only weakly affected by the cross-sectional shape of nanofibers, the fiber drag (i.e., permeability of the media) can be considerably influenced by the fiber's shape. Simulating the flow field around nano- and microfibers with circular, square, trilobal, and elliptical cross-sections, it was found that the more streamlined the fiber geometry, the lower the fiber drag caused by a nanofiber relative to that generated by its micron-sized counterpart.

Fully developed laminar slip and no-slip flow in rough microtubes

The effect of surface roughness on developed laminar flow in microtubes is investigated. The tube boundary is defined by $${r=R\left[{1+\varepsilon\, {\rm sin}\left( {\lambda \theta }\right)}\right]}$$ , with R representing the reference radius and $${\varepsilon}$$ and λ the roughness parameters. The momentum equation is solved using Fourier–Galerkin–Tau method with slip at the boundary. A novel semi-analytical method is developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow that are not restricted to small values of $${\varepsilon \lambda }$$ . The analytical solution collapses onto the perturbation solution ofDuan and Muzychka (J. Fluids Eng., 130:031102, 2008) for small enough values of $${\varepsilon \lambda }$$ .

Maximum efficiency of the electro-osmotic pump

Electro-osmotic effect in a porous medium arises from the electrically charged double layer at the fluid-solid interface, whereby an externally applied electric field can give rise to fluid flow. The electro-osmotic pump (EOP) is potentially useful for a variety of engineering and biorelated applications, but its generally low efficiency is a negative factor in this regard. A study to determine the optimal efficiency of the EOP and the condition(s) under which it can be realized is therefore of scientific interest and practical importance. We present the results of a theoretical and experimental study on the maximum efficiency optimization of the electrokinetic effect in artificially fabricated porous media with controlled pore diameters. It is shown that whereas the EOP efficiency increases with decreasing channel diameter, from 4.5 to 2.5 μm for samples fabricated on oxidized silicon wafers as expected for the interfacial nature of the electro-osmotic effect, the opposite trend was observed for samples with much smaller channel diameters fabricated on anodized aluminum oxide films, with the pore surface coated with silica. These results are in agreement with the theoretical prediction, based on the competition between interfacial area and the no-slip flow boundary condition, that an optimal efficiency of ~1% is attained at a microchannel diameter that is five times the Debye length, with a zeta potential of ~100 mV.

Slip flow forced convection in a microchannel with semi-circular cross-section

This paper offers theoretical results for fully developed slip-flow forced convection through a microchannel of semicircular cross-section. Numerical results are also presented to study the developing region. Velocity slip and temperature jump boundary conditions are applied at the uniformly heated walls. The results from the two different sources are cross validated and those pertaining to the limiting case of no-slip flow are found to be in good agreement with those available in the literature.

Theoretical investigation of hydrodynamic surface mode in a lined duct with sheared flow and comparison with experiment

A spectral collocation method is used to solve the linearized Euler equations in a duct with shear flow and lined walls in order to identify a possible hydrodynamic instability observed in published experiments. This method is first checked against a reference test case in a cylindrical duct. Then a theoretical test case in a plane bi-dimensional duct with no-slip flow is considered: the Briggs–Bers stability criterion is proved to be valid and it shows that the hydrodynamic instability does correspond to a right-running amplified wave. Eigenmode analyses are then performed on the experimental configuration. An unstable hydrodynamic surface mode is found, with an axial wavenumber and velocity eigenfunctions which are in good agreement with the experimental ones. Acoustic energy calculations show that the hydrodynamic instability paradoxically carries noticeable levels of acoustic energy in the upstream direction. Finally, the influence of Mach number and frequency is investigated.

CFD Method To Couple Three-Dimensional Transport and Reaction inside Catalyst Particles to the Fixed Bed Flow Field

A new method is presented to couple the fluid flow in a fixed bed to the transport and reaction inside a catalyst particle, using computational fluid dynamics (CFD). The particle is modeled as solid, allowing no-slip surface flow boundary conditions to be used. Species transport inside the particle is represented by user-defined scalars, and the catalytic reactions are represented by user-defined functions. The new method is validated using standard cases for which exact results are known. Previous work has used a porous representation of the catalyst particle, which results in inaccurate temperature and species profiles due to an artifact of convective flux across the particle−fluid interface. This also gives incorrect values of the particle-to-fluid heat transfer coefficient, compared to standard correlations. Simulation results are presented for methane steam reforming using spherical particles in a wall segment, under tube inlet and midtube conditions, to illustrate the solid particle method.

2-D lid-driven cavity flow of nematic polymers: an unsteady sea of defects

A classical benchmark for viscous and viscoelastic fluid codes is the lid-driven cavity, a model problem which highlights effects arising from a recirculating, geometrically confined flow. Here we simulate a square 2-D cavity for nematic liquid crystalline polymers (LCPs), which adds the physics of ordered phases and distortional elasticity to earlier cavity simulations. The range of local flow types within the cavity create ideal conditions for strong orientational conflicts: nematic polymers are prone to steady alignment in extension-dominated flow, yet sustained dynamic responses (tumbling, wagging, kayaking) in shear-dominated flow. Orientational conflicts are mediated by defects, or disordered phases, whose genesis and evolution in fully confined 2-D flows are explored here for the first time. Our algorithm extends previous LCP-flow solvers by implementation of physical boundary conditions on velocity and the orientational distribution at all four walls. We impose uniform orientational anchoring at the cavity walls (parallel on top and bottom, normal on sides) to suppress corner defect anomalies, and apply the method of Shen (J. Shen, J. Comp. Phys., 1991, 95, 228–245) for smoothing of the corner flow singularities due to the standard no-slip flow condition on solid walls. The same code simulates a viscous fluid by decoupling the orientational stress from the Navier–Stokes equations. We choose a Reynolds number for which the viscous simulation develops a stationary flow structure with a central rotating eddy and three corner eddies. We then simulate the Doi–Hess–Marrucci–Greco orientation tensor model for nematic polymers coupled to the flow equations, and apply level-set detection, tracking and graphics of defect domains (X. Yang, M. G. Forest, W. Mullins and Q. Wang, J. Rheology, 2009, 53 (3), 589–615). The viscous flow structure is qualitatively preserved, albeit with weaker corner vortices; the orientation field, however, consists of a highly transient, defect-laden texture. Our diagnostics continuously detect and track defect domains through strong fluctuations in topology as defects spawn, propagate, merge, collide and annihilate ad infinitum.

Slip flow in peristaltic transport of a Carreau fluid in an asymmetric channel

In this paper, peristaltic transport of a Carreau fluid in an asymmetric channel is studied theoretically under zero Reynolds number and long-wavelength approximation for both slip and no-slip flow (Kn = 0). The problem is analyzed using a perturbation expansion in terms of the Weissenberg number as a parameter. Analytic forms for the axial velocity component and the pressure gradient are obtained to second order. The pressure rise is computed numerically and explained graphically. Moreover, the effects of the slip parameter, Weissenberg number, power-law index, and phase difference on the pressure gradient, the axial velocity, and the trapping phenomena have been discussed.

On the calculation of viscous damping of microbeam resonators in air

Theoretical aspects concerning the calculation of the air damping of microbeam resonators in the framework of continuum fluid mechanics are discussed. A closed relationship between Knudsen and Stokes numbers is derived, which indicates that the no-slip flow regime is attained in systems that operate at high Stokes numbers only, while systems that operate at low Stokes numbers invariably enter the slip flow regime. These observations are relevant to improve the modelling and simulation of microbeam resonators integrated to micro-electromechanical systems (MEMS). In addition, analytical expressions of the viscous damping coefficients for different flow regimes are discussed in relation to experimental data.

Scaling effects for flow in micro-channels: Variable property, viscous heating, velocity slip, and temperature jump

This paper reports closed form solutions, based on perturbation techniques, for fully developed, both hydrodynamically and thermally, slip-flow forced convection in both parallel plate and circular microchannels subject to isothermal wall boundary condition. Scaling effects, including variable property, viscous dissipation, velocity slip, and temperature jump are studied in detail. The results are not only applicable to gaseous flow in the slip-flow regime but also can be used for no-slip liquid flow in microchannels.

Heat Transfer Characteristics of Gaseous Flows in Micro-Channel with Negative Heat Flux

Two-dimensional compressible momentum and energy equations are solved to obtain the heat transfer characteristics of gaseous flows in micro-channels with constant heat flux for which the value is negative for no-slip flow. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian method. The computations are performed for channels with constant heat flux ranging from −104 to −102 W/m2. The channel height ranges from 10 to 100 μ m and the aspect ratio of the channel height and length is 200. The stagnation pressure is chosen such that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in micro-channels with negative heat flux are compared with those of positive heat flux cases obtained in our previous work and also those of the incompressible flow in a conventional sized channel. In the case of fast flow, temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the micro-channel is proposed. The rarefaction effect is investigated for the cases of channel height of 10 μ m with slip boundary conditions. The magnitudes of viscous dissipation term and compressibility term are also investigated. The effect of each term on heat transfer characteristics is discussed.

Analytical Modeling of Fluid Flow and Heat Transfer in Microchannel/Nanochannel Heat Sinks

Laminar forced convection in two-dimensional rectangular microchannels and nanochannels under hydrodynamically and thermally fully developed conditions is investigated analytically in the slip-flow regime. Closed-form solutions for fluid friction and Nusselt numbers are obtained by solving the continuum momentum and energy equations with the first-order velocity slip and temperature jump boundary conditions at the channel walls. An isoflux thermal boundary condition is applied on the heat sink base. The results of the present analysis are presented in terms of the channel aspect ratio, hydraulic diameter, momentum and thermal accommodation coefficients, Knudsen number, slip velocity, Reynolds number, and Prandtl number. It is found that fluid friction decreases and heat transfer increases compared with no-slip flow conditions, depending on the aspect ratios and Knudsen numbers that include the effects of the channel size or rarefaction and the fluid/wall interaction.

Slip flow forced convection in a microporous duct of rectangular cross-section

Applying a Fourier series approach, closed form solutions for fully developed velocity and temperature distribution in a porous-saturated microduct of rectangular cross-section are presented in the slip flow regime. The Brinkman flow model is applied. Invoking the temperature jump equation, the H1 thermal boundary condition is investigated. Expressions are presented for the local and average velocity and temperature profiles, the friction factor, and the slip coefficient in terms of the key parameters. The present results, which are applicable to microducts of rectangular cross-section filled with or without a porous medium, are found to be in complete agreement with those available in the literature for both no-slip and slip flow regime.