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Title: Conditions for similitude between the fluid velocity and electric field in electroosmotic flow

Abstract

Electroosmotic flow is fluid motion driven by an electric field acting on the net fluid charge produced by charge separation at a fluid-solid interface. Under many conditions of practical interest, the resulting fluid velocity is proportional to the local electric field, and the constant of proportionality is everywhere the same. Here the authors show that the main conditions necessary for this similitude are a steady electric field, uniform fluid and electric properties, an electric Debye layer that is thin compared to any physical dimension, and fluid velocities on all inlet and outlet boundaries that satisfy the Helmholtz-Smoluchowski relation normally applicable to fluid-solid boundaries. Under these conditions, the velocity field can be determined directly from the Laplace equation governing the electric potential, without solving either the continuity or momentum equations. Three important consequences of these conditions are that the fluid motion is everywhere irrotational, that fluid velocities in two-dimensional channels bounded by parallel planes are independent of the channel depth, and that such flows exhibit no dependence on the Reynolds number.

Authors:
; ; ;
Publication Date:
Research Org.:
Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
751024
Report Number(s):
SAND99-8246
TRN: AH200019%%15
DOE Contract Number:
AC04-94AL85000
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 1 Apr 1999
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; OSMOSIS; ELECTRIC FIELDS; FLUID FLOW; FLOW RATE; ELECTRIC POTENTIAL; FLOW MODELS

Citation Formats

E. B. Cummings, S. K. Griffiths, R. H. Nilson, and P. H. Paul. Conditions for similitude between the fluid velocity and electric field in electroosmotic flow. United States: N. p., 1999. Web. doi:10.2172/751024.
E. B. Cummings, S. K. Griffiths, R. H. Nilson, & P. H. Paul. Conditions for similitude between the fluid velocity and electric field in electroosmotic flow. United States. doi:10.2172/751024.
E. B. Cummings, S. K. Griffiths, R. H. Nilson, and P. H. Paul. Thu . "Conditions for similitude between the fluid velocity and electric field in electroosmotic flow". United States. doi:10.2172/751024. https://www.osti.gov/servlets/purl/751024.
@article{osti_751024,
title = {Conditions for similitude between the fluid velocity and electric field in electroosmotic flow},
author = {E. B. Cummings and S. K. Griffiths and R. H. Nilson and P. H. Paul},
abstractNote = {Electroosmotic flow is fluid motion driven by an electric field acting on the net fluid charge produced by charge separation at a fluid-solid interface. Under many conditions of practical interest, the resulting fluid velocity is proportional to the local electric field, and the constant of proportionality is everywhere the same. Here the authors show that the main conditions necessary for this similitude are a steady electric field, uniform fluid and electric properties, an electric Debye layer that is thin compared to any physical dimension, and fluid velocities on all inlet and outlet boundaries that satisfy the Helmholtz-Smoluchowski relation normally applicable to fluid-solid boundaries. Under these conditions, the velocity field can be determined directly from the Laplace equation governing the electric potential, without solving either the continuity or momentum equations. Three important consequences of these conditions are that the fluid motion is everywhere irrotational, that fluid velocities in two-dimensional channels bounded by parallel planes are independent of the channel depth, and that such flows exhibit no dependence on the Reynolds number.},
doi = {10.2172/751024},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Apr 01 00:00:00 EST 1999},
month = {Thu Apr 01 00:00:00 EST 1999}
}

Technical Report:

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  • Analytical and numerical methods are employed to determine the electric potential, fluid velocity and late-time solute distribution for electroosmotic flow in a tube and channel when the zeta potential is not small. The electric potential and fluid velocity are in general obtained by numerical means. In addition, new analytical solutions are presented for the velocity in a tube and channel in the extremes of large and small Debye layer thickness. The electroosmotic fluid velocity is used to analyze late-time transport of a neutral non-reacting solute. Zeroth and first-order solutions describing axial variation of the solute concentration are determined analytically. Themore » resulting expressions contain eigenvalues representing the dispersion and skewness of the axial concentration profiles. These eigenvalues and the functions describing transverse variation of the concentration field are determined numerically using a shooting technique. Results are presented for both tube and channel geometries over a wide range of the normalized Debye layer thickness and zeta potential. Simple analytical approximations to the eigenvalues are also provided for the limiting cases of large and small values of the Debye layer thickness. The methodology developed here for electroosmotic flow is also applied to the Taylor problem of late-time transport and dispersion in pressure-driven flows.« less
  • Analytical methods are employed to determine the axial dispersion of a neutral non-reacting solute in an incompressible electroosmotic flow. In contrast to previous approaches, the dispersion is obtained here by solving the time-dependent diffusion-advection equation in transformed spatial and temporal coordinates to obtain the two-dimensional late-time concentration field. The coefficient of dispersion arises as a separation eigenvalue, and its value is obtained as a necessary condition for satisfying all of the required boundary conditions. Solutions based on the Debye-Huckel approximation are presented for both a circular tube and a channel of infinite width. These results recover the well-known solutions formore » dispersion in pressure-driven flows when the Debye length is very large. In this limit, the axial dispersion is proportional to the square of the Peclet number based on the characteristic transverse dimension of the tube or channel. In the tilt of very small Debye lengths, the authors find that the dispersion varies as the square of the Peclet number based on the Debye length. Simple approximations to the coefficient of dispersion as a function of the Debye length and Peclet number are also presented.« less
  • A method has been developed for determining the magnitude and direction of an unknown velocity vector utilizing two-dimensional thermal anemometry. Unlike most thermal anemometry procedures, the analysis accounts for the velocity component parellel to the sensing element. The method requires determination or calibration of the flow constants at only two flow orientations: perpendicular to each sensing element. A comparison of the analysis to calibrated nozzel flow data showed good agreement for both the flow angle and velocity magnitude within the range of applicability. This type of thermal anemometry will be used to help characterize flows in and around optical accessmore » ports. 2 refs., 1 fig., 1 tab.« less
  • This research is an integrated theoretical and experimental investigation of the nonlinear interactions which may occur between the chemical kinetics, the fluid dynamics and the unstable resonator of a continuous wave fluid flow laser. The objectives of this grant were to measure the frequency and amplitude of the time dependent pulsations in the power spectral output which have been predicted to occur in cw chemical lasers employing unstable resonators to extract power.