Lubrication theory for electro-osmotic flow in a non-uniform electrolyte

2007 ◽  
Vol 576 ◽  
pp. 139-172 ◽  
Author(s):  
T. L. SOUNART ◽  
J. C. BAYGENTS
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Lubrication Theory ◽  
Debye Screening Length ◽  
Sample Stacking ◽  
Osmotic Flow ◽  
Analytic Expressions ◽  
Electro Osmotic Flow

A lubrication theory has been developed for the electro-osmotic flow of non-uniform buffers in narrow rectilinear channels. The analysis applies to systems in which the transverse dimensions of the channel are large compared with the Debye screening length of the electrolyte. In contrast with related theories of electrokinetic lubrication, here the streamwise variations of the velocity field stem from, and are nonlinearly coupled to, spatiotemporal variations in the electrolyte composition. Spatially non-uniform buffers are commonly employed in electrophoretic separation and transport schemes, including iso-electric focusing (IEF), isotachophoresis (ITP), field-amplified sample stacking (FASS), and high-ionic-strength electro-osmotic pumping. The fluid dynamics of these systems is controlled by a complex nonlinear coupling to the ion transport, driven by an applied electric field. Electrical conductivity gradients, attendent to the buffer non-uniformities, result in a variable electro-osmotic slip velocity and, in electric fields approaching 1 kV cm−1, Maxwell stresses drive the electrohydrodynamic circulation. Explicit semi-analytic expressions are derived for the fluid velocity, stream function, and electric field. The resulting approximations are found to be in good agreement with full numerical solutions for a prototype buffer, over a range of conditions typical of microfluidic systems. The approximations greatly simplify the computational analysis, reduce computation times by a factor 4–5, and, for the first time, provide general insight on the dominant fluid physics of two-dimensional electrically driven transport.

scholarly journals Towards bio-inspired artificial muscle: a mechanism based on electro-osmotic flow simulated using dissipative particle dynamics

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ramin Zakeri
Keyword(s):  
Zeta Potential ◽  
Electric Field ◽  
Dissipative Particle Dynamics ◽  
Artificial Muscle ◽  
Particle Dynamics ◽  
Polymer Membrane ◽  
Channel Width ◽  
Micro Channel ◽  
Osmotic Flow ◽  
Electro Osmotic Flow

AbstractOne of the unresolved issues in physiology is how exactly myosin moves in a filament as the smallest responsible organ for contracting of a natural muscle. In this research, inspired by nature, a model is presented consisting of DPD (dissipative particle dynamics) particles driven by electro-osmotic flow (EOF) in micro channel that a thin movable impermeable polymer membrane has been attached across channel width, thus momentum of fluid can directly transfer to myosin stem. At the first, by validation of electro-osmotic flow in micro channel in different conditions with accuracy of less than 10 percentage error compared to analytical results, the DPD results have been developed to displacement of an impermeable polymer membrane in EOF. It has been shown that by the presence of electric field of 250 V/m and Zeta potential − 25 mV and the dimensionless ratio of the channel width to the thickness of the electric double layer or kH = 8, about 15% displacement in 8 s time will be obtained compared to channel width. The influential parameters on the displacement of the polymer membrane from DPD particles in EOF such as changes in electric field, ion concentration, zeta potential effect, polymer material and the amount of membrane elasticity have been investigated which in each cases, the radius of gyration and auto correlation velocity of different polymer membrane cases have been compared together. This simulation method in addition of probably helping understand natural myosin displacement mechanism, can be extended to design the contraction of an artificial muscle tissue close to nature.

Modeling electro-osmotic flow and thermal transport of Caputo fractional Burgers fluid through a micro-channel

2021 ◽  
pp. 095440892110259
Author(s):  
Mohammed Abdulhameed ◽  
Garba Tahiru Adamu ◽  
Gulibur Yakubu Dauda
Keyword(s):  
Electric Field ◽  
Laplace Transform ◽  
Inverse Laplace Transform ◽  
Micro Channel ◽  
Osmotic Flow ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Burgers Fluid ◽  
Electro Osmotic Flow

In this paper, we construct transient electro-osmotic flow of Burgers’ fluid with Caputo fractional derivative in a micro-channel, where the Poisson–Boltzmann equation described the potential electric field applied along the length of the microchannel. The analytical solution for the component of the velocity profile was obtained, first by applying the Laplace transform combined with the classical method of partial differential equations and, second by applying Laplace transform combined with the finite Fourier sine transform. The exact solution for the component of the temperature was obtained by applying Laplace transform and finite Fourier sine transform. Further, due to the complexity of the derived models of the governing equations for both velocity and temperature, the inverse Laplace transform was obtained with the aid of numerical inversion formula based on Stehfest's algorithms with the help of MATHCAD software. The graphical representations showing the effects of the time, retardation time, electro-kinetic width, and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameters on the temperature distribution in the micro-channel were presented and analyzed. The results show that the applied electric field, electro-osmotic force, electro-kinetic width, and relaxation time play a vital role on the velocity distribution in the micro-channel. The fractional parameters can be used to regulate both the velocity and temperature in the micro-channel. The study could be used in the design of various biomedical lab-on-chip devices, which could be useful for biomedical diagnosis and analysis.

Electrohydrodynamic rotation of drops at large electric Reynolds numbers

2016 ◽  
Vol 788 ◽  
Author(s):  
Ehud Yariv ◽  
Itzchak Frankel
Keyword(s):  
Electric Fields ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Reynolds Numbers ◽  
Mirror Image ◽  
Liquid Drops ◽  
Weakly Conducting ◽  
Strong Electric Fields ◽  
Quincke Rotation ◽  
Asymmetric Solution

When subject to sufficiently strong electric fields, particles and drops suspended in a weakly conducting liquid exhibit spontaneous rotary motion. This so-called Quincke rotation is a fascinating example of nonlinear symmetry-breaking phenomena. To illuminate the rotation of liquid drops we here analyse the asymptotic limit of large electric Reynolds numbers, $\mathit{Re}\gg 1$, within the framework of a two-dimensional Taylor–Melcher electrohydrodynamic model. A non-trivial dominant balance in this singular limit results in both the fluid velocity and surface-charge density scaling as $\mathit{Re}^{-1/2}$. The flow is governed by a self-contained nonlinear boundary-value problem that does not admit a continuous fore–aft symmetric solution, thus necessitating drop rotation. Furthermore, thermodynamic arguments reveal that a fore–aft asymmetric solution exists only when charge relaxation within the suspending liquid is faster than that in the drop. The flow problem possesses both mirror-image (with respect to the direction of the external field) and flow-reversal symmetries; it is transformed into a universal one, independent of the ratios of electric conductivities and dielectric permittivities in the respective drop phase and suspending liquid phase. The rescaled angular velocity is found to depend weakly upon the viscosity ratio. The corresponding numerical solutions of the exact equations indeed collapse at large $\mathit{Re}$ upon the asymptotically calculated universal solution.

scholarly journals Evaluation of electro-osmotic flow in a nanochannel via semi-analytical method

2012 ◽  
Vol 16 (5) ◽  
pp. 1297-1302 ◽  
Author(s):  
Payam Jalili ◽  
Domairry Ganji ◽  
Bahram Jalili ◽  
Domiri Ganji
Keyword(s):  
Shear Stress ◽  
Analytical Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Electrical Potential ◽  
Osmotic Flow ◽  
Homotopy Perturbation ◽  
Stress Profiles ◽  
Electro Osmotic Flow ◽  
Cation Distributions

In this paper, equations due to anion and cation distributions, electrical potential and shear stress profiles in a nanochannel are formed for 1-D electro-osmotic flow, and solved by homotopy perturbation method. Results are compared with numerical solutions.

scholarly journals Electromigration dispersion in a capillary in the presence of electro-osmotic flow

2012 ◽  
Vol 697 ◽  
pp. 436-454 ◽  
Author(s):  
S. Ghosal ◽  
Z. Chen
Keyword(s):  
Electric Field ◽  
Separation Efficiency ◽  
Chemical Species ◽  
General Situation ◽  
Ion Migration ◽  
Osmotic Flow ◽  
Total Dispersion ◽  
Advection Diffusion Equation ◽  
Electromigration Dispersion ◽  
Electro Osmotic Flow

AbstractThe differential migration of ions in an applied electric field is the basis for the separation of chemical species by capillary electrophoresis. Axial diffusion of the concentration peak limits the separation efficiency. Electromigration dispersion is observed when the concentration of sample ions is comparable to that of the background ions. Under such conditions, the local electrical conductivity is significantly altered in the sample zone making the electric field, and, therefore, the ion migration velocity, concentration dependent. The resulting nonlinear wave exhibits shock-like features and, under certain simplifying assumptions, is described by Burgers’ equation (Ghosal & Chen Bull. Math. Biol., vol. 72, 2010, p. 2047). In this paper, we consider the more general situation where the walls of the separation channel may have a non-zero zeta potential and are therefore able to sustain an electro-osmotic bulk flow. The main result is a one-dimensional nonlinear advection diffusion equation for the area averaged concentration. This homogenized equation accounts for the Taylor–Aris dispersion resulting from the variation in the electro-osmotic slip velocity along the wall. It is shown that in a certain range of parameters, the electro-osmotic flow can actually reduce the total dispersion by delaying the formation of a concentration shock. However, if the electro-osmotic flow is sufficiently high, the total dispersion is increased because of the Taylor–Aris contribution.

scholarly journals Dynamics of Field Amplified Sample Stacking

2001 ◽  
Author(s):  
Rajiv Bharadwaj ◽  
Juan G. Santiago
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Concentration Field ◽  
Initial Step ◽  
Step Function ◽  
Buffer Concentration ◽  
Sample Stacking ◽  
Sample Concentration ◽  
Concentration Enhancement ◽  
Channel Configuration

Abstract We present an analysis and an experimental study of field amplified sample stacking. The analysis consists of a one dimensional, unsteady electromigration model of the concentration fields in sample stacking. The model predicts that the sample concentration develops as a non-linear concentration wave with a peak concentration increasing with time that reaches a maximum value determined by ratio of electric fields in the sample and the buffer region. The experimental work is a preliminary study of the effects of electroosmotic flow on sample stacking for a single fluid-fluid interface within a glass microchannel. Using a simple cross-channel configuration a high-gradient initial step-function in the buffer concentration field was established which causes an unsteady sample concentration process. The experimental results qualitatively confirm the wave-like profile of the stacked analyte predicted by the analytical model. Experiments also provide evidence of internal pressure generation due to mis-matched electroosmotic velocities during stacking. The effect of electric field strength and sample-to-background buffer concentration ratio, γ, are also presented. Stacked sample concentration at γ = 4 is found to initially increase with increasing electric field but saturates at higher electric fields. Stacking rates at higher γ ratios indicate that concentration enhancement is quickly limited by dispersion due to internally generated pressure gradients.

Lubrication theory for electro-osmotic flow in a microfluidic channel of slowly varying cross-section and wall charge

2002 ◽  
Vol 459 ◽  
pp. 103-128 ◽  
Author(s):  
SANDIP GHOSAL
Keyword(s):  
Cross Section ◽  
Microfluidic Channel ◽  
Lubrication Theory ◽  
Wall Material ◽  
Channel Cross Section ◽  
Microfluidic Channels ◽  
Osmotic Flow ◽  
Axial Variation ◽  
Wall Charge ◽  
Electro Osmotic Flow

Electro-osmotic flow is a convenient mechanism for transporting fluid in microfluidic devices. The flow is generated through the application of an external electric field that acts on the free charges that exist in a thin Debye layer at the channel walls. The charge on the wall is due to the particular chemistry of the solid–fluid interface and can vary along the channel either by design or because of various unavoidable inhomogeneities of the wall material or because of contamination of the wall by chemicals contained in the fluid stream. The channel cross-section could also vary in shape and area. The effect of such variability on the flow through microfluidic channels is of interest in the design of devices that use electro-osmotic flow. The problem of electro-osmotic flow in a straight microfluidic channel of arbitrary cross-sectional geometry and distribution of wall charge is solved in the lubrication approximation, which is justified when the characteristic length scales for axial variation of the wall charge and cross-section are both large compared to a characteristic width of the channel. It is thereby shown that the volume flux of fluid through such a microchannel is a linear function of the applied pressure drop and electric potential drop across it, the coefficients of which may be calculated explicitly in terms of the geometry and charge distribution on the wall. These coefficients characterize the ‘fluidic resistance’ of each segment of a microfluidic network in analogy to the electrical ‘resistance’ in a microelectronic circuit. A consequence of the axial variation in channel properties is the appearance of an induced pressure gradient and an associated secondary flow that leads to increased Taylor dispersion limiting the resolution of electrophoretic separations. The lubrication theory presented here offers a simple way of calculating the distortion of the flow profile in general geometries and could be useful in studies of dispersion induced by inhomogeneities in microfluidic channels.

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