Curvilinear Channel Research Articles

Mixing of passive tracers in the decay Batchelor regime of a channel flow

We report detailed quantitative studies of passive scalar mixing in a curvilinear channel flow, where elastic turbulence in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent was achieved. For quantitative investigation of mixing, a detailed study of the profiles of mean longitudinal and radial components of the velocity in the channel as a function of Wi was carried out. Besides, a maximum of the average value as well as a rms of the longitudinal velocity was used to determine the threshold of the elastic instability in the channel flow. The rms of the radial derivatives of the longitudinal and radial velocity components was utilized to define the control parameters of the problem, the Weissenberg Wiloc and the Péclet Pe numbers. The main result of these studies is the quantitative test of the theoretical prediction about the value of the mixing length in the decay Batchelor regime. The experiment shows large quantitative discrepancy, more than 200 times in the value of the coefficient C, which appears in the theoretical expression for the mixing length, but with the predicted scaling relation. There are two possible reasons to this discrepancy. First is the assumption made in the theory about the δ-correlated velocity field, which is in odds with the experimental observations. Second, and probably a more relevant suggestion for the significantly increased mixing length and thus reduced mixing efficiency, is the observed jets, the rare, localized, and vigorous ejection of the scalar trapped near the wall, which protrudes into the peripheral region as well as the bulk. They are first found in the recent numerical calculations and then observed in the experiment reported. The jets definitely strongly reduce the mixing efficiency in particular in the peripheral region and so can lead to considerable increase of the mixing length. We hope that this result will initiate further numerical calculations of the mixing length. Finally, we analyze statistical properties of the mixing in the decay Batchelor regime by studying the power spectra, the decay exponents scaling, the structure functions of a tracer and moments of PDF of passive scalar increments, and the temporal and spatial correlation functions and find rather satisfactory agreement with theory.

Математическое моделирование криволинейных течений газа

The results of mathematical design of gas flow in curvilinear channels with the reserved contours are considered in the article. Migration of maximum of circuitous speed of gas from the wall of channels peripheral to central with the increase of corner of turn is exposed. Correlation between the parameters of flow is shown.

Generation of Helicity and the Critical Transitions in a Twisted Flow of a Single-Phase Liquid

Equations to determine the rate of change of the helicity in a dynamic liquid system are obtained. For the convenience of carrying out engineering calculations the equations are presented in dimensional and dimensionless forms. The conditions for critical transition to a helical character of a twisted flow and to the crisis-induced rearrangement of the flow velocity field due to the change in the flow vortex structure are considered. A new physical model of the vortex motion of a liquid is suggested. It allows one to explain a number of phenomena: the effect of spontaneous flow twisting in the collectors of tank-type nuclear reactors; the reason for the considerable increase in the nonuniformity of the radial distribution of pressure at the inlet into the active zone for liquid-metal heat-transfer agents as compared to the water one; the crisis-induced rearrangement of the flow velocity field with formation of large-scale vortex structures during flow in curvilinear channels and of spiral vortices on curvilinear surfaces.

Highly efficient capture and enumeration of low abundance prostate cancer cells using prostate-specific membrane antigen aptamers immobilized to a polymeric microfluidic device.

Prostate tumor cells over-express a prostate-specific membrane antigen (PSMA) that can be used as a marker to select these cells from highly heterogeneous clinical samples, even when found in low abundance. Antibodies and aptamers have been developed that specifically bind to PSMA. In this study, anti-PSMA aptamers were immobilized onto the surface of a capture bed poised within a PMMA, microchip, which was fabricated into a high-throughput micro-sampling unit (HTMSU) used for the selective isolation of rare circulating prostate tumor cells resident in a peripheral blood matrix. The HTMSU capture bed consisted of 51 ultra-high-aspect ratio parallel curvilinear channels with a width similar to the prostate cancer cell dimensions. The surface density of the PSMA-specific aptamers on an ultraviolet-modified PMMA microfluidic capture bed surface was determined to be 8.4 x 10(12) molecules/cm(2). Using a linear velocity for optimal cell capture in the aptamer-tethered HTMSU (2.5 mm/s), a recovery of 90% of LNCaP cells (prostate cancer cell line; used as a model in this example) was found. Due to the low abundance of these cells, the input volume required was 1 mL and this could be processed in approximately 29 min using an optimized linear flow rate of 2.5 mm/s. Captured cells were subsequently released intact from the affinity surface using 0.25% w/w trypsin followed by counting individual cells using a contact conductivity sensor integrated into the HTMSU that provided high detection and sampling efficiency (approximately 100%) and did not require staining of the cells for enumeration.

Experimental and numerical investigation of separated flows in subsonic diffusers

The results of a special investigation of the diffuser flowfield are presented for two models of curvilinear diffuser channels with annular and rectangular cross-sections. The flow is visualized and the total pressure fields are measured by means of low-inertia transducers. At the same time, the flows are numerically calculated using commercial programs, together with codes developed by the authors. In these calculations the stationary and time-dependent Reynolds equations closed by different turbulence models, as well as the time-dependent Navier-Stokes equations, were integrated. A considerable difference between the measured data and the results of the numerical calculations in the stationary formulation is found to exist. At the same time, it has been possible to describe the occurrence of spatial inhomogeneities, the flow pattern, and the level of the experimentally observed aerodynamic losses on the basis of the solution of time-dependent problems.

Interaction of a glow discharge with a rarefied hypersonic flow in a curvilinear channel

A two-dimensional simulation model is used to study the gasdynamic structure of a rarefied hypersonic flow of molecular nitrogen in a curvilinear channel in which the lower surface carries the cathode section of the discharge gap whereas the upper surface serves as the anode. The electrodynamic structure of the glow discharge (the distribution of concentrations of charged species, current density, and electric potential) is examined. It was demonstrated that the burning of a glow discharge in a rarefied hypersonic flow makes it possible to effectively modify the shock wave structure of the flow.

Use of the large-particle method for calculating three-phase flows in convergent channels

This study deals with applying the large-particle method to the flow of three-phase media in convergent channels (confusers). A hydrodynamic flow pattern is studied in a wide range of variation of determining parameters of an undisturbed flow. Special attention is paid to the modes of motion of gas-dispersed flows in curvilinear channels with the large mass content of a dispersed phase at the inlet of the confuser.

Asymptotic solution for a micropolar flow in a curvilinear channel

AbstractThis paper is concerned with an asymptotic approach for a micropolar flow through a thin curvilinear channel. A priori estimates (which we obtain together with the existence and the uniqueness of the solution) are used to establish the error between the exact solution and the asymptotic one and to justify the asymptotic analysis. We obtain the expression of an expansion of order K and we study the general problems for the boundary layer functions. Under some additional assumptions on the data we obtain satisfactory error estimates.

Mass transfer in a two-phase flow in a curvilinear channel

In this paper, the results of an experimental investigation of the distribution of local coefficients of mass transfer on a pipe wall for a flow of a two-phase gas-liquid mixture with a turn of 90° are presented. The mass transfer coefficients were measured by using an electrodiffusion method. It has been shown that the distribution of local mass transfer coefficients on the inner surface of a curvilinear channel is nonuniform both in length and along the perimeter and depends on the content of gas in the two-phase flow.

Pressing a rigid-plastic strip through a curvilinear matrix channel

We develop a model that describes pressing a rigid-plastic strip through a curvilinear matrix channel; this model takes into account the material strengthening, the gap between the strip and the matrix channel, and the contact friction. We present examples of computations of the strip pressing through channels of various shapes. The model imitates the technological processes of a thin strip bending by pressing it through a curvilinear matrix channel.

Structure of Hydrated Na−Nafion Polymer Membranes

We use molecular dynamics simulations to investigate the structure of the hydrated Na-Nafion membranes. The membrane is "prepared" by starting with the Nafion chains placed on a cylinder having the water inside it. Minimizing the energy of the system leads to a filamentary hydrophilic domain whose structure depends on the degree of hydration. At 5 wt % water the system does not have enough water molecules to solvate all the ions that could be formed by the dissociation of the -SO3Na groups. As a result, the -SO3Na groups aggregate with the water to form very small droplets that do not join into a continuous phase. The size of the droplets is between 5 and 8 A. As the amount of water present in the membrane is increased, the membrane swells, and SO3Na has an increasing tendency to dissociate into ions. Furthermore, a transition to a percolating hydrophilic network is observed. In the percolating structure, the water forms irregular curvilinear channels branching in all directions. The typical dimension of the cross section of these channels is about 10-20 A. Calculated neutron scattering from the simulated system is in qualitative agreement with experiment. In all simulations, the pendant sulfonated perfluorovinyl side chains of the Nafion hug the walls of the hydrophilic channel, while the sulfonate groups point toward the center of the hydrophilic phase. The expulsion of the side chains from the hydrophilic domain is favored because it allows better interaction between the water molecules. We have also examined the probability of finding water molecules around the Na+ and the -SO3(-) ions as well as the probability of finding other water molecules next to a given water molecule. These probabilities are much broader than those found in bulk water or for one ion in bulk water (calculated with the potentials used in the present simulation). This is due to the highly inhomogeneous nature of the material contained in the small hydrophilic pores.

Mathematical Modeling of the Flow of a Multiphase Heterogeneous Medium in a Permeable Tube

A mathematical model for calculating the flow of a rheologically complex disperse medium in a curvilinear permeable channel in which the concentration of suspended particles in the flow is variable and a cake is formed on the walls is proposed. The model can describe the filtration of a heterogeneous medium in permeable channels and generally takes into account the hydraulic resistance of the wall. Equations for calculating the variation of the average concentration of the disperse phase and the cake thickness are derived. A numerical computational algorithm is developed. Numerically calculated profiles of velocity, pressure, concentration, and cake thickness taking into account the process at the channel inlet section are presented.

Fluid dynamics of spacer filled rectangular and curvilinear channels

Spacers are designed to generate significant secondary flow structures and create directional changes in the flow through membrane modules. Shape of the spacers used in membrane modules strongly influences the resulting flow and therefore performance of the module. In this work fluid dynamics of rectangular channels similar to membrane modules and containing different spacers was simulated using a three-dimensional computational fluid dynamics (CFD) model. A ‘unit cell’ approach was evaluated and used for this purpose. In addition to predicting the pressure drop, the simulated results provided significant insight into fluid dynamics of spacer filled channels. The validated CFD model was used to evaluate performance of different spacer shapes and understand the role of spacer shape and resulting fluid dynamics. The models were extended for the first time to simulate flow in spacer filled curvilinear channels, which could be useful in understanding the fluid behavior in spiral modules. The results were compared with those obtained with the flat channel. The approach and results presented in this work will have significant implications for identifying improved spacers with higher propensities to reduce fouling in membrane modules.

Laminar forced convection in curved channel with vortex structures

Theoretical and experimental investigations of heat transfer in flat curvilinear channel have been carried out. Linear and non-linear effects of Dean vortexes on intensity of heat transfer were taken into account. The linear effect, which describe harmonic (sinuous) variation of the heat transfer coefficient near the concave surface of the channel and the non-linear effect causes the general increase of the heat transfer coefficient due to augmentation of heat transfer engendered by the Dean vortexes. For both effects, mathematical relations were obtained in the form of quadratures. These numerical results were modified to the form convenient in engineering calculations. The investigations have shown that both linear and nonlinear components grow up with the Dean number. Nonlinear component \(Q\frac{T}{0}\) increases more abruptly, while the linear one \(Q\frac{T}{1}\) is more conservative. This is a confirmation of stability of vortex structures.

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A Groisman and V Steinberg 2000 Nature 405 53), we present an extended account of experimental observations of elasticity-induced turbulence in three different systems: a swirling flow between two plates, a Couette–Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had a high ratio of the width of the region available for flow to the radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high-molecular-weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. They include: (i) randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales and (ii) significant increase in the rates of momentum and mass transfer (compared with those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms and parameter dependence of the elastic turbulence are compared with those of the conventional high-Re hydrodynamic turbulence in Newtonian fluids. Some similarities as well as multiple principal differences were found. In two out of three systems (swirling flow between two plates and flow in the curvilinear channel), power spectra of velocity fluctuations decayed rather quickly, following power laws with exponents of about −3.5. It suggests that, being random in time, the flow is rather smooth in space, in the sense that the main contribution to deformation and mixing (and, possibly, elastic energy) is coming from flow at the largest scale of the system. This situation, random in time and smooth in space, is analogous to flows at small scales (below the Kolmogorov dissipation scale) in high-Re turbulence.

Curvature-Induced Dispersion in Electro-Osmotic Serpentine Flows

Flow and transport phenomena occurring within serpentine microchannels are analyzed for both two- and three-dimensional curvilinear configurations. The microfluidic conduit is modeled as a spatially periodic "thin" channel, enabling asymptotic expansions of the pertinent transport fields in terms of a small parameter $\epsilon$, representing the ratio of channel (half-)width to curvilinear channel length per serpentine period. The electric potential distribution, as well as the attendant electro-osmotic flow field, is calculated for the limiting case where the Debye layer thickness is small relative to the channel width. Generalized Taylor--Aris dispersion theory is employed to calculate the serpentine-scale velocity and dispersivity of a charged point-size colloidal Brownian particle ("molecule") entrained in the solvent Stokes flow engendered by the electrokinetic forces. These respective macrotransport coefficients are expressed, inter alia, in terms of quadratures of the local curvature within a unit cell of the serpentine device.

Laminar Forced Convection in Curved Channel with Vortex Structures

Theoretical and experimental investigations of heat transfer in flat curvilinear channel have been carried out. Linear and non-linear effects of Dean vortexes on intensity of heat transfer were taken into account. The linear effect, which describe harmonic (sinuous) variation of the heat transfer coefficient near the concave surface of the channel and the non-linear effect causes the general increase of the heat transfer coefficient due to augmentation of heat transfer engendered by the Dean vortexes. For both effects, mathematical relations were obtained in the form of quadratures. These numerical results were modified to the form convenient in engineering calculations. The investigations have shown that both linear and nonlinear components grow up with the Dean number. Nonlinear component \(Q\frac{T}{0}\) increases more abruptly, while the linear one \(Q\frac{T}{1}\) is more conservative. This is a confirmation of stability of vortex structures.

Spatial Connectivity: From Variograms to Multiple-Point Measures

Anisotropy and curvilinearity are common characteristics of geological structures. Traditional measures of connectivity such as the variogram are rectilinear in that they do not take into account the curvilinearity of these structures. Recent developments in geostatistics have demonstrated and simulated the effect of curvilinearity and multiple-point (mp) connectivity on the output of transfer functions such as flow simulators. A set of curvilinear channels and set of elliptical lenses may share the same variogram and rectilinear connectivity but would yield different flow responses because of their different curvilinearity. A measure of curvilinearity generalizing the variogram measure is therefore proposed. The proposed measure is directional with a tolerance cone and depends on distance with a tolerance, as with an experimental variogram.

Dispersion by Pressure-Driven Flow in Serpentine Microfluidic Channels

Microfluidic hydrodynamic chromatography performed in serpentine microchannels etched on chips is analyzed in the limiting case of chips containing a large number of periodically arrayed turns. Comparison is made between these results and those for a straight channel of the same length as the curvilinear channel, all other things being equal. Explicitly, generalized Taylor−Aris dispersion (macrotransport) theory for spatially periodic systems is adapted to compute the chip-scale solute velocity Ū* and dispersivity D* for effectively point-size, physicochemically inert Brownian particles entrained in a low Reynolds number, pressure-driven solvent flow occurring within the curvilinear interstices of such serpentine devices. Attention is focused upon relatively thin channels of uniform cross section, enabling the various transport fields pertinent to the problem to be expressed as regular perturbation expansions with respect to a small dimensionless parameter e, representing the ratio of channel half-width ...

Method of calculating planar and nonplanar problems of molecular gas flow in curvilinear channel with moving walls

The article presents a theoretical model for calculating the planar and nonplanar problems of the molecular gas flow through channels with moving walls. The useful approximations of impingent fluxes of molecule number, impulse and kinetic energy for reducing the calculating time are given. The principle equations for the mathematical description of gas flow in planar and nonplanar problems are presented. The suggested equations one can solve by iteration techniques.