Behind the dogmas of good old hydrodynamics

A new theory, which gives new insights into the transport of liquid flowing along the surface under applied electric field, was developed by the group of Russian scientists lead by Olga Vinogradova who is a professor at the M.V.Lomonosov Moscow State University and also a head of laboratory at the A.N. Frumkin Institute of Physical chemistry and Electrochemistry of the Russian Academy of Sciences. It may be used in the future in research in physics, chemistry and biology and in many applications including medicine and pharmaceutics. The article describing the theory and simulations is published in Physical Review Letter which is one of the one of the most prestigious journals in physics. It's impact factor is 7.8.

The motion of liquid through the capillaries, porous membranes, or thin channel under applied electric field is called an electroosmotic flow. This effect was discovered by the professor of the Moscow University Ferdinand Friedrich Reuss in 1807 during a pretty simple experiment. It involves the curved glass tube filled with water and its bend filled with insoluble powdered substance such as grated stone or sand which creates a porous barrier separating both ends of the tube from each other. When the voltage is applied to the water, it begins to seep through the barrier as shown in Figure 2. The motion of dispersed particles relative to a fluid under the influence of electric field was named electrophoresis.

Behind the apparent simplicity of the effect lies pretty complicated physics. It was understood only a century later in 1909 when the Polish physicist Marian Smoluchowski succeeded in describing the process of electroosmotic flow theoretically. Nobody questioned his theory during the XX century, and now it turned to be only a special case of more general theory. Moreover, it is applicable only to cases similar to Smoluchowski's one when the liquid flows past the wettable hydrophilic surface and no-slip boundary conditions are taken into account. Now it appears that entirely different conditions are needed to be applied in cases of hydrophobic poorly wettable surfaces.

This small “nuance” was discovered just in time, because such sciences as microfluidics and nanofluidics deal with the fluid flowing through ultrathin channels. And it is difficult to drive flows mechanically in extremely thin channels even by applying a pressure drop which in this case should be enormously high. However, if the conventional pump is replaced by the battery, then it is possible to establish fast electroosmotic flow in the ultrathin channel.

Sometimes physicists have to leave behind the dogmas of good old hydrodynamics. The authors of the article, who in addition to Olga Vinogradova are the young scientists Salim Maduar and Alexey Belyaev, have shown theoretically and confirmed in computer experiments that in quantitative description of flows in electric fields for hydrophobic surface electro-hydrodynamic slip boundary condition should be imposed. The new approach has immediately changed the picture.

Tthe electro-osmotic flow is caused by the cloud of ions with the opposite sign, which forms near the charged surface of the fluid. There are two possible cases. In the first one the surface charges are immobile and able to move along the surface under the electric field applied. In the case of immobile charges everything is relatively simple as the speed of electro-osmotic flow increases due to hydrophobic slippage. In case surface charges can react on the applied electric field, as scientists imply, lots of different variants arise, some of which are quite unexpected. For instance, in the article it is shown that it is possible to induce the electro-osmotic flow even near uncharged surface, or, on the contrary, to suppress such a flow completely in the channels with perfectly slipping charged walls. The lead role in the Smoluchowski theory was given to so-called zeta potential which is a physiochemical parameter calculated with a special formula and reflects the degree of electroosmotic and electrophoretic mobility. The higher the zeta potential is the faster is the flow of a liquid or particle motion. Until recently zeta potential was considered equal to the surface potential of the solid at its boundary with the liquid. In the new theory zeta-potential also plays the leading role, but its interpretation became much more complicated.

«In the Smoluchowski theory zeta potential is equal to the potential of the surface itself and is independent of neighbouring surfaces, — Olga Vinogradova explains — These conclusions are the result of the classical no-slip hydrodynamic conditions». Olga Vinorgradova and her colleagues have shown that in the case of hydrophobic surfaces it occurs differently as the hydrophobic surfaces are slippery and ions associated with the slippery surface can respond to an electric field.

So zeta potential appears to be connected with the parameters which characterize the mobility of surface charge and hydrodynamic slippage on the surface and the dependency of the possible presence of the other surface.

The new theory makes life both more complicated and more coherent as it has immediately allowed to resolve a number of paradoxes, which were doubtful for years. For instance, it gave an explanation to the zeta potential measurements of bubbles and drops.

“These measurements have been consistently showing that their zeta potentials are similar to those of the solid body” – Olga Vinogradova says – “Which was explained in particular by the presence of impurities on the surfaces of bubbles and drops. We have shown that the impurities are irrelevant and that zeta potential in this case is indeed the same as for the solid body, but due to completely different reasons.” The theory also helped to understand the highly debated electro-osmotic flows in foam films.

According to Olga Vinogradova, the possible practical implementations of the new theory are quite extensive at least for the reason that the concept of zeta potential is widely used in many fields of science and technology, such as medicine, pharmaceuticals, mineral processing, water treatment, purification of soil from pollution and even more.

New interpretation of the parameter will give a better understanding of the results of its experimental measurements and will also make possible to control its value. Particularly promising application of the new theory lies in the field of microfluidics and nanofluidics. Especially it could be used for the creation of Lab-on-a-Chip (LOC) devices and nanofluidic diodes, which are already used for the detection and the separation of biomolecules and for the energy harvesting.

«Without no doubt, the path from the new theory to practical applications is always very long, — Olga Vinogradova says, — And I suppose the experimentalists would be the first ones to use our results».