Near-wall Velocity Research Articles

Effect of non-uniform, out-of-plane illumination, shear rate andparticle distribution on the accuracy of nPIV velocity measurement

Nanoparticle image velocimetry (nPIV) uses evanescent-wave illumination to measure two velocity components, U and V, tangential to a wall in a region with thickness of the order of hundreds of nanometers. In this region the illumination intensity decays exponentially with distance normal to the wall, z, and hence tracers closer to the wall have ‘brighter’ and ‘bigger’ images than those that are further away, i.e. at larger z. Moreover, fluid velocity varies in this region with z and hence tracers at different distance from the wall move at different speeds. Furthermore, presence of the wall has a significant effect on particle distribution, and particle displacement due to local fluid velocity and Brownian displacement of particle tracers in this region. The variation in the displacement of particle images in this region, with different brightness and velocities, can bias the near-wall velocities obtained using standard correlation-based PIV method. Artificial nPIV images of nanoparticles in a flow field with linear out-of-plane velocity profile were used in this work to investigate the impact of these issues upon the accuracy of nPIV data. Uniform and Gaussian random distribution noise were added to the images to simulate electronic noise and shot noise, respectively. The artificial images were obtained and processed for various experimental parameters to incorporate different illumination profiles, shear rates and distribution profiles. The results demonstrate that non-uniform illumination, as well as particle distribution, affects the bias in the estimated tracer velocity for the shear flow. Non-uniform intensity also affects the bias due to Brownian diffusion; however, correction for Brownian diffusion canreduce this bias error.

Nanoscale Brownian motion-based thermometry in near wall region

In nanoparticle image velocimentry (nPIV), evanescent wave illumination is used to measure near-wall velocity fields with an out-of-plane resolution of less than 200nm. Similar methodology can be extended for temperature measurements using Brownian motion characteristics of the sub-micron tracer particles in this region. Temperature change affects Brownian motion of tracer particles through a change in Brownian diffusion coefficient and a change in viscosity. The present study tries to numerically investigate the possibilities of utilizing this effect in near-wall thermometry. Synthetic nPIV images of the illuminated particle tracer of 100nm diameter are initially generated. The spatial distribution of the particles takes in to account near wall forces such as buoyancy, electrostatic repulsion and Van Der Waals attraction, in addition to the hindered Brownian motion. Validation studies are carried out using stationary liquids at constant temperatures. It is believed that this observation would help in explaining the anomalous heat transfer characteristics of nanofluids.

The mean velocity profile of a smooth-flat-plate turbulent boundary layer at high Reynolds number

Smooth flat-plate turbulent boundary layers (TBLs) have been studied for nearly a century. However, there is a relative dearth of measurements at Reynolds numbers typical of full-scale marine and aerospace transportation systems (Reθ = Ueθ/ν > 105, where Ue = free-stream speed, θ = TBL momentum thickness and ν = kinematic viscosity). This paper presents new experimental results for the TBL that forms on a smooth flat plate at nominal Reθ values of 0.5 × 105, 1.0 × 105 and 1.5 × 105. Nominal boundary layer thicknesses (δ) were 80–90mm, and Karman numbers (δ+) were 17000, 32000 and 47000, respectively. The experiments were conducted in the William B. Morgan Large Cavitation Channel on a polished (k+ < 0.2) flat-plate test model 12.9m long and 3.05m wide at water flow speeds up to 20ms−1. Direct measurements of static pressure and mean wall shear stress were obtained with pressure taps and floating-plate skin friction force balances. The TBL developed a mild favourable pressure gradient that led to a streamwise flow speed increase of ~2.5% over the 11m long test surface, and was consistent with test section sidewall and model surface boundary-layer growth. At each Reθ, mean streamwise velocity profile pairs, separated by 24cm, were measured more than 10m from the model's leading edge using conventional laser Doppler velocimetry. Between these profile pairs, a unique near-wall implementation of particle tracking velocimetry was used to measure the near-wall velocity profile. The composite profile measurements span the wall-normal coordinate range from y+ < 1 to y > 2δ. To within experimental uncertainty, the measured mean velocity profiles can be fit using traditional zero-pressure-gradient (ZPG) TBL asymptotics with some modifications for the mild favourable pressure gradient. The fitted profile pairs satisfy the von-Kármán momentum integral equation to within 1%. However, the profiles reported here show distinct differences from equivalent ZPG profiles. The near-wall indicator function has more prominent extrema, the log-law constants differ slightly, and the profiles' wake component is less pronounced.

The accuracy of tomographic particle image velocimetry for measurements of a turbulent boundary layer

To investigate the accuracy of tomographic particle image velocimetry (Tomo-PIV) for turbulent boundary layer measurements, a series of synthetic image-based simulations and practical experiments are performed on a high Reynolds number turbulent boundary layer at Reθ = 7,800. Two different approaches to Tomo-PIV are examined using a full-volume slab measurement and a thin-volume “fat” light sheet approach. Tomographic reconstruction is performed using both the standard MART technique and the more efficient MLOS-SMART approach, showing a 10-time increase in processing speed. Random and bias errors are quantified under the influence of the near-wall velocity gradient, reconstruction method, ghost particles, seeding density and volume thickness, using synthetic images. Experimental Tomo-PIV results are compared with hot-wire measurements and errors are examined in terms of the measured mean and fluctuating profiles, probability density functions of the fluctuations, distributions of fluctuating divergence through the volume and velocity power spectra. Velocity gradients have a large effect on errors near the wall and also increase the errors associated with ghost particles, which convect at mean velocities through the volume thickness. Tomo-PIV provides accurate experimental measurements at low wave numbers; however, reconstruction introduces high noise levels that reduces the effective spatial resolution. A thinner volume is shown to provide a higher measurement accuracy at the expense of the measurement domain, albeit still at a lower effective spatial resolution than planar and Stereo-PIV.

Four-Dimensional Flow Magnetic Resonance Imaging With Wall Shear Stress Analysis Before and After Repair of Aortopulmonary Fistula

We used 4D flow magnetic resonance imaging1 to evaluate a 34-year-old man with a complicated course after aortic coarctation repair including development of an aortopulmonary fistula. Our initial 4D flow study (Figure 1) reveals abnormal vortical-type flow in the aneurysmal distal aortic arch. Evaluation of wall shear stress calculated from near-wall velocity gradients using proprietary software ( flow tool , University of Freiburg, Germany; software is experimental and not FDA approved)2 demonstrates skewing of higher shear values along the posterior and left lateral aortic arch, just upstream of a pseudoaneurysm. Figure 1. A 34-year-old man with complicated course status after aortic coarctation repair. A, 3D contrast-enhanced magnetic resonance imaging that demonstrates an aneurysm of the distal aortic arch extending …

Measurements in the near-wall region of a boundary layer over a wall with large transverse curvature

Measurements of the near-wall velocity field of the flow over cylinders aligned with a uniform flow are presented. The broader objective of this investigation was to quantify and understand the role of transverse curvature in the limit as cylinder diameter approaches zero. The specific goal was to begin with a turbulent boundary layer over a larger radius cylinder and see what happens as the radius is reduced. Spatially and temporally resolved digital particle image velocimetry (DPIV) measurements were made on three different radius cylinders, 0.14 cm ≤a≤ 3.05 cm, extending along the length of a large free-surface water tunnel. Mean and fluctuating profiles are presented at a fixed streamwise location and free-stream speed. For the first time, spatially resolved measurements were made very close to the wall, permitting direct determination of wall shear stress, i.e.uτ, from near-wall velocity profiles. The measurements revealed a region close to the wall for small radii where the mean streamwise velocity profile is inflectional. This has significant implications on assumptions regarding what happens in the limit of a vanishing cylinder radius.

An experimental study of slip considering the effects of non-uniform colloidal tracer distributions

Various studies have suggested that the no-slip condition may not hold for Newtonian liquids flowing over (for the most part) non-wetting surfaces. This paper describes an experimental study of steady Poiseuille flow at various Reynolds numbers up to 0.12 of four different aqueous monovalent electrolyte solutions through naturally hydrophilic and hydrophobically coated fused-silica channels with a depth of 33 μm. The slip lengths for these flows were estimated using a local method based on a new particle velocimetry technique that determines velocities at three different wall-normal distances within the first 400 nm next to the wall. These results are corrected using direct measurements of the near-wall particle distribution, which is highly non-uniform as expected due to repulsive electric double-layer interactions between the 100 nm tracer particles and the wall. In all cases, the slip lengths were not more than 23 nm and for all but one case, zero within their uncertainties. As illustrated here, the standard assumption of uniformly distributed tracers can significantly increase slip length estimates obtained using local methods and near-wall velocity data.

Analytical method for softness abrasive flow field based on discrete phase model

Aiming at the problem of difficult contact finishing for mini structural surface in course of mould manufacturing, a new no-tool precision machining method based on soft abrasive flow machining (SAFM) was proposed. It allocated restrained component near surface machined, constituted restrained abrasive flow passage, and made the surface become a segment of passage wall. It could control turbulence abrasive flow in restrained passage, realize micro cutting for passage wall, and utilize the irregular motion of abrasive flow to eliminate the mono-directional marks on machined surfaces, and the precision could reach the specular level. A two-phase dynamic model of abrasive flow oriented to SAFM combined with discrete phase model (DPM) was established, the law of two-phase flow motion and the related physical parameters was obtained by corresponding numerical simulation method, and the mechanism of precision machining in SAFM was discussed. Simulation results show that the abrasive flow machining process mainly appears as translation of ablating location with the influence by granular pressure, and as the variation of machining efficiency with the influence by near-wall particle velocity. Thus via control of the inlet velocity and its corresponding machining time, it is supposed to work out the machining process according to the machining requirements by using the Preston equation to seek the relationship among velocity, pressure and material removing rate. By tracking near-wall particles, it can be confirmed that the movement of near-wall abrasive particles is similar to stream-wise vortices. The cutting traces on workpiece surfaces assume disorderly arrangement, so the feasibility of the SAFM method can be reaffirmed.

Modelling and simulation of the near-wall velocity of a turbulent ceiling attached plane jet after its impingement with the corner

At present, ceiling-mounted diffusers are very popular for indoor air distribution, particularly in offices, owing to greater efficiency in the distribution of the air supply and a more comfortable indoor environment. The objective of this study is to construct an effective model to design the indoor airflow of an attached plane jet after its impingement with the corner in a room. In this study, a full-scale test facility was set up to obtain detailed experimental data. One commercial CFD tool, CFX 11.0, was used to simulate the air velocity distribution of an attached plane air jet bounded by the ceiling and an insulated wall. One semi-empirical model was also constructed to predict the impingement jet velocity. The results show that bout the semi-empirical model and CFX 11.0 were able to predict the maximum velocity of an impinging jet at low Reynolds numbers, 1000 and 2000, with an inaccuracy of ±11%. However, the semi-empirical model could be more conveniently used to predict the maximum jet velocity decay after its impingement the corner in a room than CFD simulation in terms of accuracy and the time required to design the indoor airflow pattern.

A simulation environment for validating ultrasonic blood flow and vessel wall imaging based on fluid‐structure interaction simulations: Ultrasonic assessment of arterial distension and wall shear rate

Ultrasound (US) is a commonly used vascular imaging tool when screening for patients at high cardiovascular risk. However, current blood flow and vessel wall imaging methods are hampered by several limitations. When optimizing and developing new ultrasound modalities, proper validation is required before clinical implementation. Therefore, the authors present a simulation environment integrating ultrasound and fluid-structure interaction (FSI) simulations, allowing construction of synthetic ultrasound images based on physiologically realistic behavior of an artery. To demonstrate the potential of the model for vascular ultrasound research, the authors studied clinically relevant imaging modalities of arterial function related to both vessel wall deformation and arterial hemodynamics: Arterial distension (related to arterial stiffness) and wall shear rate (related to the development of atherosclerosis) imaging. An in-house code ("TANGO") was developed to strongly couple the flow solver FLUENT and structural solver ABAQUS using an interface quasi-Newton technique. FIELD II was used to model realistic transducer and scan settings. The input to the FSI-US model is a scatterer phantom on which the US waves reflect, with the scatterer displacement derived from the FSI flow and displacement fields. The authors applied the simulation tool to a 3D straight tube, representative of the common carotid artery (length: 5 cm; and inner and outer radius: 3 and 4 mm). A mass flow inlet boundary condition, based on flow measured in a healthy subject, was applied. A downstream pressure condition, based on a noninvasively measured pressure waveform, was chosen and scaled to simulate three different degrees of arterial distension (1%, 4%, and 9%). The RF data from the FSI-US coupling were further processed for arterial wall and flow imaging. Using an available wall tracking algorithm, arterial distensibility was assessed. Using an autocorrelation estimator, blood velocity and shear rate were obtained along a scanline. The authors obtained a very good agreement between the flow and the distension as obtained from the FSI-US model and the reference FSI values. The wall application showed a high sensitivity of distension measurements to the measurement location, previously reported based on in vivo data. Interestingly, the model indicated that strong reflections between tissue transitions can potentially cloud a correct measurement. The flow imaging application demonstrated that maximum shear rate was underestimated for a relevant simulation setup. Moreover, given the difficulty of measuring near-wall velocities with ultrasound, maximal shear rate was obtained at a distance from the wall [0.812 mm for the anterior and 0.689 mm for the posterior side (9% distension case)]. However, ultrasound shear rates correlated well with the FSI ground truth for all distension degrees, suggesting that correction of the severe underestimation by ultrasound might be feasible in certain flow conditions. The authors demonstrated a simulation environment to validate and develop ultrasonic vascular imaging. An elaborate technique to integrate FSI and FIELD II ultrasound simulations was presented. This multiphysics simulation tool was applied to two imaging applications where distensible ultrasound phantoms are indispensable: Wall distension and shear rate measurement. Results showed that the method to couple fluid-structure interaction and ultrasound simulations provides realistic RF signals from the tissue and the blood pool.

Slip due to surface roughness for a Newtonian liquid in a viscous microscale disk pump

In the present study, hydrophobic roughness is used to induce near-wall slip in a single rotating-disk micropump operating with Newtonian water. The amount of induced slip is altered by employing different sizes of surface roughness on the rotating disk. The magnitudes of slip length and slip velocities increase as the average size of the surface roughness becomes larger. In the present study, increased slip magnitudes from roughness are then associated with reduced pressure rise through the pump and lower radial-line-averaged shear stress magnitudes (determined within slip planes). Such shear stress and pressure rise variations are similar to those which would be present if the slip is induced by the intermolecular interactions which are associated with near-wall microscale effects. The present slip-roughness effects are quantified experimentally over rotational speeds from 50 to 1200 rpm, pressure increases from 0 to 312 kPa, net flow rates of 0–100 μl/min, and fluid chamber heights from 6.85 to 29.2 μm. Verification is provided by comparisons with analytic results determined from the rotating Couette flow forms of the Navier–Stokes equations, with different disk rotational speeds, disk roughness levels, and fluid chamber heights. These data show that slip length magnitudes show significant dependence on radial-line-averaged shear stress for average disk roughness heights of 404 and 770 nm. These slip length data additionally show a high degree of organization when normalized using by either the average roughness height or the fluid chamber height. For the latter case, such behavior provides evidence that the flow over a significant portion of the passage height is affected by the roughness, and near-wall slip velocities, especially when the average roughness height amounts to 11% of the h=6.86 μm passage height of the channel. Such scaling of the disk slip length bdisk with fluid chamber height h is consistent with d-type roughness scaling in macroscale flows.

Investigation of boundary layers in internal combustion engines using a hybrid algorithm of high speed micro-PIV and PTV

Heat transfer properties vary locally and temporally in internal combustion engines due to variations in the boundary layer flow. In order to characterize the dynamics in the boundary layer, crank-angle resolved high-speed micro particle image velocimetry (μPIV) and particle tracking velocimetry (PTV) have been used for near-wall velocity measurements in a spark-ignition direct-injection single cylinder engine. A 527-nm dual cavity green Nd:YLF laser was used for velocity measurements near the cylinder head wall between the intake and exhaust valves in the tumble mean flow plane parallel to the cylinder axis. A long-distance microscope was used to obtain a spatial resolution of 45 μm. Flow fields were determined from 180 to 490 CAD in the compression and expansion strokes. The data show significant variation in the flow during the compression and expansion strokes and from cycle to cycle. Flow deceleration was observed during the end of the compression that continued during the expansion stroke until 400 CAD when the flow direction reverses. Sub-millimeter-sized vortical structures were observed within the boundary layer over extended periods of time.

Evanescent-wave/volume illuminated velocity measurements of transient eletrokinetically driven flow with nonuniform wall electrostatic potential

Time-resolved velocity measurements using fluorescent submicron particles have been conducted to examine transient electrokinetically driven flow with nonuniform wall electrostatic potential, i.e. the zeta-potential. Evanescent wave- and volume illumination-based optical systems were used, respectively, to measure the near-wall and bulk velocities. Particle tracking velocimetry with phase sampling at low concentration of tracers achieved a spatial resolution of 9.8 µm × 36.1 µm with images of high signal-to-noise ratio. A microchannel having a step-change wall zeta-potential with intervals of 50 µm, which was generated by the surface modification on the wall, was prepared. Since particles do not follow the fluid flow due to electrophoresis, the time evolution of the particle and fluid flows were investigated with a temporal resolution of 0.4 ms. Measurement uncertainty was 0.05 mm s−1 for the particle velocity, and 0.11 mm s−1 for the fluid velocity. Near-wall fluid velocities with the step-change zeta-potential of 20% difference generated 50% difference of the particle velocities due to electrophoresis. The depth-wise velocities were induced by the mass conservation. It is found that the transient flow field is characterized by the ratio of the stream-wise to depth-wise velocities. The fluid flow depending on the momentum diffusion yielded the temporally constant velocity gradients derived from the step-change zeta-potential.

Special section on the 13th International Symposium on Flow Visualization

The 13th International Symposium on Flow Visualization (ISFV 13, http://isfv13.univ-fcomte.fr) was held at the Acropolis Convention Center, Nice, France on July 1–4, 2008. The 12th French congress on visualization in fluid mechanics (Fluvisu 12) was jointly held at the same venue. Every 2 years, the ISFV series gathers the international communities of Fluids and Thermal Engineering around the common theme of imagery and optical measurements, including the development of new visualization techniques, visualization of transport phenomena, characterization of fields of velocity, temperature and pressure, and of course, the validation of theoretical models. The ISFV-13 symposium attracted a total of 298 participants from 27 countries and was organized in 40 standard sessions, four invited lectures, and a poster exhibition. The standard sessions included Acoustics, Specific PIV/ PTV, Periodic Phenomena, Aeronautics and Space, High Speed, Multiphase, Turbulence/Vortices, Computer Visualization, Industrial Applications, DGV/DPV, Cavities, Refractometry, Stereo and 3D, Heat and Mass Transfer, BOS/Stereo Schlieren, Walls/Boundaries, Microflows, Combustion, Hybrid/Specific Methods, Coating Sensors, Interferometry, Terrestrial Vehicles, Rotating/Oscillating/ Swirling Flows, Advanced Image Processing, Optical and Electrical Manipulations, Natural Life, Human Life, Earth and Environment, and Art and Learning. In addition, more than 40 posters were displayed throughout the duration of the conference. The special committee of eight internationally recognized researchers (Kyung Chun Kim, Sang Joon Lee, Osamu Mochizuki, Robert Nelson, Jean-Michel Desse, Daniel H. Fruman, Godfrey Mungal, and Kenneth D. Kihm) attended the presentation sessions to invite selected authors to submit their manuscripts for the special section for Experiments in Fluids. A total of 20 conference proceeding papers were solicited, 15 authors responded with manuscript submissions, and seven completed their revisions as finally accepted contributions. This special section begins with a review article on the surface plasmon resonance (SPR) imaging technique as a new far-field visualization tool for near-field transport characterization. The second study presents an experimental study with the use of PIV for the vortex flow characteristics along a sharp-edged delta wing with apex strake. A third study presents the ‘‘Interfacial PIV’’ technique for application in near-wall velocity profile determinations. The fourth study proposes a new PTV image processing algorithm adopted from an ant colony optimization. The next study in this section deals with supersonic flows for characterization of shock wave discontinuities inside a shock tube using nanosecond space discharge. A sixth study presents planar fluorescence imaging for identification of bubbles in an axisymmetric two-phase jet flow. The final paper in this section presents the effect of rim-shroud clearance on flows around a rotating disk. Two International Awards were presented during the plenary session to two international experts for their outstanding contributions to the field of flow visualization: (1) Dr. Juergen Kompenhans, DLR, Germany, Asanuma K. D. Kihm (&) Mechanical, Aerospace, and Biomedical Engineering Department, University of Tennessee, Knoxville, TN 37996, USA e-mail: kkihm@utk.edu

Friction drag reduction through damping of the near-wall spanwise velocity fluctuation

Direct numerical simulation (DNS) of a turbulent channel flow is performed in order to explore the possibility of reducing wall friction drag and saving energy through damping of the spanwise velocity fluctuation. Starting from an idealized feedback control, we extend the idea to a practically realizable control, in which only the streamwise wall shear stress is required as sensor input, while actuators of finite size are employed. This control scheme offers drag reduction of up to 20%, which is the highest value achieved by existing feedback controls based on the streamwise wall shear stress. In addition, the control power input remains two orders of magnitude smaller than the pumping power for the uncontrolled flow.

High Reynolds number effects in wall turbulence

A review of recent advances in the study of high Reynolds number turbulent boundary layers is given. The emergent regime of very large-scale structures in the logarithmic region and their subsequent influence on the near-wall cycle challenges many of the previously held assumptions regarding scaling of turbulent boundary layers at high Reynolds numbers. Experimental results are presented to illustrate the superimposition of large-scale energy onto the near-wall cycle, together with an interaction well described by an amplitude modulation effect. Both phenomena are shown to increase in magnitude (as compared to viscous-scaled events) as Reynolds number increases. These observations lead to a possible model for a statistically representative near-wall velocity signal (giving accurate energy spectra) based on a given filtered velocity signal from the log region of a high Reynolds number turbulent flow.

Interfacial PIV to resolve flows in the vicinity of curved surfaces

PIV measurements near a wall are generally difficult due to low seeding density, low velocity, high velocity gradient, and strong reflections. Such problems are often compounded by curved boundaries, which are commonly found in many industrial and medical applications. To systematically solve these problems, this paper presents two novel techniques for near-wall measurement, together named Interfacial PIV, which extracts both wall-shear gradient and near-wall tangential velocity profiles at one-pixel resolution. To deal with curved walls, image strips at a curved wall are stretched into rectangles by means of conformal transformation. To extract the maximal spatial information on the near-wall tangential velocity field, a novel 1D correlation function is performed on each horizontal pixel line of the transformed image template to form a “correlation stack”. This 1D correlation function requires that the wall-normal displacement component of the particles be smaller than the particle image diameter in order to produce a correlation signal. Within the image regions satisfying this condition, the correlation function yields peaks that form a tangential velocity profile. To determine this profile robustly, we propose to integrate gradients of tangential velocity outward from the wall, wherein the gradient at each wall-normal position is measured by fitting a straight line to the correlation peaks. The capability of Interfacial PIV was validated against Particle Image Distortion using synthetic image pairs generated from a DNS velocity field over a sinusoidal bed. Different velocity measurement schemes performed on the same correlation stacks were also demonstrated. The results suggest that Interfacial PIV using line fitting and gradient integration provides the best accuracy of all cases in the measurements of velocity gradient and velocity profile near wall surfaces.

Wall shear stress measurement of near-wall flow over inclined and curved boundaries by stereo interfacial particle image velocimetry

In investigations of laminar or turbulent flows, wall shear is often important. Nevertheless, conventional particle image velocimetry (PIV) is difficult in near-wall regions. A near-wall measurement technique, named interfacial PIV (IPIV) [Nguyen, C., Nguyen, T., Wells, J., Nakayama, A., 2008. Proposals for PIV of near-wall flow over curved boundaries. In: Proceedings of 14th International Symposium on Applications of Laser Technique to Fluid Mechanics], handles curved boundaries by means of conformal transformation, directly measures the wall gradient, and yields the near-wall tangential velocity profile at one-pixel resolution. In this paper, we show the feasibility of extending IPIV to measure wall gradients by stereo reconstruction. First, we perform a test on synthetic images generated from a direct numerical simulation (DNS) snapshot of turbulent flow over sinusoidal bed. Comparative assessment of wall gradients derived by IPIV, stereo-IPIV and particle image distortion (PID) [Huang, H.T., Fiedler, H.E., Wang, J.J., 1993. Limitation and improvement of PIV. Experiments in Fluids 15(4), 263–273] is evaluated with DNS data. Also, the sensitivity of IPIV and stereo-IPIV results to the uncertainty of identified wall position is examined. As a practical application of IPIV and stereo-IPIV to experimental images, results from turbulent open channel flow over a backward-facing step are discussed in detail.

SUPERCRITICAL TWO‐FLUID INTERACTIONS WITH SURFACE TENSION AND GRAVITY

Gravity and surface-tension effects are examined for inviscid–inviscid interactions between two fluids close to a wall. The ratios of density and viscosity of the two fluids are taken to be small. A nonlinear integro–differential equation is found to govern the near-wall flow velocity, interface shape and pressure; analysis, computation and comparisons are then applied. Travelling-state solutions are of particular interest.

Laminar dispersion at high Péclet numbers in finite-length channels: Effects of the near-wall velocity profile and connection with the generalized Leveque problem

This article develops the theory of laminar dispersion in finite-length channel flows at high Péclet numbers, completing the classical Taylor–Aris theory which applies for long-term, long-distance properties. It is shown, by means of scaling analysis and invariant reformulation of the moment equations, that solute dispersion in finite length channels is characterized by the occurrence of a new regime, referred to as the convection-dominated transport. In this regime, the properties of the dispersion boundary layer and the values of the scaling exponents controlling the dependence of the moment hierarchy on the Péclet number are determined by the local near-wall behavior of the axial velocity. Specifically, different scaling laws in the behavior of the moment hierarchy occur, depending whether the cross-sectional boundary is smooth or nonsmooth (e.g., presenting corner points or cusps). This phenomenon marks the difference between the dispersion boundary layer and the thermal boundary layer in the classical Leveque problem. Analytical and numerical results are presented for typical channel cross sections in the Stokes regime.