In a historical context the interface between two phases has played only a minor role in the physics of fluid dynamics. It is of course true that boundary conditions at interfaces, usually imposed as continuity of ve­ locity and stress, determine the velocity field of a given flow; however, this is a more or less passive use of the interface that allows one to ignore the structure of the transition between two phases. When an interface has been assigned a more active role in flow processes, it generally has been assumed that one parameter, the interfacial (surface) tension, accounts for all mech­ anical phenomena (Young et al. 1 959, Levich & Krylov 1969). In these studies, kinematic effects of the interface were not considered, and the "no-slip" condition on the velocity at interfaces was retained. The basic message of this article is that the interface is a region of small but finite thickness, and that dynamical processes occurring within this region lead not only to interfacial stresses but also to an apparent "slip velocity" that, on a macroscopic length scale, appears to be a violation of the no-slip condition. The existence of a slip velocity at solid/fluid interfaces opens a class of flow problems not generally recognized by the fluid-dynamics community. Three previous articles in this series deal with flow caused by interactions between interfaces and external fields such as electrical potential, tem­ perature, and solute concentration. Melcher & Taylor ( 1969) and Levich & Krylov (1969) consider fluid/fluid interfaces where stresses produced at the interface by the external field dictate the flow. Saville ( 1977), on the other hand, discusses the action of an electric field on a charged solid/fluid interface and reviews the currently accepted model for electrophoretic

Colloid Transport by Interfacial Forces

The response of a model microelectrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem consists of a symmetric binary electrolyte between parallel-plate blocking electrodes, which suddenly apply a voltage. Compact Stern layers on the electrodes are also taken into account. The Nernst-Planck-Poisson equations are first linearized and solved by Laplace transforms for small voltages, and numerical solutions are obtained for large voltages. The "weakly nonlinear" limit of thin double layers is then analyzed by matched asymptotic expansions in the small parameter epsilon= lambdaD/L, where lambdaD is the screening length and L the electrode separation. At leading order, the system initially behaves like an RC circuit with a response time of lambdaDL/D (not lambdaD2/D), where D is the ionic diffusivity, but nonlinearity violates this common picture and introduces multiple time scales. The charging process slows down, and neutral-salt adsorption by the diffuse part of the double layer couples to bulk diffusion at the time scale, L2/D. In the "strongly nonlinear" regime (controlled by a dimensionless parameter resembling the Dukhin number), this effect produces bulk concentration gradients, and, at very large voltages, transient space charge. The article concludes with an overview of more general situations involving surface conduction, multicomponent electrolytes, and Faradaic processes.

http://web.mit.edu/bazant/www/papers/pdf/Bazant_2004_Phys_Rev_E_DD1.pdf

Diffuse-charge dynamics in electrochemical systems.

We proposed a novel separation method, which is the first report using ion concentration polarization (ICP) to separate particles continuously. We analyzed the electrical forces that cause the repulsion of particles in the depletion region formed by ICP. Using the electrical repulsion, micro- and nano-sized particles were separated based on their electrophoretic mobilities. Because the separation of particles was performed using a strong electric field in the depletion region without the use of internal electrodes, it offers the advantages of simple, low-cost device fabrication and bubble-free operation compared with conventional continuous electrophoretic separation methods, such as miniaturizing free-flow electrophoresis (μ-FFE). This separation device is expected to be a useful tool for separating various biochemical samples, including cells, proteins, DNAs and even ions.

/pdf/correction-corrigendum-ion-concentration-polarization-based-4vc121jhqp.pdf

Correction: Corrigendum: Ion concentration polarization-based continuous separation device using electrical repulsion in the depletion region

http://web.mit.edu/bazant/www/papers/pdf/Bazant_2009_ACIS_preprint.pdf

Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions

The evolution from microfluidic to nanofluidic systems has been accompanied by the emergence of new fluid phenomena and the potential for new nanofluidic devices. This review provides an introduction to the theory of nanofluidic transport, focusing on the various forces that influence the movement of both solvents and solutes through nanochannels, and reviews the applications of nanofluidic devices in separation science and energy conversion.

Principles and applications of nanofluidic transport

When a particle is placed in a fluid in which there is a non-uniform concentration of solute, it will move toward higher or lower concentration depending on whether the solute is attracted to or repelled from the particle surface. A quantitative understanding of this phenomenon requires that the equations representing conservation of mass and momentum within the fluid in the vicinity of the particle are solved. This is accomplished using a method of matched asymptotic expansions in a small parameter L/a, where a is the particle radius and L is the length scale characteristic of the physical interaction between solute and particle surface. This analysis yields an expression for particle velocity, valid in the limit L/a → 0, that agrees with the expression obtained by previous researchers. The result is cast into a more useful algebraic form by relating various integrals involving the solute/particle interaction energy to a measurable thermodynamic property, the Gibbs surface excess of solute Γ. An important result is that the correction for finite L/a is actually O(Γ/C∞ a), where C∞ is the bulk concentration of solute, and could be O(1) even when L/a is orders of magnitude smaller.

Motion of a particle generated by chemical gradients. Part 2. Electrolytes

(1982). STABLE CONCENTRATION GRADIENTS IN A VERTICAL TUBE. Chemical Engineering Communications: Vol. 18, No. 1-4, pp. 93-96.

Stable concentration gradients in a vertical tube

Forces acting over small but finite distances between the surface of a rigid particle and the surrounding solute molecules of a nonuniform concentration field cause the particle to move. If the solute is an electrolyte, then the force field is electrostatic and the electrolyte gradient perturbs the equilibrium double layer, thereby generating particle motion. Nonelectrolyte gradients can also cause motion due to those intermolecular forces other than electrostatic which exist between the solute molecules and the particle. The effect of the solute-particle interaction on particle velocity is predicted by solving the following equations governing mass and momentum conservations: v ’ cv4 kT 0, v2c + --

Motion of Colloids due to Nonelectrolyte Gradients

Despite the widespread adoption of neural networks, their training dynamics remain poorly understood. We show experimentally that as the size of the dataset increases, a point forms where the magnitude of the gradient of the loss becomes unbounded. Gradient descent rapidly brings the network close to this singularity in parameter space, and further training takes place near it. This singularity explains a variety of phenomena recently observed in the Hessian of neural network loss functions, such as training on the edge of stability and the concentration of the gradient in a top subspace. Once the network approaches the singularity, the top subspace contributes little to learning, even though it constitutes the majority of the gradient.

Mark E. Lowell

Papers

Motion of a particle generated by chemical gradients. Part 2. Electrolytes

Stable concentration gradients in a vertical tube

Motion of Colloids due to Nonelectrolyte Gradients

There is a Singularity in the Loss Landscape