Tuning the dispersion of reactive solute by steady and oscillatory electroosmotic–Poiseuille flows in polyelectrolyte-grafted micro/nanotubes

2019 ◽  
Vol 880 ◽  
pp. 73-112
Author(s):  
Milad Reshadi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Hydrodynamic Dispersion ◽  
Asymptotic State ◽  
Late Time ◽  
Band Broadening ◽  
Zeta Potentials ◽  
Tracer Particles ◽  
Ion Partitioning ◽  
Analytical Approaches ◽  
Benchmark Solutions ◽  
Poiseuille Flows

This paper extends the analysis of solute dispersion in electrohydrodynamic flows to the case of band broadening in polyelectrolyte-grafted (soft) capillaries by accounting for the effects of ion partitioning, irreversible catalytic reaction and pulsatile flow actuation. In the Debye–Hückel limit, we present the benchmark solutions of electric potential and velocity distribution pertinent to steady and oscillatory mixed electroosmotic–pressure-driven flows in soft capillaries. Afterwards, the mathematical models of band broadening based on the Taylor–Aris theory and generalized dispersion method are presented to investigate the late-time asymptotic state and all-time evolution of hydrodynamic dispersion, respectively. Also, to determine the heterogeneous dispersion behaviour of solute through all spatiotemporal stages and to relax the constraint of small zeta potentials, a full-scale numerical simulation of time-dependent solute transport in soft capillaries is presented by employing the second-order-accurate finite difference method. Then, by inspecting the dispersion of passive tracer particles in Poiseuille flows, we examine the accuracy of two analytical approaches against the simulation results of a custom-built numerical algorithm. Our findings from hydrodynamic dispersion in Poiseuille flows reveal that, compared to rigid capillaries, more time is required to approach the longitudinal normality and transverse uniformity of injected solute in soft capillaries. For the case of dispersion in mixed electrohydrodynamic flows, it is found that the characteristics of the soft interface, including the thickness, permittivity, fixed charge density and friction coefficient of the polymer coating layer, play a significant role in determining the Taylor diffusion coefficient, advection speed and dispersion rate of solutes in soft capillaries.

scholarly journals Thermal Accelerometer Simulation by the R‑Functions Method

2020 ◽  
Vol 10 (23) ◽  
pp. 8373
Author(s):  
Mikhail Basarab ◽  
Alain Giani ◽  
Philippe Combette
Keyword(s):  
Mathematical Simulation ◽  
Performance Optimization ◽  
Transfer Problem ◽  
Thermal Characteristics ◽  
Temperature Response ◽  
Novel Approach ◽  
Diffusion Convection ◽  
Analytical Approaches ◽  
Benchmark Solutions ◽  
R Functions

As well as many modern devices, thermal accelerometers (TAs) need a sophisticated mathematical simulation to find the ways for their performance optimization. In the paper, a novel approach for solving computational fluid dynamics (CFD) problems in the TA’s cavity is proposed (MQ-RFM), which is based on the combined use of Rvachev’s R-functions method (RFM) and the Galerkin technique with multiquadric (MQ) radial basis functions (RBFs). The semi-analytical RFM takes an intermediate position between traditional analytical approaches and numerical methods, such as the finite-element method (FEM), belonging to the family of the so-called meshless techniques which became popular in the last decades in solving various CFD problems in complex-shaped cavities. Mathematical simulation of TA by using the MQ-RFM was carried out with the purpose to simulate the temperature response of the device and to study and improve its performance. The results of numerical experiments were compared with well-known analytical and numerical benchmark solutions for the circular annulus geometry and it demonstrated the effectiveness of the MQ-RFM for solving the convective heat-transfer problem in the TA’s cavity. The use of solution structures allows one to take a relatively small number of expansion terms to achieve an appropriate accuracy of the approximate solution satisfying at the same time the given boundary conditions exactly. The application of the MQ-RFM gives the possibility to obtain semi-analytical solutions to the diffusion-convection problems and to identify the main thermal characteristics of the TA, that allows one to improve the device performance.

Electroosmotic Fluid Motion and Late-Time Solute Transport for Large Zeta Potentials

2000 ◽  
Vol 72 (20) ◽  
pp. 4767-4777 ◽  
Author(s):  
Stewart K. Griffiths ◽  
Robert H. Nilson
Keyword(s):  
Solute Transport ◽  
Fluid Motion ◽  
Late Time ◽  
Zeta Potentials

Dispersion due to Electroosmotic Flow Through a Circular Tube With Axial Step Changes of Zeta Potential and Hydrodynamic Slippage

2013 ◽  
Author(s):  
Qi Zhou ◽  
Chiu-On Ng
Keyword(s):  
Boundary Condition ◽  
Zeta Potential ◽  
Dispersion Coefficient ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Axial Position ◽  
Hydrodynamic Dispersion ◽  
Lubrication Approximation ◽  
Slip Boundary ◽  
Zeta Potentials

The hydrodynamic dispersion of a neutral non-reacting solute due to steady electro-osmotic flow in a circular channel with longitudinal step changes of zeta potential and hydrodynamic slippage is analyzed in this study. The channel wall is periodically micro-patterned along the axial position with alternating slip-stick stripes of distinct zeta potentials. Existing studies on electrically driven hydrodynamic dispersion are based on flow subject to either the no-slip boundary condition on the capillary surface or the simplification of lubrication approximation. Taking wall slippage into account, a homogenization analysis is performed in this study to derive the hydrodynamic dispersion coefficient without subject to the long-wave constraint of the lubrication approximation, but for a general case where the length of one periodic unit of wall pattern is comparable with the channel radius. The flow and the hydrodynamic dispersion coefficient are calculated numerically, using the packages MATLAB and COMSOL, as functions of controlling parameters including the period length of the wall pattern, the area fraction of the slipping region (EOF-suppressing) in a periodic unit, the ratio of the two zeta potentials, the intrinsic hydrodynamic slip length, the Debye parameter, and the Péclet number. The dispersion coefficient is found to show notable, non-monotonic in certain situations, dependence on these controlling parameters. It is noteworthy that the introduction of hydrodynamic slippage will generate much richer behaviors of the hydrodynamic dispersion than the situation with no-slip boundary condition, as slippage interacts with zeta potentials in the EOF-suppressing and EOF-supporting regions (either likewise or oppositely charged).

THE IDENTIFICATION OF PARAMETERS OF THEORIES USED FOR PROGNOSES OF POST MINING DEFORMATIONS BY MEANS OF PRESENT SOFTWARE / IDENTYFIKACJA WARTOŚCI PARAMETRÓW TEORII PROGNOZOWANIA WPŁYWÓW PRZY WYKORZYSTANIU WSPÓŁCZESNYCH NARZĘDZI INFORMATYCZNYCH

2013 ◽  
Vol 58 (4) ◽  
pp. 1347-1357 ◽  
Author(s):  
Roman Ścigała
Keyword(s):  
Rock Mass ◽  
Land Surface ◽  
Underground Mining ◽  
Transient State ◽  
Computer Programs ◽  
Asymptotic State ◽  
Software System ◽  
Practical Utilization ◽  
Identification Of Parameters ◽  
Graphical Processing

Abstract The characteristic of specialized computer programs has been presented, serving for identification of W. Budryk-S. Knothe theory parameters, used for description of asymptotic state of post-mining deformations, as well as for transient state. The software is the result of several years of authors’ work. It is a part of complete software system designed for forecasting of underground mining influences on the rock mass and land surface and graphical processing of calculations results. Apart from software description, a short example of its practical utilization has been attached.

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