Laminar Shear Flow Research Articles

A nonlinear PSE method for two-fluid shear flows with complex interfacial topology

A nonlinear stability method is developed for laminar two-fluid shear flows which undergo changes in the interface topology. The method is based on the nonlinear parabolized stability equations (PSE) and incorporates a scalar-based interface capturing (IC) scheme in order to track complex deformations of the fluid interface. In doing so, the formulation retains the flexibility and physical insight of instability-wave based methods, while providing hydrodynamic modeling capabilities similar to direct numerical calculations: the new formulation, referred to as the IC-PSE, can capture the nonlinear physical mechanisms responsible for generating large-scale, two-fluid structures, without incurring heavy computational costs. This approach is valid for spatially developing, laminar two-fluid shear flows which are convectively unstable, and can naturally account for the growth of finite amplitude interfacial waves, along with changes to the interfacial topology. We demonstrate the accuracy of the IC-PSE against direct Navier–Stokes calculations for two-fluid mixing layers with density and viscosity stratification. The comparisons show that the IC-PSE can predict the dynamics of the instability waves and capture the formation of Kelvin–Helmholtz vortex rolls and large scale liquid structures, at an order of magnitude less computational cost than direct calculations. The role of surface tension in the IC-PSE formulation is shown to be valid for flows in which Re/We ≲ 1, and the method accurately predicts the formation and non-linear evolution of flow structures in this limit. This is demonstrated for spatially developing mixing layers which lead to vortex roll-up and ligaments, prior to droplet formation. The pinch-off process itself is a high surface tension phenomenon and in not considered herein. The method also accurately captures the effect of interfacial waves on the mean flow, and the topology changes during the non-linear evolution of the two-fluid structures.

Evaluation of steerable filter for detection of fibers in flowing suspensions

Steerable filters are concluded to be useful in order to determine the orientation of fibers captured in digital images. The fiber orientation is a key variable in the study of flowing fiber suspensions. Here, digital image analysis based on a filter within the class of steerable filters is evaluated for suitability of finding the position and orientation of fibers suspended in flowing suspensions. In sharp images with small noise levels, the steerable filter succeeds in determining the orientation of artificially generated fibers with well-defined angles. The influence of reduced image quality on the orientation has been quantified. The effect of unsharpness and noise is studied and the results show that the error in orientation is less than 1° for moderate levels. Images from two flow cases, one laminar shear flow and one turbulent, are also analyzed. The fiber orientation distribution is determined in the flow-vorticity plane. For the laminar case a comparison is made to a robust, but computationally more expensive, method involving convolutions with an oriented elliptic filter. A good agreement is found when comparing the resulting fiber orientation distributions obtained with the two methods. For the turbulent case, it is demonstrated that correct results are obtained and that the method can handle overlapping fibers.

Surface collision theory for suspension-based cleaning of particle-contaminated solid substrates

To quantify removal kinetics of contaminant particles on solid surfaces, we study collisions between nonspherical particles when one particle is suspended in laminar shear flow while the second is adhered to a solid surface. Based on kinetic theory of rigid nonspherical particles, we outline a theoretical framework for our previously developed binary-collision contaminant-removal model. We show that a distribution of adhered contaminant particles over orientation, size, and shape results in multiexponential decay of surface concentration of particles with time, in agreement with experimental findings [Andreev et al., J. Electrochem. Soc. 158, H55 (2011)]. Theory predicts a linear increase of removal rate constant with shear rate and with suspended solids concentration near the substrate surface, also in agreement with experiment [Andreev et al., J. Electrochem. Soc. 158, H55 (2011); Ind. Eng. Chem. Res. 49, 12461 (2010)]. To reveal the effect of geometry and size of colliding entrained particles on removal rates, an approximate singlet distribution function is derived for particles in flow at the level of the Smoluchowski theory for orthocoagulation. Two shapes of flow-suspended particles are considered: spheres and cuboids with high aspect ratio, while contaminant particles on the surface are small and spherical. Removal kinetic rate constants scale with contaminant particle size, aA, as aA3/2 for spheres and as aA for cuboids. Thus, rectangular platelet particles are effective for removal of small contaminant particles, confirming experimental observation [Andreev et al., J. Electrochem. Soc. 158, H55 (2011)]. The influence of platelet aspect ratio on removal rates is analyzed. Due to interplay between solids velocity and collision cross section, small aspect ratios improve cleaning efficiency when the size ratio of the entrained to contaminant particles is large.

Shear flow-induced optical inhomogeneity of blood assessed in vivo and in vitro by spectral domain optical coherence tomography in the 1.3 μm wavelength range

The optical inhomogeneity of flowing blood, which appears as a waisted double fan-shaped intensity pattern inside vessels in cross-sectional optical coherence tomography (OCT) images, was investigated for the first time. High resolution spectral domain OCT in the 1.3 μm wavelength region is used to assess this inhomogeneous intravascular backscattering of light in an in vivo mouse model and flow phantom measurements. Based on a predicted alignment of the red blood cells toward laminar shear flow, an angular modulation of the corresponding backscattering cross-section inside the vessels is assumed. In combination with the signal attenuation in depth by absorption and scattering, a simple model of the intravascular intensity modulation is derived. The suitability of the model is successfully demonstrated in the in vivo experiments and confirmed by the in vitro measurements. The observed effect appears in flowing blood only and shows a strong dependency on the shear rate. In conclusion, the shear-induced red blood cell alignment in conjunction with the vessel geometry is responsible for the observed intensity distribution. This inherent effect of blood imaging has to be considered in attenuation measurements performed with OCT. Furthermore, the analysis of the intravascular intensity pattern might be useful to evaluate flow characteristics.

Dissipative particle dynamics simulation of circular and elliptical particles motion in 2D laminar shear flow

The dissipative particle dynamics (DPD) method is a relatively new computational method for modeling the dynamics of particles in laminar flows at the mesoscale. In this study, we use the DPD approach to model the motion of circular and elliptical particles in a 2D shear laminar flow. Three examples are considered: (i) evaluation of the drag force exerted on a circular particle moving in a stagnant fluid, (ii) rotation of an elliptical particle around its center in a shear flow, and (iii) motion of an ellipsoidal particle in a linear shear flow. For all cases, we found a good agreement with theoretical and finite element solutions available. These results show that the DPD method can effectively be applied to model motion of micro/nano-particles at the mesoscale. The method proposed can be used to predict the performances of intravascularly administered particles for drug delivery and biomedical imaging.

Hemolysis caused by surface roughness under shear flow

In this study, the relationship between the degree of roughness of blood contact surfaces under laminar shear flow conditions and the level of hemolysis resulting from this roughness was investigated using a rotational shear stressor. Unlike previous in vitro experiments that used a pumped circuit, the level of hemolysis was directly evaluated under a constant shear flow. In total, 1.8% of the blood contact area was roughened to an arithmetic mean roughness (Ra) value of between 0.4 and 9.2 microm by machine processing and a shear load was applied for 30 min at a shear flow rate of 3750 s(-1). As a result, the threshold Ra value for the induction of hemolysis was found to be between 0.4 and 0.8 microm. In addition, the results of this experiment suggested that the high shear stress resulting from surface roughness plays a major role in determining the level of hemolysis caused by surface roughness.

Shear Stress Modulation of Smooth Muscle Cell Marker Genes in 2-D and 3-D Depends on Mechanotransduction by Heparan Sulfate Proteoglycans and ERK1/2

BackgroundDuring vascular injury, vascular smooth muscle cells (SMCs) and fibroblasts/myofibroblasts (FBs/MFBs) are exposed to altered luminal blood flow or transmural interstitial flow. We investigate the effects of these two types of fluid flows on the phenotypes of SMCs and MFBs and the underlying mechanotransduction mechanisms.Methodology/Principal FindingsExposure to 8 dyn/cm2 laminar flow shear stress (2-dimensional, 2-D) for 15 h significantly reduced expression of α-smooth muscle actin (α-SMA), smooth muscle protein 22 (SM22), SM myosin heavy chain (SM-MHC), smoothelin, and calponin. Cells suspended in collagen gels were exposed to interstitial flow (1 cmH2O, ∼0.05 dyn/cm2, 3-D), and after 6 h of exposure, expression of SM-MHC, smoothelin, and calponin were significantly reduced, while expression of α-SMA and SM22 were markedly enhanced. PD98059 (an ERK1/2 inhibitor) and heparinase III (an enzyme to cleave heparan sulfate) significantly blocked the effects of laminar flow on gene expression, and also reversed the effects of interstitial flow on SM-MHC, smoothelin, and calponin, but enhanced interstitial flow-induced expression of α-SMA and SM22. SMCs and MFBs have similar responses to fluid flow. Silencing ERK1/2 completely blocked the effects of both laminar flow and interstitial flow on SMC marker gene expression. Western blotting showed that both types of flows induced ERK1/2 activation that was inhibited by disruption of heparan sulfate proteoglycans (HSPGs).Conclusions/SignificanceThe results suggest that HSPG-mediated ERK1/2 activation is an important mechanotransduction pathway modulating SMC marker gene expression when SMCs and MFBs are exposed to flow. Fluid flow may be involved in vascular remodeling and lesion formation by affecting phenotypes of vascular wall cells. This study has implications in understanding the flow-related mechanobiology in vascular lesion formation, tumor cell invasion, and stem cell differentiation.

Effective slip boundary conditions for arbitrary periodic surfaces: the surface mobility tensor

In a variety of applications, most notably microfluidics design, slip-based boundary conditions have been sought to characterize fluid flow over patterned surfaces. We focus on laminar shear flows over surfaces with periodic height fluctuations and/or fluctuating Navier scalar slip properties. We derive a general formula for the ‘effective slip’, which describes equivalent fluid motion at the mean surface as depicted by the linear velocity profile that arises far from it. We show that the slip and the applied stress are related linearly through a tensorial mobility matrix, and the method of domain perturbation is then used to derive an approximate formula for the mobility law directly in terms of surface properties. The specific accuracy of the approximation is detailed, and the mobility relation is then utilized to address several questions, such as the determination of optimal surface shapes and the effect of random surface fluctuations on fluid slip.

Salt finger fluxes in a laminar shear flow

Subtropical ocean waters are susceptible to the occurrence of salt finger instability. The effect of salt fingers in modifying water mass properties may depend upon the ubiquitous presence of oceanic shear produced by internal wave motion. We present an experimental study of the buoyancy fluxes produced by sugar–salt fingers in the presence of a laminar shear flow. As is commonly done in the laboratory, sugar (the slower diffuser) was used as a proxy for salt, and salt (the faster diffuser compared to sugar) was used as a proxy for cold. Sugar–salt fingers, initially aligned vertically, were observed to tilt when a shear flow was imposed. A consistent decrease in the salt fluxes was measured as the Reynolds number (Re) was increased by increasing the shear velocity magnitude. Through regression analysis, the salt fluxes were found to depend upon the Reynolds number as Re−0.025, Re−0.1 and Re−0.34, for density ratio values (Rρ) equal to 1.2, 1.54 and 2.1 respectively. The salt fluxes produced by the sheared fingers were also found to decrease by one order of magnitude when Rρ increased from 1.2 to 2.1. A computation of the salt Nusselt number revealed that the finger fluxes approach molecular flux values when Rρ = 2.1 and Re ≃ 140.

A first integral of Navier–Stokes equations and its applications

Although it is well known that Bernoulli's equation is obtained as the first integral of Euler's equations in the absence of vorticity and that in the case of non-vanishing vorticity a first integral of them can be found using the Clebsch transformation for inviscid flow, generalization of the procedure for viscous flow has remained elusive. Accordingly, in this paper, a first integral of the Navier–Stokes equations for steady flow is constructed. In the case of a two-dimensional flow, this is made possible by formulating the governing equations in terms of complex variables and introducing a new scalar potential. Associated boundary conditions are considered, and an extension of the theory to three dimensions is proposed. The capabilities of the new approach are demonstrated by calculating a Reynolds number correction to the laminar shear flow generated in the narrow gap between a flat moving and a stationary wavy wall, as is often encountered in lubrication problems. It highlights the first integral as a suitable tool for the development of new analytical and numerical methods in fluid dynamics.

Flow banding in basaltic pillow lavas from the Early Archean Hooggenoeg Formation, Barberton Greenstone Belt, South Africa

Well-preserved pillow lavas in the uppermost part of the Early Archean volcanic sequence of the Hooggenoeg Formation in the Barberton Greenstone Belt exhibit pronounced flow banding. The banding is defined by mm to several cm thick alternations of pale green and a dark green, conspicuously variolitic variety of aphyric metabasalt. Concentrations of relatively immobile TiO2, Al2O3 and Cr in both varieties of lava are basaltic. Compositional differences between bands and variations in the lavas in general have been modified by alteration, but indicate mingling of two different basalts, one richer in TiO2, Al2O3, MgO, FeOt and probably Ni and Cr than the other, as the cause of the banding. The occurrence in certain pillows of blebs of dark metabasalt enclosed in pale green metabasalt, as well as cores of faintly banded or massive dark metabasalt, suggest that breakup into drops and slugs in the feeder channel to the lava flow initiated mingling. The inhomogeneous mixture was subsequently stretched and folded together during laminar shear flow through tubular pillows, while diffusion between bands led to partial homogenisation. The most common internal pattern defined by the flow banding in pillows is concentric. In some pillows the banding defines curious mushroom-like structures, commonly cored by dark, variolitic metabasalt, which we interpret as the result of secondary lateral flow due to counter-rotating, transverse (Dean) vortices induced by the axial flow of lava towards the flow front through bends, generally downward, in the tubular pillows. Other pillows exhibit weakly-banded or massive, dark, variolitic cores that are continuous with wedge-shaped apophyses and veins that intrude the flow banded carapace. These cores represent the flow of hotter and less viscous slugs of the dark lava type into cooled and stiffened pillows.

Surfactant effect on the bubble motions and bubbly flow structures in a vertical channel

It is well known that a small amount of surfactant can drastically change the motion of a single bubble and this causes a dramatic change of the whole bubbly flow structure. In our previous studies using upward vertical channel flows, it was shown that surfactant influences the shear-induced lift and the lateral migration of a bubble, which causes bubble accumulation and clustering near the wall. In this paper, the dependence of surfactant concentration on the motions of a 1 mm bubble rising through the laminar shear flow is investigated using 1-, 3-Pentanol and Triton X-100. The results are compared with the numerical ones, which show quantitative agreement on the lift and drag forces. Furthermore, we analyze the experimental data for the condition of bubble clustering in upward channel flows with the consideration of contaminant level in tap water. The results indicate that lower contaminant level and higher shear rate cause the significant bubble migration toward the wall, which leads to the formation of bubble clusters.

Sediment dynamics. Part 1. Bed-load transport by laminar shearing flows

We propose a two-phase model having a Newtonian rheology for the fluid phase and friction for the particle phase to describe bed-load transport in the laminar viscous regime. We have applied this continuum model to sediment transport by viscous shearing flows. The equations are shown to reduce to the momentum equation for the mixture and the Brinkman equation for the fluid velocity. This modelling is able to provide a description of the flow of the mobile granular layer. At some distance from threshold of particle motion, where the continuum approach is more realistic as the mobile layer is larger than one particle diameter, there is very little slip between the two phases and the velocities inside the mobile bed have approximately a parabolic profile. When the Poiseuille (or Couette) flow is not significantly perturbed, simple analytical results of the particle flux varying cubically with the Shields number and of the bed-load thickness varying linearly with it can then be obtained. These predictions compare favourably with experimental observations of bed-load transport in pipe flows.

M-Calpain antagonizes RhoA overactivation and endothelial barrier dysfunction under disturbed shear conditions

It has been reported that laminar shear flow (LF) improves barrier functions in vascular endothelial cells (ECs), whereas disturbed flow (DF) impairs the barrier. Our previous study showed that LF stimulus led to the activation of the cysteine protease, m-calpain, in ECs, which can influence RhoA activity. We hypothesized that m-calpain participates in the shear pattern-dependent EC barrier maintenance through RhoA signalling. m-Calpain expression levels in the intima in the inferior aspect of mouse aortic arch where DF dominates were higher than those in adjacent regions. Elevation in transendothelial albumin permeability, which was induced by administration of a calpain inhibitor (ALLM), was prominent in the inferior arch; moreover, this elevation was abolished by Rho kinase (ROCK) inhibitor (Y-27632). Similarly, short interfering RNA (siRNA)-induced silencing of m-calpain resulted in increased RhoA activity and hyperpermeability in the aortic arch, which was accompanied by ROCK inhibitor-sensitive phosphorylation of downstream effecter LIM kinase 2 (LIMK2), stress fibre accumulation in endothelium and enhanced interendothelial gaps. Exposure of human umbilical vein endothelial cells to LF diminished RhoA activity; in contrast, DF facilitated the activity. siRNA-induced m-calpain silencing further accelerated the DF-induced RhoA overactivation, phosphorylation of LIMK2, and cytoskeletal rearrangement, resulting in barrier dysfunction in the cells. Our findings revealed relatively high m-calpain expression levels in the inferior arch. The m-calpain activity antagonizes DF-induced overactivation of RhoA/ROCK/LIMK2 signalling and subsequent cytoskeletal rearrangement in ECs, which leads to barrier improvement.

A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow

A numerical model for the simulation of incompressible two-phase flows of a flat granular bed submitted to a laminar shearing flow is presented, considering a two-fluid model and a mixed-fluid one. The governing equations are discretized by a finite element method and a penalisation method is introduced to cope with the incompressibility constraint. A regularisation technique is used to deal with the visco-plastic behaviour of the granular phase. Validations are carried out on three flow test cases: a Bingham fluid between two infinite parallel planes, a Bingham fluid in a square lid-driven cavity and a Newtonian fluid over a granular bed in a two-dimensional configuration, for which we compare our numerical results with existing analytical or numerical results. The accuracy and efficiency of the numerical models have been compared for the two formulations of the two-phase flow model. It turns out that the two-fluid model requires ten times more CPU time than the mixed-fluid one for a comparable accuracy, which can be achieved provided one takes a smaller regularisation parameter in the latter model. Finally, three-dimensional computations are presented for the flow of a Newtonian fluid over a granular bed in a square and circular cross-section ducts.

Action at a distance: lengthening adhesion bonds with poly(ethylene glycol) spacers enhances mechanically stressed affinity for improved vascular targeting of microparticles.

Poly(ethylene glycol) (PEG) chains were used to decorate microparticles with long adhesion ligands to emulate the efficacy of selectin-mediated leukocyte homing mechanisms. Ligands for P-selectin, an endothelial cell inflammatory marker, were coupled to PEG spacers of two sizes (MW 3400 and 10,000 Da) to investigate the effects on adhesion kinetics to P-selectin substrates. Under shear flow 80 nm PEG spacers improved P-selectin-antibody adhesion frequency by up to 4.5-fold and bond lifetimes by 7-fold compared to microparticles bearing chemisorbed antibody. Presentation of the glycosulfopeptide P-selectin ligands (2-GSP-6) and its nonsulfated low affinity form (2-GP-6) by long PEG spacers led to improved lifetimes of stressed bonds formed with P-selectin in shear flow and the rolling fluxes. Thus, structural features far removed from the binding pocket of a receptor that increase molecular contour length may enhance affinity in mechanically stressed environments such as those existing within the confines of the blood vessel. Such features may be useful for improving the performance of vascular-targeted micro- and nanoparticles used for drug, gene, and image contrast delivery. Ligand presentation on molecularly extended stalks may also serve to enhance any particle-surface interaction that takes place in laminar shear flow.

STIRRING FREE SURFACE FLOWS DUE TO HORIZONTAL CIRCULATORY OSCILLATION OF A PARTIALLY FILLED CONTAINER

Mixing in a partially filled beaker or conical flask using oscillator shaker tables is routinely used for cultivation of biological cells. The present study seeks to gain a better understanding of fluid flow inside a beaker on a shaker table and the fluid motion influence on the mixing of cells within the fluid medium used for their cultivation. The imposed oscillatory motion on the beaker induces free surface deformations, which may cause laminar and low shear flow environments thus uniformly mixing the fluid medium. The low shear and uniformly mixed cell culture medium are requirements necessary for optimum cellular growth. In this study, fluid flow due to periodic and horizontal circulatory oscillations at a beaker boundary has been analyzed both numerically and experimentally. A partially filled beaker was modeled as a circular cylinder, and the cell culture medium was modeled as an incompressible fluid with a free and deformable liquid interface. The three-dimensional numerical model that can resolve the free surface deformation was based on finite difference scheme based on the “Marker-and-Cell” method. The method was used to determine the free surface deformation, its coupling to the flow dynamics within the beaker, and the resulting stirring effects. To verify the numerical model and validate the results, a simple flow visualization experiment was performed using an ion laser sheet to optically section flow chamber and reveal the flow pattern. The flow patterns obtained using numerical simulations were similar to those obtained experimentally through flow visualization. This study provides useful information that can be used to optimize the operation of a shaker table necessary to mix uniformly the cell culture, ensuring cell growth. In addition, this model can be extended to study the mixing processes in any chemical reactions within a partially filled container subjected to oscillatory forces.

Eddy genesis and manipulation in plane laminar shear flow

Eddy formation and presence in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one has a sinusoidal profile and is fixed. The governing equations are solved via a full finite element formulation for the general case and semianalytically at the Stokes flow limit. The effects of varying geometry (involving changes in the mean plate separation or the amplitude and wavelength of the lower plate) and inertia are explored separately. For Stokes flow and varying geometry, excellent agreement between the two methods of solution is found. Of particular interest with regard to the flow structure is the importance of the clearance that exists between the upper plate and the tops of the corrugations forming the lower one. When the clearance is large, an eddy is only present at sufficiently large amplitudes or small wavelengths. However, as the plate clearance is reduced, a critical value is found, which triggers the formation of an eddy in an otherwise fully attached flow for any finite amplitude and arbitrarily large wavelength. This is a precursor to the primary eddy to be expected in the lid-driven cavity flow, which is formed in the limit of zero clearance between the plates. The influence of the flow driving mechanism is assessed by comparison with corresponding solutions for the case of gravity-driven fluid films flowing over an undulating substrate. When inertia is present, the flow generally becomes asymmetrical. However, it is found that for large mean plate separations the flow local to the lower plate becomes effectively decoupled from the inertia dominated overlying flow if the wavelength of the lower plate is sufficiently small. In such cases the local flow retains its symmetry. A local Reynolds number based on the wavelength is shown to be useful in characterizing these large-gap flows. As the mean plate separation is reduced, the form of the asymmetry caused by inertia changes and becomes strongly dependent on the plate separation. For lower plate wavelengths which do not exhibit a kinematically induced secondary eddy, an inertially induced secondary eddy can be created if the mean plate separation is sufficiently small and the global Reynolds number is sufficiently large.

Onset of motion of a partly hidden cylinder in a laminar shear flow

In this paper, the onset of motion of an isolated cylinder partially exposed to a shear flow is experimentally investigated. The experiments are performed in a small narrow channel which provides a vertical shear layer flow whose sizes correspond with the channel width. The bottom of the channel is smooth except in the test zone, at long distance from the inlet, where the cylinder is placed with its principal axis perpendicularly directed to the main flow. The geometry of the channel bottom at the test zone is such that the cylinder is partially buried and presents different expositions to the incident flow. In this way, the geometrical constraints imposed by the sediment bed on a single particle in a natural sediment transport situation are reproduced in an idealized context. The results are interpreted in terms of the relation between the particle mobility parameter at the critical condition and the here defined particle burial degree with respect to the bed geometrical constraints beta . We emphasize the role played by this burial degree that is dependent on the particle exposure to the incident flow E and the resistance to the motion by mechanical contacts with its surroundings given by the so-called static pivot angle varphi .

The effect of locally induced flow structure on global heat transfer for plane laminar shear flow

Heat transfer in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one, which is fixed, has a regular sinusoidally varying profile. A closed form analytical solution for velocity, based on lubrication theory, together with a semi-analytic one for temperature, from application of Ritz’s direct method, is derived for creeping flow. In addition, detailed numerical solutions are obtained from a finite element formulation of the weak form of the governing equations for mass, momentum and energy (temperature) conservation, enabling the effects of inertia to be explored. It is shown that changes in the mean plate separation, that is the geometry, and the level of inertia present affect the local hydrodynamic flow structure in the form of kinematically and inertially induced eddies, respectively. These in turn impact on the local “laminar thermal mixing”, and consequently enhance the global heat transfer. Results are reported for a wide range of Peclét, Reynolds and Nusselt numbers with agreement between the two methods of solution, for the case of creeping flow, found to be extremely good. The key flow features that emerge are (i) For creeping flow and varying Peclét number, the thermal field is asymmetric for all values of the Peclét number other than the limiting conditions of zero and infinity, at which extremes the corresponding thermal field is symmetric. In the limit of infinite Peclét number the eddy becomes a basin of fluid at uniform temperature. (ii) Global heat transfer in the case of creeping flow, expressed in terms of the Nusselt number, for a given Peclét number increases as the mean plate separation decreases, that is as the local kinematically induced eddy structure becomes more pronounced. (iii) There exists a subtle interplay between variations in the mean plate separation and the level of inertia imposed, in that both influence the presence or otherwise of eddies. Starting from a creeping flow condition the introduction of inertia can in addition both enlarge and skew an existing eddy. When this information is condensed to a series of Nusselt number curves the indication is that it should be possible, from a practical standpoint, to find a critical mean plate separation, for a given Peclét number, for which local inertially influenced eddy effects on the global heat transfer are at a minimum.