A Depth-Averaged Model for Electrokinetic Flows in a Thin Microchannel Geometry

2004 ◽  
Author(s):  
Hao Lin ◽  
Brian D. Storey ◽  
Juan G. Santiago
Keyword(s):  
Three Dimensional ◽  
Momentum Equation ◽  
Plane Motion ◽  
Width Ratio ◽  
Three Dimensional Modeling ◽  
Depth Direction ◽  
Averaged Equations ◽  
Electrokinetic Flows ◽  
Averaged Model ◽  
Shallow Channel

We have developed a generalized electrokinetic model suitable for the study of microchannel flows with conductivity gradients and shallow channel depths. An asymptotic analysis was performed with channel depth-to-width ratio as the smallness parameter, and three dimensional transport equations are reduced to a set to depth-averaged equations governing flow dynamics in the streamwise-spanwise plane of a shallow channel. The momentum equation uses a Darcy-Brinkman-Forchheimer type formulation, and the convective-diffusive transport of the conductivity field in the depth direction manifests itself as a dispersion effect on in-plane motion. Accuracy of the model was assessed by comparing the numerical results with direct numerical simulations. These depth-averaged equations provide the accuracy of three-dimensional modeling with a convenient quasi-two-dimensional equation set applicable to a fairly wide class of microfluidic devices.

scholarly journals A depth-averaged electrokinetic flow model for shallow microchannels

2008 ◽  
Vol 608 ◽  
pp. 43-70 ◽  
Author(s):  
HAO LIN ◽  
BRIAN D. STOREY ◽  
JUAN G. SANTIAGO
Keyword(s):  
Electromechanical Coupling ◽  
Three Dimensional ◽  
Momentum Equation ◽  
Width Ratio ◽  
Complex Flow ◽  
Electrokinetic Flow ◽  
Plane Flow ◽  
Depth Direction ◽  
Averaged Equations ◽  
Electrokinetic Flows

Electrokinetic flows with heterogeneous conductivity configuration occur widely in microfluidic applications such as sample stacking and multidimensional assays. Electromechanical coupling in these flows may lead to complex flow phenomena, such as sample dispersion due to electro-osmotic velocity mismatch, and electrokinetic instability (EKI). In this work we develop a generalized electrokinetic model suitable for the study of microchannel flows with conductivity gradients and shallow-channel geometry. An asymptotic analysis is performed with the channel depth-to-width ratio as a smallness parameter, and the three-dimensional equations are reduced to a set of depth-averaged equations governing in-plane flow dynamics. The momentum equation uses a Darcy–Brinkman–Forchheimer-type formulation, and the convective–diffusive transport of the conductivity field in the depth direction manifests itself as a dispersion effect on the in-plane conductivity field. The validity of the model is assessed by comparing the numerical results with full three-dimensional direct numerical simulations, and experimental data. The depth-averaged equations provide the accuracy of three-dimensional modelling with a convenient two-dimensional equation set applicable to a wide class of microfluidic devices.

scholarly journals Comments on “The Depth-Dependent Current and Wave Interaction Equations: A Revision”

2011 ◽  
Vol 41 (10) ◽  
pp. 2008-2012 ◽  
Author(s):  
Anne-Claire Bennis ◽  
Fabrice Ardhuin
Keyword(s):  
Surf Zone ◽  
Three Dimensional ◽  
Wave Interaction ◽  
Momentum Equation ◽  
Momentum Balance ◽  
Averaging Operators ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Sloping Bottom

Abstract Equations for the wave-averaged three-dimensional momentum equations have been published in this journal. It appears that these equations are not consistent with the known depth-integrated momentum balance, especially over a sloping bottom. These equations should thus be considered with caution, because they can produce erroneous flows, particularly outside of the surf zone. It is suggested that the inconsistency in the equations may arise from the different averaging operators applied to the different terms of the momentum equation. It is concluded that other forms of the momentum equations, expressed in terms of the quasi-Eulerian velocity, are better suited for three-dimensional modeling of wave–current interactions.

scholarly journals Architecture of Open Source Program for Numerical Modeling of Flows on Mountain Slopes

2020 ◽  
Vol 32 (6) ◽  
pp. 183-200
Author(s):  
Daria Igorevna Romanova
Keyword(s):  
Mathematical Model ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Continuum Mechanics ◽  
Numerical Solutions ◽  
Turbulent Viscosity ◽  
Three Dimensional ◽  
Velocity Model ◽  
Three Dimensional Modeling ◽  
Averaged Equations

In this paper, we compare two approaches to describe the dynamics of flows on mountain slopes using the depth-averaged equations of continuum mechanics and using the complete, not depth-averaged, equations of continuum mechanics for three-dimensional modeling. Using these two approaches, a simulation of an experimental slush flow in the tank and the interaction of the flow with dam barrier protection was carried out. Numerical solutions are compared with experimental data. Also, both approaches are applied to the calculation of an avalanche in the 22nd avalanche cite of Mount Yukspor (Khibiny). Avalanche run-out distance and the shape of the avalanche deposits are compared with field data obtained from the measurement of a real avalanche. In the course of a numerical experiment, distributions of such quantities as flow velocity, depth, density, molecular and turbulent viscosity, values of the density of turbulent kinetic energy, dissipation of turbulent kinetic energy, and shear stress at the bottom of the flow were obtained. Using the obtained data a mathematical model is developed to describe the entrainment of the underlying material by the flow during slope erosion and the deposition of the flow material on the slope. To implement the obtained mathematical model, the architecture of the multiphaseEulerChangeFoam solver was developed, which implements a three-phase multi-velocity model with phase exchange between the material of the underlying surface and the material of the flow. The classic solver multiphaseEulerFoam from the OpenFOAM package is taken as a basis for the developed solver.

scholarly journals Multiscale modelling of hydraulic conductivity in vuggy porous media

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130383 ◽  
Author(s):  
K. R. Daly ◽  
T. Roose
Keyword(s):  
Porous Media ◽  
Soil Aggregates ◽  
Three Dimensional ◽  
Computation Time ◽  
X Ray ◽  
Averaged Equations ◽  
Full Structure ◽  
X Ray Computed ◽  
Flow Pathways ◽  
Averaged Model

Flow in both saturated and non-saturated vuggy porous media, i.e. soil, is inherently multiscale. The complex microporous structure of the soil aggregates and the wider vugs provides a multitude of flow pathways and has received significant attention from the X-ray computed tomography (CT) community with a constant drive to image at higher resolution. Using multiscale homogenization, we derive averaged equations to study the effects of the microscale structure on the macroscopic flow. The averaged model captures the underlying geometry through a series of cell problems and is verified through direct comparison to numerical simulations of the full structure. These methods offer significant reductions in computation time and allow us to perform three-dimensional calculations with complex geometries on a desktop PC. The results show that the surface roughness of the aggregate has a significantly greater effect on the flow than the microstructure within the aggregate. Hence, this is the region in which the resolution of X-ray CT for image-based modelling has the greatest impact.

scholarly journals Influence of the topographic effect on the seismic response of buried pipelines

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Jahangir Elyasi ◽  
Morteza Bastami ◽  
Mohsen Kamalian ◽  
Mehdi Derakhshandi
Keyword(s):  
Three Dimensional ◽  
Width Ratio ◽  
Topographic Effects ◽  
Potential Hazard ◽  
Buried Pipelines ◽  
Soil Stiffness ◽  
Wave Characteristics ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Financial Losses

AbstractDetailed study of the response of pipelines during seismic excitation can help reduce physical and financial losses during and after an earthquake. The current research investigated the seismic behavior of pipelines passing through variations in topography using two-dimensional and three-dimensional modeling. Their behavior has been modeled at the crest and toe of a slope and during longitudinal passage through the topography. The effects of the soil stiffness, diameter-to-thickness ratio of the pipeline, height-to-half-width ratio (shape factor), and input wave characteristics on the performance of the pipeline have been investigated. The results indicate that topographic effects can increase the strain on pipelines and the factors studied are crucial to accommodating this potential hazard.

Measurements in 3D images

1991 ◽  
Vol 49 ◽  
pp. 408-409
Author(s):  
John C. Russ
Keyword(s):  
Three Dimensional ◽  
Image Plane ◽  
X Rays ◽  
Traditional Use ◽  
3D Images ◽  
Confocal Scanning Laser Microscope ◽  
Hard Materials ◽  
Depth Direction ◽  
Confocal Scanning ◽  
Confocal Scanning Laser

Three-dimensional (3D) images consisting of arrays of voxels can now be routinely obtained from several different types of microscopes. These include both the transmission and emission modes of the confocal scanning laser microscope (but not its most common reflection mode), the secondary ion mass spectrometer, and computed tomography using electrons, X-rays or other signals. Compared to the traditional use of serial sectioning (which includes sequential polishing of hard materials), these newer techniques eliminate difficulties of alignment of slices, and maintain uniform resolution in the depth direction. However, the resolution in the z-direction may be different from that within each image plane, which makes the voxels non-cubic and creates some difficulties for subsequent analysis.

Dependence of the Deformation of 128×128 InSb Focal-plane Arrays on the Silicon Readout Integrated Circuit Thickness

2015 ◽  
Vol 9 (1) ◽  
pp. 170-174 ◽  
Author(s):  
Xiaoling Zhang ◽  
Qingduan Meng ◽  
Liwen Zhang
Keyword(s):  
Thermal Shock ◽  
Indium Antimonide ◽  
Integrated Circuit ◽  
Focal Plane ◽  
Three Dimensional ◽  
Fracture Probability ◽  
Focal Plane Arrays ◽  
Thermal Shock Test ◽  
Readout Integrated Circuit ◽  
Three Dimensional Modeling

The square checkerboard buckling deformation appearing in indium antimonide infrared focal-plane arrays (InSb IRFPAs) subjected to the thermal shock tests, results in the fracturing of the InSb chip, which restricts its final yield. In light of the proposed three-dimensional modeling, we proposed the method of thinning a silicon readout integrated circuit (ROIC) to level the uneven top surface of InSb IRFPAs. Simulation results show that when the silicon ROIC is thinned from 300 μm to 20 μm, the maximal displacement in the InSb IRFPAs linearly decreases from 7.115 μm to 0.670 μm in the upward direction, and also decreases linearly from 14.013 μm to 1.612 μm in the downward direction. Once the thickness of the silicon ROIC is less than 50 μm, the square checkerboard buckling deformation distribution presenting in the thicker InSb IRFPAs disappears, and the top surface of the InSb IRFPAs becomes flat. All these findings imply that the thickness of the silicon ROIC determines the degree of deformation in the InSb IRFPAs under a thermal shock test, that the method of thinning a silicon ROIC is suitable for decreasing the fracture probability of the InSb chip, and that this approach improves the reliability of InSb IRFPAs.

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