Fluid Velocity Gradient Research Articles

An analytical model for bedload layer thickness

A theoretical study has been carried out to determine the thickness of the bedload layer in an open channel turbulent flow with non-cohesive sediment, which is very crucial in sediment transport problems as this is treated as saltation height of a sediment particle and the reference level in suspension studies. A new expression of viscous shear stress is proposed, which is a function of effective viscosity of sediment–fluid mixture, velocity gradient and volumetric concentration of sediment particles. During particle collisions, impact shear stress is generated, which is another important parameter near the sediment bed. By including both the shear stresses, an expression for the thickness of the bedload layer is developed. The predicted bedload layer thickness is a function of viscous coefficient, impact coefficient, particle diameter, relative mass density of sediment particle, maximum bed concentration and non-dimensional shear stress. It agrees reasonably well when compared with a wide class of experimental data under different hydraulic conditions.

Floc Roll-Up and Its Implications for the Spacing of Inclined Settling Devices

Inclined plate and tube settlers are commonly used to make sedimentation tanks more compact. Conventional design equations for inclined settling devices are based on obtaining a desired particle capture velocity; these equations suggest that a suitable capture velocity can be achieved by reducing plate settler spacing or tube settler diameter below that specified in conventional design guidelines. Smaller spacing would reduce capital costs by decreasing the sedimentation tank volume. However, existing literature does not explain why smaller values of plate or tube spacing cannot be used, and failure mechanisms that set the minimum spacing recommended in design practice have not been documented. This research shows that the fluid velocity gradient at the tube or plate surface is the limiting constraint for spacing, and for very small spacing, particles that settle on the solid surface are carried up the incline. This failure mode, termed “floc roll-up,” occurs when the terminal velocity of a floc along the incline is less than the upward velocity of the fluid at the center of the floc. This article presents an experimental and theoretical investigation of the floc roll-up failure mode and its implications for plate settler design. A model was developed to explain the physics of floc roll-up, and experiments in a bench-scale water treatment apparatus demonstrated its effects on sedimentation performance. When subject to an increasing velocity gradient between the surfaces, turbidity removal in an experimental tube settler decreased from 90% to near zero, even when the traditional design equations would predict no degradation in performance. Both the model predictions and experimental results show that under some conditions, inclined settlers can employ closer spacing than the typical 5-cm design value without sacrificing turbidity removal performance.

Fabrication of Robust Hierarchical Micro/Nanostructures on Tin-Bronze Substrate

To reduce the generated heat due to fluid friction, it is desirable to minimize the drag force at the solid–liquid interface. The boundary slip facilitates fluid velocity gradient and then the drag reduction. This endeavor intends to seek a practical process for fabrication robust hierarchical structures on tin-bronze substrate. The ordered structures at micrometer scale are successfully fabricated by through-mask electrochemical micromachining (TM-EMM) and three candidate fabrication processes involving electroless galvanic deposition, surface oxidation and ZnO nanostructures growth via wet-chemical route for structures at nanometer scale on metal surface are investigated. The fabricated results have been demonstrated and their properties of stability and wettability were evaluated. Experimental study results show that combining TH-EMM with ZnO nanostructures growth presents an effective process for fabrication of firm multi-level structures on metal surface.

Development of a Fluorescent Molecular Rotor‐Based Approach for Concurrent Measurement of Blood Viscosity and Hemodynamics

Shear stress measurements are routinely calculated using local fluid velocity gradients and estimated static viscosity values. However, since blood viscosity is dependent on local hematocrit and is affected by non‐Newtonian shear‐thinning, a methodology allowing concurrent blood velocity and viscosity measurement should improve intracardiac shear mapping accuracy. Our objective was to develop such a methodology using viscosity‐sensitive fluorescent molecular rotors coupled to inert microspheres and validate the approach in a zebrafish model. Microinjection parameters have been optimized for effective delivery of rotors into the zebrafish vascular bed. Age‐dependent injection targets have been identified to facilitate reproducible bolus delivery. Finally, FCVJ reflect local hemodynamic profiles demonstrating a functionality consistent with their in vitro performance. Taken together, our data indicate that fluorescent molecular rotors provide the spatial and temporal resolution required for use in planar and volumetric digital defocusing particle image velocimetry (DDPIV) technology to facilitate real‐time 3‐dimensional in vivo shear mapping. (This work funded by AHA 10IRG4020025.)

Bacterial rheotaxis

The motility of organisms is often directed in response to environmental stimuli. Rheotaxis is the directed movement resulting from fluid velocity gradients, long studied in fish, aquatic invertebrates, and spermatozoa. Using carefully controlled microfluidic flows, we show that rheotaxis also occurs in bacteria. Excellent quantitative agreement between experiments with Bacillus subtilis and a mathematical model reveals that bacterial rheotaxis is a purely physical phenomenon, in contrast to fish rheotaxis but in the same way as sperm rheotaxis. This previously unrecognized bacterial taxis results from a subtle interplay between velocity gradients and the helical shape of flagella, which together generate a torque that alters a bacterium's swimming direction. Because this torque is independent of the presence of a nearby surface, bacterial rheotaxis is not limited to the immediate neighborhood of liquid–solid interfaces, but also takes place in the bulk fluid. We predict that rheotaxis occurs in a wide range of bacterial habitats, from the natural environment to the human body, and can interfere with chemotaxis, suggesting that the fitness benefit conferred by bacterial motility may be sharply reduced in some hydrodynamic conditions.

Kinetic responses of Dunaliella in moving fluids

The objective of this work was to quantify the kinetic behavior of Dunaliella primolecta (D. primolecta) subjected to controlled fluid flow under laboratory conditions. In situ velocities of D. primolecta were quantified by micron-resolution particle image velocimetry and particle tracking velocimetry. Experiments were performed under a range of velocity gradients and corresponding energy dissipation levels at microscopic scales similar to the energy dissipation levels of natural aquatic ecosystems. An average swimming velocity of D. primolecta in a stagnant fluid was 41 microm/s without a preferential flow direction. In a moving fluid, the sample population velocities of D. primolecta follow a log-normal distribution. The variability of sample population velocities was maximal at the highest fluid flow velocity in the channel. Local fluid velocity gradients inhibited the accrual of D. primolecta by twofold 5 days after the initiation of the experiment in comparison to the non-moving fluid control experiment.

Field synergy principle of heat and mass transfer

Simultaneous heat and mass transfer widely exists in nature and engineering, and it is of vital importance to enhance heat and mass transfer efficiency. In this paper, field synergy equation of heat and mass transfer is derived from its energy equation. Results show that the total transferred heat (including the conducted heat and the heat transferred by mass diffusion through the heat transfer interface) is determined by the values of fluid velocity and enthalpy gradient as well as the value of synergy angle α of velocity vector and enthalpy gradient field. Decreasing the value of α enhances the heat and mass transfer. This means the higher the synergy of velocity vector and enthalpy gradient field, the higher the total transferred heat. By the synergy principle of heat and mass transfer, some methods may be developed to improve the heat and mass transfer efficiency.

Fault-related dilation, permeability enhancement, fluid flow and mineral precipitation patterns: numerical models

Abstract Fault-related host rock deformation and dilation control fluid flow and mineralization in many world-class mineral deposits. This numerical modelling study explores the interactions between deformation, faulting, dilation, fluid flow and chemical processes, which are suggested to result in this control, with special attention to fault dilatant jog structures. Our two-dimensional numerical models focus on faulting-related deformation, dilation and permeability enhancement, fluid flow patterns and fluid focusing/mixing locations, while three-dimensional models examine several different cases of fault underlap and overlap. The results show that fault-dilation and faulting-induced permeability enhancement, which are closely associated with tensile failure, represent important ways to generate fluid flow conduits for more effective fluid flow and mixing. Dilation during strike–slip faulting is localized near fault tips (wing crack locations) and jog sites, where fluids are strongly focused and mixed. These locations are the tensile domains of the strike–slip regime. In overlapping-fault (dilatant jog) cases, the magnitude of dilation and the extent of the dilatant region are closely related to the extent of fault overlap. These results provide insight into the transport of fluids through low-permeability rocks with isolated, but more permeable, faults. Gold and quartz precipitation patterns as a result of the coupling of chemical reactions to deformation induced fluid flow velocities are also computed. The rates of precipitation depend on structural and fluid flow conditions and on the geometrical relation between local fluid velocity and chemical concentration gradients generated by mixing. Maximum precipitation rates for gold occur in the dilation zones and in faults where high fluid flow rates, sufficient fluid mixing and high concentration gradients of critical chemical species are all present, while the quartz precipitation rate is predominantly controlled, in this isothermal situation, by the rate of fluid flow across concentration gradients in the aqueous silica concentration.

A Unifying Perspective on the Quasi-steady Analysis of Magnetorheological Dampers

A magnetorheological (MR) fluid, modeled as a Bingham plastic (BP) material, is characterized by a field dependent yield stress, and a (nearly constant) postyield plastic viscosity. Based on viscometric measurements, such a BP model is an idealization to physical MR behavior, albeit a useful one. A better approximation involves modifying both the preyield and postyield constitutive behavior as follows: (1) assume a high viscosity preyield behavior when the shear stress is less than the transition stress, and (2) assume a power law fluid (i.e., strain rate dependent viscosity) when the shear stress is greater than the transition stress. Assuming a power law fluid in postyield allows the model to account for shear thinning behavior exhibited by MR fluids at higher strain rates. Such an idealization for MR fluid constitutive behavior is called an viscous-power law model, or a Herschel—Bulkley (HB) model with preyield viscosity. This study develops a quasi-steady analysis for such a constitutive MR fluid behavior applied to an MR flow mode damper. Closed form solutions are developed for the fluid velocity, as well as key performance metrics, such as damping capacity and dynamic range (ratio of field-on to field-off force). For the given fluid properties and flow mode damper geometry, the fluid velocity profile and gradient, and the relationship of the damper force and piston velocity are analyzed. In addition, specializations to existing models, such as the HB, biviscous, and BP models, are shown to be easily captured by this model when physical constraints (idealizations) are placed on the rheological behavior of the MR fluid.

Sequential Field-Flow Cell Separation Method in a Dielectrophoretic Chip With 3-D Electrodes

This paper presents a sequential dielectrophoretic field-flow separation method for particle populations using a chip with a 3-D electrode structure. A unique characteristic of our chip is that the walls of the microfluidic channels also constitute the device's electrodes. This property confers the opportunity to use the electrodes' shape to generate not only the electric field gradient required for dielectrophoretic force but also a fluid velocity gradient. This interesting combination gives rise to a new solution for the dielectrophoretic separation of two particle populations. The proposed sequential field-flow separation method consists of four steps. First, the microchannel is filled with the mixture of the two populations of particle. Second, the particle populations are trapped in different locations of the microfluidic channels. The population, which exhibits positive dielectrophoresis (DEP), is trapped in the area where the distance between the electrodes is the minimum, while the other population that exhibits negative DEP is trapped in locations of maximum distance between electrodes. In the next step, increasing the flow in the microchannels will result in an increased hydrodynamic force that sweeps the cell population trapped by positive DEP out of the chip. In the last step, the electric field is removed, and the second population is swept out and collected at the outlet. For theoretical and experimental exemplification of the separation method, a population of viable and nonviable yeast cells was considered.

Inertial particles driven by a telegraph noise

We present a model for the Lagrangian dynamics of inertial particles in a compressible flow, where fluid velocity gradients are modeled by a telegraph noise. The model allows for an analytic investigation of the role of time correlation of the flow in the aggregation-disorder transition of inertial particles. The dependence on the Stokes number St and the Kubo number Ku of the Lyapunov exponent of particle trajectories reveals the presence of a region in parameter space (St, Ku), where the leading Lyapunov exponent changes sign, thus signaling the transition. The asymptotics of short- and long-correlated flows are discussed, as well as the fluid-tracer limit.

Electrokinetic Hydrogen Generation from Liquid Water Microjets

We describe a method for generating molecular hydrogen directly from the charge separation effected via rapid flow of liquid water through a metal orifice, wherein the input energy is the hydrostatic pressure times the volume flow rate. Both electrokinetic currents and hydrogen production rates are shown to follow simple equations derived from the overlap of the fluid velocity gradient and the anisotropic charge distribution resulting from selective adsorption of hydroxide ions to the nozzle surface. Pressure-driven fluid flow shears away charge balancing hydronium ions from the diffuse double layer and carries them out of the aperture. Downstream neutralization of the excess protons at a grounded target electrode produces gaseous hydrogen molecules. The hydrogen production efficiency is currently very low (ca. 10-6) for a single cylindrical jet but can be improved with design changes.

Continuous field-flow separation of particle populations in a dielectrophoretic chip with three dimensional electrodes

This letter presents a dielectrophoretic (DEP) separation method of particles under continuous flow. The method consists of flowing two particle populations through a microfluidic channel, in which the vertical walls are the electrodes of the DEP device. The irregular shape of the electrodes generates both electric field and fluid velocity gradients. As a result, the particles that exhibit negative DEP can be trapped in the fluidic dead zones, while the particles that experience positive DEP are concentrated in the regions with high velocity and collected at the outlet. The device was tested with dead and living yeast cells.

An upper bound for passive scalar diffusion in shear flows

This study is concerned with the diffusion of a passive scalar Θ(r,t) advected by general n-dimensional shear flows u=u(y,z,…,t)x̂ having finite mean-square velocity gradients. The unidirectionality of the incompressible flows conserves the streamwise scalar gradient, ∂xΘ, allowing only the cross-stream components to be amplified by shearing effects. This amplification is relatively weak because an important contributing factor, ∂xΘ, is conserved, effectively rendering a slow diffusion process. It is found that the decay of the scalar variance ⟨Θ2⟩ satisfies d⟨Θ2⟩∕dt≥−Cκ1∕3, where C>0 is a constant, depending on the fluid velocity gradients and initial distribution of Θ, and κ is the molecular diffusivity. This result generalizes to axisymmetric flows on both the plane and sphere having finite mean-square angular velocity gradients.

Direct measurement of fluid velocity gradients at a wall by PIV image processing with stereo reconstruction

Velocity gradient is typically estimated in Particle Image Velocimetry (PIV) by differentiating a measured velocity field, which amplifies noise in the measured velocities. If gradients near a boundary are sought, such noise is usually greater than in bulk fluid, because of small tracer displacement, uncertainty in the effective positions of velocity vectors, intense deformation of tracer patterns, and laser reflection. We consider here a modified form of the Particle Image Distortion (PID) method to directly calculate velocity gradients at a fixed wall, and refer it as "PIV/IG" ("Interface Gradiometry"). Results from synthetic 2D PIV images suggest our method achieves higher SNR and accuracy than velocity differentiation. Also, we have developed a procedure to reconstruct three-dimensional velocity gradient at a fixed wall the two non-zero components from PIV/IG data obtained in stereo views; these equations simplify considerably thanks to the no-slip condition. Experimental data from the bottom wall of turbulent open channel flow appear to suffer from a form of pixel locking. As with standard PIV, this underlines the importance of adequate tracer diameter in the images, sufficient seeding density, and of dynamic range of the camera sensor.

Orientation distribution of cylindrical particles suspended in a turbulent pipe flow

A model of turbulent cylindrical particle suspensions is proposed to predict the orientation distribution of particles. The fluctuating equation for the orientation distribution function (ODF) of cylindrical particles is theoretically solved using the method of characteristics. The orientation-correlated terms in the mean equation for the ODF due to the random motion of cylindrical particles are related to the correlations of the mean ODF and the fluid velocity gradient. Thus, the evolution of the mean ODF is described by a modified convection-dispersion equation. The model and modified equation are used to calculate the ODF in a pipe flow numerically. The results compare qualitatively with the experimental data and show that the turbulent dispersion makes cylindrical particles have a broad orientation distribution, while the velocity gradient plays an opposite role. The increase of the particle aspect ratio leads to a less aligned distribution in the vicinity of the axis and a narrower orientation distribution at positions far from the axis.

Characterization of near-wall accumulation regions for inertial particles in turbulent boundary layers

In this paper, we examine particle distribution in the wall region of turbulent boundary layers, considering specific flow conditions (Reτ=150) and spanning two orders of magnitude of particle inertial parameter—the particle timescale. First, we identify the flow timescales that govern particle distribution, examining the degree of particle preferential concentration and determining the optimum in connection with particle timescale. Second, we identify which of the flow variables may be used to control particle distribution. These are the streamwise and spanwise shear stress components at the wall, which correspond to the only nonvanishing elements of the fluctuating fluid velocity gradient tensor.

Full Lagrangian methods for calculating particle concentration fields in dilute gas-particle flows

The paper discusses two Full Lagrangian methods for calculating the particle concentration and velocity fields in dilute gas-particle flows. The methods are mathematically similar but crucially different in application. By examining the analytical solution for two-phase stagnation-point flow, it is shown that Osiptsov's method is more general than that of Fernandez de la Mora and Rosner. In Osiptsov's method, the Jacobian of the Eulerian–Lagrangian transformation is computed by integration along particle pathlines. The particle concentration is then obtained algebraically from the Lagrangian form of the particle continuity equation. It is shown that the correct specification of the initial conditions is non-trivial and of vital importance. A technique to alleviate problems of mathematical ‘stiffness’ at small Stokes numbers is also described. Full Lagrangian methods require knowledge of the fluid velocity gradient field and, if the carrier flowfield is calculated numerically, differentiation of a ‘noisy’ field can result in serious errors. The paper describes a method for reducing these errors. The incompressible, inviscid flow over a cylinder provides a useful test case for validation and the Osiptsov method proves its worth by revealing a region, hitherto unknown, of crossing particle pathlines in the mathematical solution. Crossing pathlines and their relationship to Robinson's integral are then discussed, and calculations of particle flow through a turbine cascade at high Mach numbers are presented to illustrate the engineering potential of the method.

Is the tracer velocity of a fluid continuum equal to its mass velocity?

Owing to its size independence in the so-called near-continuum vanishingly small Knudsen number regime (Kn<<1) , thermophoretic particle motion occurring in an otherwise quiescent gas under the influence of a temperature gradient is here interpreted as representing the motion of a tracer, namely, an effectively point-size test particle monitoring the local velocity of the undisturbed, particle-free, compressible gas continuum through space. "Compressibility" refers here not to the usual effect of pressure on the gas's mass density rho but rather to the effect thereon of temperature. Our unorthodox continuum interpretation of thermophoresis differs from the usual one, which regards the existence of thermophoretic forces in gases as a strictly noncontinuum phenomenon, involving thermal stress-induced Maxwell slip ("thermal creep") of the gas's mass velocity vm at the surface of the particle, with vm denoting the velocity appearing in the continuity equation expressing the law of conservation of mass. Explicitly, instead of regarding the thermally animated particle as moving through the gas, we regard the particle (in its hypothesized role as a tracer of the undisturbed, particle-free, fluid motion) as moving with the gas, through space; that is, the particle is viewed as simply being entrained in the flowing gas, which, as a result of an externally applied temperature gradient, was already in motion prior to the tracer's introduction into the fluid--albeit not mass motion (which is, in fact, identically zero) but rather volume motion. This tracer-particle interpretation of experimental thermophoretic particle velocity measurements raises fundamental issues in regard to the universally accepted Newtonian rheological law constitutively specifying the viscous or deviatoric stress T as being proportional to the (symmetrized, traceless) fluid velocity gradient inverted Deltav , with v identified as being the fluid's mass velocity vm . Rather, it is argued in the case of compressible fluids, including liquids, that v should, instead, be chosen as the fluid's volume flux density or current density nv , the latter being formally equivalent to the fluid's volume velocity vv , which differs from vm except in the case of incompressible fluids. Apart from this strictly constitutive issue in regard to T , it is further argued that the fluid's tracer or Lagrangian velocity vl:=(deltax/deltat) (x0) along the fluid's spatiotemporal trajectory x=x (x0,t) is equal to vv, rather than to vm. This too is contrary to the heretofore unquestioned supposition that the conceptually distinct fluid velocities vl and vm are not only equal but are, in fact, synonymous. To the extent that vl not equal vm in the nonisothermal fluid case, an optical dye- or photochromic-type experiment (each of the latter two experiments presumably serving to measure vm) will record a different velocity than would a comparable tracer particle velocity measurement, one that measures vl .

Analysis of field synergy on natural convective heat transfer in porous media

Based on the mathematical model to describe simultaneous heat, moisture and gas migration in porous media, the idea of enhancing convective heat transfer by the synergy between velocity and temperature gradient is appliedto derive the expressions about natural convective heat transfer in unsaturated porous media. The final expressions are written as two formulas for the overall and local heat transfer coefficients between the fluid and the wall. For the rectangular porous enclosure with the length-to-width aspect ratio of three, the phenomenon of field synergy on natural convection in unsaturated porous media is observed and verified through numerical calculations, which indicates that the strength of natural convection in porous media is determined not only by temperature difference, fluid velocity and fluid properties, but also by the synergy between fluid velocity and temperature gradient.