Non-equilibrium electric double layers in narrow channels
Chemical and Thermal Process Engineering
Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Final Report Abstract
In this theoretical project transport processes in narrow channels due to non-equilibrium electric double layers (EDLs) were studied. Three different mechanisms that induce deviations from equilibrium were considered: 1. A temperature gradient along the channel; 2. An electrostatic wall potential due to a surface acoustic wave that varies in space and time; 3. Surface reactions at the channel walls that change the wall charge. The studies were based on analytical and numerical solutions of the transport equations. Concerning mechanism 1, an extensive study of the transport phenomena induced by a) the conventional Soret effect due to the intrinsic thermophoretic mobilities of the ions; b) a pressure gradient superposed to the temperature gradient; c) the temperature-dependent electrophoretic ion mobility that changes the structure of the EDL; and d) thermoosmosis that may be caused by the temperature dependence of the dielectric permittivity, the intrinsic thermophoretic mobilities of the ions, and the temperature-dependent electrophoretic ion mobility was performed. Closed-form analytical expressions were derived, for example for the thermovoltage or the thermoosmotic velocity. These studies initiated a number of follow-up activities. Mechanism 2 was studied based on numerical solutions. The most important result is that travelling surface acoustic waves (SAWs) can induce a net electroosmotic flow in narrow slit channels of very significant magnitude (flow velocities in excess of 1 mm/s). At the same time, for such scenarios acoustic fluid propoulsion is quite inefficient, making SAW-induced electroosmotic flow the dominant transport mechanism in many cases. Since SAW-driven actuation is prominent in microfluidics, it can be speculated that on this basis SAWs will find applications for the pumping of liquids through narrow channels. Mechanism 3 refers to the coupling of the flow field with surface reactions at the channel walls. The flow alters the chemical composition in the liquid close to the walls, which in turn shifts the chemical equilibrium and alters the charge distribution at the walls, impacting the flow field. This coupled scenario was studied based on numerical solutions of the transport equations for the case of electroosmotic flow. It was shown that at high electric field strength the flow indeed has a significant influence on the charge distribution at the channel walls, making this a highly coupled problem govered, among others, by the surface reactions. In parallel to our activities, a group in the Netherlands studied the related problem of pressure-driven flow and published their results in the journal Physical Review Letters. These results, unfortunately, precluded us from publishing our results in a peer-reviewed journal. Nevertheless, the fact that in some situations flow phenomena and surface chemistry are closely coupled is an important insight that is relevant for a number of different scenarios.
Publications
- Flow and streaming potential of an electrolyte in a channel with an axial temperature gradient, Journal of Fluid Mechanics 813 (2017), 1060–1111
M. Dietzel and S. Hardt
(See online at https://doi.org/10.1017/jfm.2016.844) - Electroosmotic flow in small-scale channels induced by surface acoustic waves, Physical Review Fluids 5 (2020), 123702
M. Dietzel and S. Hardt
(See online at https://doi.org/10.1103/PhysRevFluids.5.123702)
