Electro-hydrodynamics of binary electrolytes driven by modulated surface potentials

We study the electro-hydrodynamics of the Debye screening layer that arises in an aqueous binary solution near a planar insulating wall when applying a spatially modulated AC-voltage. Combining this with first order perturbation theory we establish the governing equations for the full non-equilibrium problem and obtain analytic solutions in the bulk for the pressure and velocity fields of the electrolyte and for the electric potential. We find good agreement between the numerics of the full problem and the analytics of the linear theory. Our work provides the theoretical foundations of circuit models discussed in the literature. The non-equilibrium approach also reveals unexpected high-frequency dynamics not predicted by circuit models.Comment: 9 pages including 4 figures. Accepted for PRE

Flow reversal at low voltage and low frequency in a microfabricated ac electrokinetic pump

Microfluidic chips have been fabricated to study electrokinetic pumping generated by a low voltage AC signal applied to an asymmetric electrode array. A measurement procedure has been established and followed carefully resulting in a high degree of reproducibility of the measurements. Depending on the ionic concentration as well as the amplitude of the applied voltage, the observed direction of the DC flow component is either forward or reverse. The impedance spectrum has been thoroughly measured and analyzed in terms of an equivalent circuit diagram. Our observations agree qualitatively, but not quantitatively, with theoretical models published in the literature.Comment: RevTex, 9 pages, 6 eps figure

Quantized conductance in atom-sized wires between two metals

We present experimental and theoretical results for the conductance and mechanical properties of atom-sized wires between two metals. The experimental part is based on measurements with a scanning tunneling microscope (STM) where a point contact is created by indenting the tip into a gold surface. When the tip is retracted, a 10-20 Angstrom long nanowire is formed. Our measurements of the conductance of nanowires show clear signs of a quantization in units of 2e(2)/h. The scatter around the integer values increases considerably with the number of quanta, and typically it is not possible to observe more than up to four quanta in these experiments. A detailed discussion is given of the statistical methods used in the analysis of the experimental data. The theoretical part of the paper addresses some questions posed by the experiment: Why can conductance quantization be observed, what is the origin of the scatter in the experimental data, and what is the origin of the scaling of the scattering with the number of conductance quanta? The theoretical discussion is based on a free-electron-like model where scattering from the boundary of the nanowire is included. The configurations of the nanowires are deduced from molecular dynamics simulations, which also give information about the mechanical properties of the system. We show that such a model can account semiquantitatively for several of the observed effects. One of the main conclusions of the theoretical analysis is that,; due to the plastic deformation of the nanowires formed by the STM, the typical length scale of the variations in the shape of the boundary is not an atomic radius but rather bye times that value. This is the reason why scattering is sufficiently small to make conductance quantization observable by STM

Strongly nonlinear dynamics of electrolytes in large ac voltages

We study the response of a model micro-electrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two novel features - significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasi-equilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination", since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.Comment: 30 pages, 17 eps-figures, RevTe

A High-level Programming-language Implementation of Topology Optimization Applied to Steady-state Navier-Stokes Flow

We present a versatile high-level programming-language implementation of nonlinear topology optimization. Our implementation is based on the commercial software package Femlab, and it allows a wide range of optimization objectives to be dealt with easily. We exemplify our method by studies of steady-state Navier-Stokes flow problems, thus extending the work by Borrvall and Petersson on topology optimization of fluids in Stokes flow [Int. J. Num. Meth. Fluids 2003; 41:77--107]. We analyze the physical aspects of the solutions and how they are affected by different parameters of the optimization algorithm. A complete example of our implementation is included as Femlab code in an appendix.Comment: RevTex 4, 19 pages including 10 figure