Overlimiting Current in Nonuniform Arrays of Microchannels: Recirculating Flow and Anticrystallization

Nano Letters ◽  
2021 ◽  
Author(s):  
Hyekyung Lee ◽  
Seoyun Sohn ◽  
Shima Alizadeh ◽  
Soonhyun Kwon ◽  
Tae Jin Kim ◽  
...  
Keyword(s):  
Recirculating Flow ◽  
Overlimiting Current

Laminar natural convection about an isothermally heated sphere at small Grashof number

1968 ◽  
Vol 34 (1) ◽  
pp. 163-176 ◽  
Author(s):  
Francis E. Fendell
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Perturbation Expansion ◽  
Outer Sphere ◽  
Convective Transport ◽  
Convection Flow ◽  
Constant Density ◽  
Boussinesq Model ◽  
Grashof Number ◽  
Recirculating Flow

The flow induced by gravity about a very small heated isothermal sphere introduced into a fluid in hydrostatic equilibrium is studied. The natural-convection flow is taken to be steady and laminar. The conditions under which the Boussinesq model is a good approximation to the full conservation laws are described. For a concentric finite cold outer sphere with radius, in ratio to the heated sphere radius, roughly less than the Grashof number to the minus one-half power, a recirculating flow occurs; fluid rises near the inner sphere and falls near the outer sphere. For a small heated sphere in an unbounded medium an ordinary perturbation expansion essentially in the Grashof number leads to unbounded velocities far from the sphere; this singularity is the natural-convection analogue of the Whitehead paradox arising in three-dimensional low-Reynolds-number forced-convection flows. Inner-and-outer matched asymptotic expansions reveal the importance of convective transport away from the sphere, although diffusive transport is dominant near the sphere. Approximate solution is given to the nonlinear outer equations, first by seeking a similarity solution (in paraboloidal co-ordinates) for a point heat source valid far from the point source, and then by linearization in the manner of Oseen. The Oseen solution is matched to the inner diffusive solution. Both outer solutions describe a paraboloidal wake above the sphere within which the enthalpy decays slowly relative to the rapid decay outside the wake. The updraft above the sphere is reduced from unbounded growth with distance from the sphere to constant magnitude by restoration of the convective accelerations. Finally, the role of vertical stratification of the ambient density in eventually stagnating updrafts predicted on the basis of a constant-density atmosphere is discussed.

Turbulence structure of a reattaching mixing layer

1981 ◽  
Vol 110 ◽  
pp. 171-194 ◽  
Author(s):  
C. Chandrsuda ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Shear Stress ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Flow Region ◽  
Turbulent Energy ◽  
Turbulence Structure ◽  
Hot Wire ◽  
Recirculating Flow

Hot-wire measurements of second- and third-order mean products of velocity fluctuations have been made in the flow behind a backward-facing step with a thin, laminar boundary layer at the top of the step. Measurements extend to a distance of about 12 step heights downstream of the step, and include parts of the recirculating-flow region: approximate limits of validity of hot-wire results are given. The Reynolds number based on step height is about 105, the mixing layer being fully turbulent (fully three-dimensional eddies) well before reattachment, and fairly close to self-preservation in contrast to the results of some previous workers. Rapid changes in turbulence quantities occur in the reattachment region: Reynolds shear stress and triple products decrease spectacularly, mainly because of the confinement of the large eddies by the solid surface. The terms in the turbulent energy and shear stress balances also change rapidly but are still far from the self-preserving boundary-layer state even at the end of the measurement region.

Theoretical and Experimental Characterization of Emulsion Flow in a Cavity Transfer Mixer

2003 ◽  
Author(s):  
A. H. Raza ◽  
R. A. Lai-Fook ◽  
C. J. Lawrence
Keyword(s):  
Flow Characteristics ◽  
Axial Direction ◽  
Solution Procedure ◽  
Modes Of Operation ◽  
Flow Equations ◽  
Recirculating Flow ◽  
Rectangular Pattern ◽  
Mean Pressure ◽  
Emulsion Processing ◽  
Dependent Flow

A theoretical model of time-dependent flow based on Reynolds equation using emulsion processing in a Cavity Transfer Mixer (CTM) has been developed in Mathematica and is presented in this work. It is a continuum model, which allows the study of materials undergoing rapid deformation. The flow of a fluid in a CTM is examined using a finite difference analysis (FDA) to solve the flow equations for an unwound section with cavities arranged in a rectangular pattern. Periodic boundary conditions are included in the model to predict the pressure distribution, which allows subsequent determination of the flow field. The solution procedure gives a smooth function for the pressure field, with equal pressures at the boundaries in the y-direction and an overall mean pressure gradient in the x-direction. Once the pressure has been found, several flow properties follow directly. The flow in the downstream axial direction is seen to consist of purely pressure-driven flow. In contrast, the flow in the cross-cavity direction is a recirculating flow driven by the drag velocity of the moving rotor surface. These two flows taken together combine into a helical flow travelling through the cavity. Because of this, there is likely to bre a high degree of laminar and distributive flow in this type of machine. The experimental part of this work addresses the processing of an emulsion in the CTM when it is run under batch and continuous modes of operation. The flow characteristics have been studied for varying rotor speeds of 0 rpm, 16 rpm, 32 rpm, 48 rpm and 64 rpm. Also studied were the changes that the emulsion exhibits along the mixer length and with time in the mixer. The experiments indicate that increase in the rotational speed causes the viscosity to reduce systematically in both batch and continuous modes of operation.

The Effects of a Hydrostatic Pocket Aspect Ratio, Supply Orifice Position, and Attack Angle on Steady-State Flow Patterns, Pressure, and Shear Characteristics

1993 ◽  
Vol 115 (4) ◽  
pp. 678-685 ◽  
Author(s):  
M. J. Braun ◽  
F. K. Choy ◽  
Y. M. Zhou
Keyword(s):  
Stokes Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Computational Error ◽  
Convergence Criteria ◽  
Steady State Flow ◽  
Shear Forces ◽  
Navier Stokes Equations ◽  
Recirculating Flow ◽  
Shear Characteristics

The flow in a hydrostatic pocket is described by a mathematical model that uses the Navier-Stokes equations written in terms of the primary variables, u, v, and p. Using the conservative formulation, a finite difference method is applied through a staggered grid. The power law scheme is applied in the treatment of the convective terms for this highly recirculating flow. The discussion pertaining to the convergence of the numerical scheme and the computational error, shows that the strict convergence criteria applied to both velocities and pressure were successfully statisfied. The numerical model is applied in a parametric mode to the study of the velocities, the pressure patterns, and shear forces that characterize the flow in a square (α = 1), deep (α>1), and shallow (α≪1) hydrostatic pocket. The effects of the variation of the location and angle of the hydrostatic jet are also investigated.

Effects of the air layer of an idealized superhydrophobic surface on the slip length and skin-friction drag

2016 ◽  
Vol 790 ◽  
Author(s):  
Taeyong Jung ◽  
Haecheon Choi ◽  
John Kim
Keyword(s):  
Drag Reduction ◽  
Skin Friction ◽  
Superhydrophobic Surface ◽  
Slip Length ◽  
Joint Probability ◽  
Turbulent Channel Flow ◽  
Water Interface ◽  
Friction Drag ◽  
Recirculating Flow ◽  
Air Water Interface

The anisotropy of the slip length and its effect on the skin-friction drag are numerically investigated for a turbulent channel flow with an idealized superhydrophobic surface having an air layer, where the idealized air–water interface is flat and does not contain the surface-tension effect. Inside the air layer, both the shear-driven flow and recirculating flow with zero net mass flow rate are considered. With increasing air-layer thickness, the slip length, slip velocity and percentage of drag reduction increase. It is shown that the slip length is independent of the water flow and depends only on the air-layer geometry. The amount of drag reduction obtained is in between those by the empirical formulae from the streamwise slip only and isotropic slip, indicating that the present air–water interface generates an anisotropic slip, and the streamwise slip length ($b_{x}$) is larger than the spanwise one ($b_{z}$). From the joint probability density function of the slip velocities and velocity gradients at the interface, we confirm the anisotropy of the slip lengths and obtain their relative magnitude ($b_{x}/b_{z}=4$) for the present idealized superhydrophobic surface. It is also shown that the Navier slip model is valid only in the mean sense, and it is generally not applicable to fluctuating quantities.

scholarly journals Influence of Rayleigh-Bénard convection on electrokinetic instability in overlimiting current conditions

2017 ◽  
Vol 2 (3) ◽  
Author(s):  
Joeri C. de Valença ◽  
Aziz Kurniawan ◽  
R. Martijn Wagterveld ◽  
Jeffery A. Wood ◽  
Rob G. H. Lammertink
Keyword(s):  
Electrokinetic Instability ◽  
Bénard Convection ◽  
Benard Convection ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Overlimiting Current

Electrokinetic instability due to streamwise conductivity gradients in microchip electrophoresis

2021 ◽  
Vol 925 ◽  
Author(s):  
Kaushlendra Dubey ◽  
Sanjeev Sanghi ◽  
Amit Gupta ◽  
Supreet Singh Bahga
Keyword(s):  
Electric Field ◽  
Numerical Simulations ◽  
Electric Fields ◽  
Quantitative Measure ◽  
Underlying Mechanism ◽  
Scaling Analysis ◽  
Recirculating Flow ◽  
Electrokinetic Instability ◽  
Spatial Features ◽  
Proper Orthogonal Decomposition Technique

We present an experimental and numerical investigation of electrokinetic instability (EKI) in microchannel flow with streamwise conductivity gradients, such as those observed during sample stacking in capillary electrophoresis. A plug of a low-conductivity electrolyte solution is initially sandwiched between two high-conductivity zones in a microchannel. This spatial conductivity gradient is subjected to an external electric field applied along the microchannel axis, and for sufficiently strong electric fields an instability sets in. We have explored the physics of this EKI through experiments and numerical simulations, and supplemented the results using scaling analysis. We performed EKI experiments at different electric field values and visualised the flow using a passive fluorescent tracer. The experimental data were analysed using the proper orthogonal decomposition technique to obtain a quantitative measure of the threshold electric field for the onset of instability, along with the corresponding coherent structures. To elucidate the physical mechanism underlying the instability, we performed high-resolution numerical simulations of ion transport coupled with fluid flow driven by the electric body force. Simulations reveal that the non-uniform electroosmotic flow due to axially varying conductivity field causes a recirculating flow within the low-conductivity region, and creates a new configuration wherein the local conductivity gradients are orthogonal to the applied electric field. This configuration leads to EKI above a threshold electric field. The spatial features of the instability predicted by the simulations and the threshold electric field are in good agreement with the experimental observations and provide useful insight into the underlying mechanism of instability.

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