Transient analysis of combined electroosmotic and pressure driven flow with multi-layer immiscible fluids in a narrow capillary

Abstract

Because the development of techniques for pumping parallel flows in miniaturized systems are required, in the present investigation, a semi-analytical solution based in the matrix inverse method and by Laplace transform for the transient flow of multi-layer immiscible fluids in a narrow capillary, under electroosmotic and pressure driven effects, is obtained. The dimensionless mathematical model to solve the electric potential distribution and the velocity field in the start-up of flow, consist on the Poisson-Boltzmann and momentum equations, respectively. Here, the transported fluids are considered symmetrical electrolytes and because the interfaces between them are polarizable and impermeable to charged particles, interesting interfacial effects appear on the velocity profiles when an external electric field is applied. The results show graphically the influence of the different dimensionless parameters involved in the dynamics of the fluid flow. This study demonstrates that by considering electrical interfacial effects, produce velocity jumps at liquid-liquid interfaces, whose magnitude and direction depend on the concentration and polarity of electric charges in those regions; finally, it is observed that the time to reach the steady-state regime of the fluid flow is only controlled by the dimensionless viscosity ratios. This investigation is a theoretical contribution to simulate transient multi-layer fluid flows under electric interfacial effects, covering different implications that emerge in the design of small devices into the chemical, biological and clinical areas.

Start-Up Electroosmotic Flow of Multi-Layer Immiscible Maxwell Fluids in a Slit Microchannel

“…which has been solved using the inverse matrix method in a process analogous to that of the electric potential distribution. Therefore, the constants D n and E n in Equation (49), and the constants A n and B n found through Equation ( 51), are replaced into Equation (50), where the inverse Laplace transform is numerically applied to solve the velocity distribution in this electroosmotic flow. To this, the method based on concentrated matrix exponential (CME) distributions is used [66]; in this framework, a finite linear combination of the transform values approximatesū, viā…”

“…However, other studies about the flow of two immiscible parallel fluids, consider that both fluids are conductive (i.e., fluids based in electrolytic solutions), increasing the complexity of the electrostatic boundary conditions in the liquid-liquid interface through a potential difference and the Gauss’s law for the electrical displacement, together with the hydrodynamic boundary conditions via the combination of viscous and electric Maxwell stresses [ 44 , 45 , 46 , 47 ]. In addition, to cover the different flow-focusing applications in microdevices, the study of parallel flows under electrokinetic effects also has been extended to multi-layer systems [ 48 , 49 , 50 ].…”

Role of electromagnetic analysis in radiative immiscible Newtonian and non‐Newtonian fluids through a microchannel with chemical reactions

“…It is concluded that Helmholtz–Smoluchowski velocity has a notable effect on velocity. Torres et al 16 studied the electro‐osmotic flow of multilayer fluid in a narrow capillary and revealed that produced velocity gradient leads to strong changes in the velocity. Escandón et al 17 investigated the flow of multilayered viscoelastic fluid in a slit microchannel in the presence of pressure‐driven and electroosmotic effects and observed that characteristics of multilayer flow are associated with the type of electrolyte solutions.…”