Helical vortex formation in three-dimensional electrochemical systems with ion-selective membranes

Sang V. Pham, Hyuckjin Kwon, Bumjoo Kim, Jacob K. White, Geunbae Lim, and Jongyoon Han

Phys. Rev. E 93, 033114 – Published 14 March 2016

Abstract

The rate of electric-field-driven transport across ion-selective membranes can exceed the limit predicted by Nernst (the limiting current), and encouraging this “overlimiting” phenomenon can improve efficiency in many electrochemical systems. Overlimiting behavior is the result of electroconvectively induced vortex formation near membrane surfaces, a conclusion supported so far by two-dimensional (2D) theory and numerical simulation, as well as experiments. In this paper we show that the third dimension plays a critical role in overlimiting behavior. In particular, the vortex pattern in shear flow through wider channels is helical rather than planar, a surprising result first observed in three-dimensional (3D) simulation and then verified experimentally. We present a complete experimental and numerical characterization of a device exhibiting this recently discovered 3D electrokinetic instability, and show that the number of parallel helical vortices is a jump-discontinuous function of width, as is the overlimiting current and overlimiting conductance. In addition, we show that overlimiting occurs at lower fields in wider channels, because the associated helical vortices are more readily triggered than the planar vortices associated with narrow channels (effective 2D systems). These unexpected width dependencies arise in realistic electrochemical desalination systems, and have important ramifications for design optimization.

Received 16 June 2015

DOI:https://doi.org/10.1103/PhysRevE.93.033114

Physics Subject Headings (PhySH)

Electrochemistry Vortex flows

Membrane structures

Fluid DynamicsPolymers & Soft MatterNonlinear Dynamics

Authors & Affiliations

Sang V. Pham^1,2,3, Hyuckjin Kwon^1,4, Bumjoo Kim¹, Jacob K. White¹, Geunbae Lim⁴, and Jongyoon Han^1,2,5,*

¹Research Laboratory of Electronics, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
²Singapore-MIT Alliance for Research and Technology (SMART), Singapore 138602
³Department of Ship Engineering and Fluid Mechanics, Hanoi University of Science and Technology, No1 DaiCoViet, Hanoi, Vietnam
⁴Pohang Universities of Science and Technology, Pohang, Gyeoungbuk 790784, Republic of Korea
⁵Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

^*jyhan@mit.edu

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Vol. 93, Iss. 3 — March 2016

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Images

Figure 1
(a) Schematic of ICP-desalination system including a microchannel with two CEMs located on top and bottom, and insulating sidewalls; electric field is introduced between the CEMs. (b) Design of ICP-desalination device used in the experiment.
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Figure 2
Simulation result (SIM) and 3D microscopic image (EXP) for concentration at the outlet and on a symmetry plane are shown in different regimes: Ohmic (b), limiting (c), and overlimiting (d) for device with $w / d = 1$ . Under electric field introduced between the CEMs, the near bottom CEMs region of salt solution is a highly depleted flow which is represented by blue in the simulation and by the dark region in the microscopic image. In Ohmic and limiting regimes, the ion depletion zone is uniform in the $z$ direction and getting thicker as applied field increases (b,c) (note that a full cross-section picture is shown in SIM, while only the lower half is shown in EXP). In the overlimiting regime, helical vortices form at the corners resulting in a nonuniform depletion zone of which the thickness at midchannel is even thinner than in the limiting regime (c,d). Note that only in the lower half of the EXP cross section it is shown that the dimensions $(w / d / l)$ of the experimental device and simulation model are 1/1/2 mm and 10/10/25 μm, respectively.
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Figure 3
Modeling observations for forms of instability vortex in narrow channel and wide channel. (a) Unidirectional vortices in channel with aspect ratio $w / d = 0.1 / 1$ . (b) Helical vortex pair forming in channel with aspect ratio $w / d = 1 / 1$ .
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Figure 4
I-V responses obtained in experiment (a) and simulation (b) for various $w / d$ aspect ratios. (c) Measured conductance (representing slope in I-V response) in overlimiting regime for different aspect, showing jumps at $w / d = 0.7, 1.1$ , and 1.7. (d) Simple diagram for explaining periodic characteristic in overlimiting conductance; $① \to ②$ as channel width increases the vortices get thicker while the same number of vortex pairs remain, resulting in a decrease in overlimiting conductance; $② \to ③$ emergence of new vortex pairs leads a to a jump in the conductance.
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Figure 5
Three-dimensional microscopic image (a,c–f) and simulation result (b,g,h) for concentration near bottom CEM. The helical vortex can be seen as dark long regions, indicating low concentration flow coming out from the depletion layer of the bottom CEM, merging down the stream, and leading to the change in number of depletion regions. Image of lateral cross section shows vortex merge indicated by depletion zone in both experiment $(w / d / l = 2.5 / 1 / 5 mm)$ (a) and simulation $(w / d / l = 20 / 10 / 50 μ m)$ (b). (c–f) show depletion regions in the flow direction; merging process is exhibited though the change of number of vortices from 18 pairs at inlet to five pairs at outlet indicating merging of helical vortices. (g,h) corresponding picture from simulation. Note that in (c–f) only lower half of cross sections is shown.
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