Stability of two layers dielectric-electrolyte microflow subjected to an alternating external electric field.

The stability of the electroosmotic flow of the two-phase system electrolyte-dielectric with a free interface in the microchannel under an external electric field is examined theoretically. The mathematical model includes the Nernst-Plank equations for the ion concentrations. The linear stability of the 1D nonstationary solution with respect to the small, periodic perturbations along the channel, is studied. Two types of instability have been highlighted. The first is known as the long-wave instability and is connected with the distortion of the free charge on the interface. In the long-wave area, the results are in good agreement with the ones obtained theoretically and experimentally in the literature. The second type of instability is a short-wave and mostly connected with the disturbance of the electrolyte conductivity. The short-wave type of instability has not been found previously in the literature and constitutes the basis and the strength of the present work. It is revealed that with the increase of the external electric field frequency, the 1D flow is stabilized. The dependence of the flow on the other parameters of the system is qualitatively the same as for the constant electric field.

On two-liquid AC electroosmotic system for thin films.

Lab-on-chip devices employ EOF for transportation and mixing of liquids. However, when a steady (DC) electric field is applied to the liquids, there are undesirable effects such as degradation of sample, electrolysis, bubble formation, etc. due to large magnitude of electric potential required to generate the flow. These effects can be averted by using a time-periodic or AC electric field. Transport and mixing of nonconductive liquids remain a problem even with this technique. In the present study, a two-liquid system bounded by two rigid plates, which act as substrates, is considered. The potential distribution is derived by assuming a Boltzmann charge distribution and using the Debye-Hückel linearization. Analytical solution of this time-periodic system shows some effects of viscosity ratio and permittivity ratio on the velocity profile. Interfacial electrostatics is also found to play a significant role in deciding velocity gradients at the interface. High frequency of the applied electric field is observed to generate an approximately static velocity profile away from the Electric Double Layer (EDL).

Effect of interfacial Maxwell stress on time periodic electro-osmotic flow in a thin liquid film with a flat interface.

Electro-osmotic flows (EOF) have seen remarkable applications in lab-on-a-chip based microdevices owing to their lack of moving components, durability, and nondispersive nature of the flow profiles under specifically designed conditions. However, such flows may typically suffer from classical Faradaic artifacts like electrolysis of the solvent, which affects the flow rate control. Such a problem has been seen to be overcome by employing time periodic EOFs. Electric field induced transport of a conductive liquid is another nontrivial problem that requires careful study of interfacial dynamics in response to such an oscillatory flow actuation. The present study highlights the role of electric field generated Maxwell stress and free surface potential along with the electric double layer thickness and forcing frequency, toward influencing the interfacial transport and fluid flow in free-surface electro-osmosis under a periodically varying external electric field, in a semi-analytical formalism. Our results reveal interesting regimes over which the pertinent interfacial phenomena as well as bulk transport characteristics may be favorably tuned by employing time varying electrical fields.

Free-surface instability in electro-osmotic flows of ultrathin liquid films.

The stability of a free surface under electro-osmotic flow in thin liquid films is investigated where the film thickness can be varied over the scale of a thick to thin electrical double layer while considering the relative contribution from the van der Waals forces. The role of interfacial Maxwell stress on thin film stability is highlighted. This configuration gives some interesting insights into the physics of free surface stability at a scale where various competing forces such as the Coulombic force, van der Waals force, and surface tension come into play. The effects of the mentioned forces are incorporated in the Navier-Stokes equations and a linear stability analysis of the resulting governing equations is performed to obtain the Orr-Sommerfeld equations. The characteristic stability curve of the system is obtained through an asymptotic analysis of the Orr-Sommerfeld equations in the long wave limit. In this study, special focus is given to the effect of the interfacial zeta potential on the free surface stability. It is found that when the free surface and the substrate zeta potential have the same polarity the system is unstable. Since the strength of the free surface potential depends upon the nature of the fluid substrate interaction, this study can help in choosing a proper combination of fluid and substrate to design microfluidic and nanofluidic channels with a desired flow rate without triggering the interfacial instability.

Mixing generated by Faraday instability between miscible liquids.

The mixing between two miscible liquids subject to vertical vibrations is studied by way of experiments and a two-dimensional numerical model. The experimental setup consisted of a rectangular cell in which the lighter fluid was placed above the denser one. The diffuse interface was then visualized by a high-speed camera. After an initial period of diffusion growth, the interface becomes unstable with a defined wavelength, which depends on the amplitude and frequency of the acceleration. The waviness of the interfacial region disappears once the mixing of the two fluids takes place. The mixing is characterized by a mixing layer thickness (MLT) which measures the thickness of the mixed region between the two pure fluid domains. We find that the MLT shows an exponential growth with time due to an initial fingering that appears at the interface and then a growth with a defined slope after the mixing takes place. The MLT also increases with amplitude of driving motion. Experimentally determined MLTs are always greater than those determined by computations since the latter assume a jump discontinuity between the fluids prior to shaking, whereas in an experiment an initial diffusive region establishes itself prior to shaking and this is destabilizing. In addition, it is found from computations that mixing is best for low gravity levels at earlier times and high gravity levels at longer times. Explanations are advanced for each of these observations.

Lattice Boltzmann simulation of thermofluidic transport phenomena in a DC magnetohydrodynamic (MHD) micropump.

A comprehensive non-isothermal Lattice Boltzmann (LB) algorithm is proposed in this article to simulate the thermofluidic transport phenomena encountered in a direct-current (DC) magnetohydrodynamic (MHD) micropump. Inside the pump, an electrically conducting fluid is transported through the microchannel by the action of an electromagnetic Lorentz force evolved out as a consequence of the interaction between applied electric and magnetic fields. The fluid flow and thermal characteristics of the MHD micropump depend on several factors such as the channel geometry, electromagnetic field strength and electrical property of the conducting fluid. An involved analysis is carried out following the LB technique to understand the significant influences of the aforementioned controlling parameters on the overall transport phenomena. In the LB framework, the hydrodynamics is simulated by a distribution function, which obeys a single scalar kinetic equation associated with an externally imposed electromagnetic force field. The thermal history is monitored by a separate temperature distribution function through another scalar kinetic equation incorporating the Joule heating effect. Agreement with analytical, experimental and other available numerical results is found to be quantitative.

Lattice kinetic simulation of nonisothermal magnetohydrodynamics.

In this paper, a lattice kinetic algorithm is presented to simulate nonisothermal magnetohydrodynamics in the low-Mach number incompressible limit. The flow and thermal fields are described by two separate distribution functions through respective scalar kinetic equations and the magnetic field is governed by a vector distribution function through a vector kinetic equation. The distribution functions are only coupled via the macroscopic density, momentum, magnetic field, and temperature computed at the lattice points. The novelty of the work is the computation of the thermal field in conjunction with the hydromagnetic fields in the lattice Boltzmann framework. A 9-bit two-dimensional (2D) lattice scheme is used for the numerical computation of the hydrodynamic and thermal fields, whereas the magnetic field is simulated in a 5-bit 2D lattice. Simulation of Hartmann flow in a channel provides excellent agreement with corresponding analytical results.

Piston-effect-induced thermal oscillations at the Rayleigh-Bénard threshold in supercritical 3He.

We perform a Navier-Stokes numerical simulation of the transient Rayleigh-Bénard convection onset in nearly supercritical 3He in the exact conditions in experiments performed by Kogan, Murphy, and Meyer [Phys. Rev. Lett. 82, 4635 (1999)]Phys. Rev. E 63, 056310 (2001)]]. We find an interpretation of the observed unexpected temperature oscillations at the convection onset in terms of the piston effect. This is our first result towards the exploration of the whole instability diagram as recently mapped in those experiments.