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Copyright Brian J. Kirby. With questions, contact Prof. Kirby here. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.

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Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

16.3 Induced-charge flow phenomena [AC electrokinetics top]

Native double layers in equilibrium with a surface charge density or surface potential caused by chemical reactions or adsorption at the wall are described by a straightforward geometric picture: one field, which we term the intrinsic field, is maintained by equilibrium chemical or adsorption processes and leads to the electrical double layer. A separate field, which we term the extrinsic field, moves the double layer ions (and thus the fluid) around in a microdevice. Because the intrinsic field is maintained by an insulating surface, it is simple to separate these fields when considering nativeelectroosmosis andelectrophoresis. In this section, we considerdouble layers that are caused by applied electric fields rather than being caused by reaction or adsorption. Because the intrinsic and extrinsic fields can no longer be separated, these processes are inherently nonlinear.

16.3.1 Induced-charge double layers

Consider a finite 1D system with two idealized parallel-plate electrodes at which there is neither current nor reaction. If a potential is applied between these electrodes (Figure 16.3, the electrolyte reorients in response to the electric field, and in so doing, the potential drop at equilibrium occurs mostly over the electrical double layers rather than the bulk fluid. After a time τ (in microfabricated systems this is often approximately 1 ms), the system is at equilibrium, and each electrode has a double layer composed primarily ofcounterions–the cathode attracts cations and the anode attracts anions. These double layers have been termed induced-charge double layers–the modifier induced-charge implying that the charge density is induced by the motion of ions in response to an applied field, rather than occurring naturally owing to reaction or absorption. Because larger voltages can be applied with electrodes than are observed in native double layers, this gives the potential for more dramatic double layer effects, faster fluid flows and faster particle flows.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 16.3: Schematic of circuit between two parallel plate electrodes.


Comments in the previous paragraph notwithstanding, the electrode configuration described above does not lead to any fluid flow. Recall that electroosmosis requires both a charge density in the double layer itself, and a transverse electrical field that actuates the net charge density in the double layer. In the case of a 1D parallel-plate system as described above, a double layer is created, but there is no transverse field. The presence of conducting electrodes at the wall prevents creation of a transverse electric field. In addition, the ideal zero-current electrode (i.e., electrode without current or chemical reactions at the metal-electrolyte interface) can only be approximated experimentally if AC fields are used—in the AC case, reactions (which always happen to some extent) are reversed every time the polarity changes and reaction products do not build up. Because of this, electroosmosis owing to induced charges requires at minimum a 2D variation in the electric field.

16.3.2 Flow due to induced-charge double layers—induced-charge electroosmosis

In the previous case, the simplicity of the geometry prevented the field that induced the double layer to simultaneously actuate the net charge density created. However, we need only perturb the geometry slightly to seean effect. For example, consider a circular conductor in an applied 2D electric field. If the cylinder is treated as an ideal conductor with no Faradaic reactions at the surface, then a suddenly applied electric field causes one side of the cylinder to acquire a net negatively charged double layer while the other side acquires a net positively charged double layer. The resulting space charge alters the electric field so that it becomes similar to that for the electric field around an insulator. Unlike the 1D case described above, this field actuates the double layers, leading to a quadrupolar flow. This can be seen in Figure 16.4.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 16.4: (a-b): Electric field lines before (a) and after (b) double layer charging in response to a suddenly applied DC field. (c): the resulting flow streamlines. Reproduced from [172].


Note that this flow is approximately independent of the sign of the applied electric field. Because of this, an AC field can drive this DC flow. The frequency f of the field must be such that D is not 1.

The full solution of induced-charge electroosmosis problems requires simultaneous solution of the Poisson, Nernst-Planck, and Navier-Stokes equations. However, an approximate solution for thin double layer systems can be obtained by calculating the double layer solutions in the t = 0 and t →∞ limits, and then assuming that the time constant of the transition between these two limits is given by the RC time constant of the equivalent resistor-capacitor circuit. With this estimate, the spatiotemporal dependence of the double layer potential is known, and the bulk electric field and electroosmosis can thus be calculated.

The full solution of flow in these systems requires, at minimum, simultaneous solution of the Poisson, Nernst-Planck, and Navier-Stokes equations as a function of time. However, a much simpler process which can lead to useful approximate solutions in the thin double layer limit entails predicting the double layer potentials with RC circuit approximations and using the double layer potentials to guide a Laplace solution of the electric field combined with a slip condition to describe electroosmosis.

16.3.3 Flow due to induced-charge double layers—AC electroosmosis

Another geometry in which electric fieldssimultaneously create and actuate double layers is on alternating positive and negative electrodes actuated with AC signals. This configuration is similar to the interdigitated arrays often used for electrochemical detection or for dielectrophoretic trapping (see Chapter 17). In this geometry, double layers are created at both electrodes, first in the inner regions and later in the outer regions. No fluid flow is generated at short times because no double layer yet exists, and no fluid flow is generated at long times because the field is screened by the double layer. However, when the double layers have been formed in the inner regions of the electrodes but not at the outer regions, the inner regions provide the double layer and the outer regions provide unshielded electrodes and therefore a bulk field. Thus DC fluid pumping (see Figure 16.5 for a schematic of field lines and induced flow in these geometries) occurs if the frequency of the applied AC field corresponds to the time required for part of the electrodes to form double layers but not all.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 16.5: (a) field lines and (b) streamlines for AC electroosmosis. Reproduced from [173].


This flow is visualized in experiments and computation in Figures 16.6 and 16.7. Figure 16.6 shows particle streaklines for flow induced by AC electroosmosis.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 16.6: Particle streaklines for flow induced by 2V AC signals at (a) 100 Hz (b) 300 Hz and (c) 1000 Hz. Electrolyte is 2.1 mSm KCl. Reproduced from [173].


Figure 16.7 shows comparisons between streaklines and computed streamlines.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 16.7: Comparison between particle streaklines (left) and computed streamlines (right). Reproduced for from [173].


Figure 16.8 shows a schematic of how asymmetric electrodes lead to net DC pumping of the liquid.


microfluidics textbook nanofluidics textbook Brian Kirby CornellFigure 16.8: Schematic of how asymmetric electrodes lead to net DC pumping of the liquid. Reproduced from [174].


[Return to Table of Contents]



Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

Copyright Brian J. Kirby. Please contact Prof. Kirby here with questions or corrections. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.


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