Time periodic electroosmotic flow between oscillating boundaries in narrow confinements

Abstract

Analytical and semi-analytical solutions are obtained for time-periodic electroosmotic flows between periodically oscillating boundaries constituting a narrow confinement, as a function of the relative frequencies and amplitudes of the two flow actuation mechanisms. The results are first validated in the asymptotic limits of stationary walls, for which closed form expressions have been benchmarked in the literature. It is demonstrated that with a suitable combination of the two exciting frequencies, a resonating condition is likely to be obtained, resulting in appreciable augmentation in the instantaneous rates of volumetric transport, more emphatically for the cases with thick electrical double layers (EDL). Significant insights are also developed regarding the vorticity transport as a complex interplay between the oscillatory fields and their relative phase differences. The analysis is also extended towards higher wall potentials beyond the Debye Hückel limits, for which semi-analytical solutions are obtained through numerical integration of the transformed governing equations. Distinctive implications of various important parameters such the dimensionless frequencies as well as the frequency ratios on the pertinent transport mechanisms are also pinpointed both for thin and thick EDL limits, as well as for high and low wall potentials.

The effect of the finite size of ions and Debye layer overspill on the screened Coulomb interactions between charged flat plates

“…For instance, κ −1 as large as 1 µm was observed in charged colloids of silica in ethanol and deionized water. Although a closed‐form analytical solution of the PB equation in such situations has been deemed infeasible , several approximate analytical solutions of the PB equation or its modified variants have been undertaken for conditions exhibiting the interaction or merging of Debye layers . Philipse et al.…”

Electroosmotic flows with simultaneous spatio-temporal modulations in zeta potential: cases of thick electrical double layers beyond the Debye Hückel limit

“…A majority of fluidic functionalities required in these applications includes pumping, mixing, thermal cycling, dispensing and separating. Many of these processes are executed electrokinetically (Pal and Chakraborty 2011;Goswami and Chakraborty 2011;Srivastava and Chakraborty 2010;Das and Chakraborty 2010;Munshi and Chakraborty 2009;Chakraborty 2006;Chakraborty and Paul 2006), implying that electrical fields are employed in manipulating the relative movements between the various particles, solid, and fluid phases. The convenience in transporting fluids or charged particles by applying electrical voltages turns out to be significantly advantageous from an implementation perspective as well, keeping in view that the electric and fluidic circuits can be integrated on the same microchip for building complex miniaturized systems without any moving components (Jakeway et al 2000;Whitesides and Stroock 2000).…”