Multilayer Analysis of Phan-Thien-Tanner Immiscible Fluids Under Electro-Osmotic and Pressure-Driven Effects in a Slit Microchannel

Abstract

Because the pumping of samples by viscous drag forces and the use of flow-focusing for several sheath flows are widely used in microfluidic devices applications, the present investigation treats about the transport of multilayer immiscible viscoelastic fluids into a slit microchannel by electro-osmotic and pressure-driven effects. The mathematical formulation for the steady-state analysis of the flow field is based on the Poisson–Boltzmann equation and the Cauchy momentum equation. Each fluid layer has independent physical and electrical properties and is formed by a mixture of an electrolyte with a fluid that provides a viscoelastic behavior that follows the simplified Phan-Thien-Tanner (sPTT) rheological model. In the problem, the fluids are conductive and the walls of the microchannel are dielectrics, yielding electric double layers in the liquid–liquid and solid–liquid interfaces; therefore, the flow field is controlled by interfacial electrostatic conditions. The semi-analytical results are centered in the description of the velocity profiles and in the flowrate as a function of a series of dimensionless parameters arising from the mathematical modeling, where we can observe that the multilayer flow characteristics are related to the type of electrolyte solutions, since when the flow field is formed by two or more, interesting interfacial effects appear that modify the shape of velocity profiles and change the magnitude of flowrate in favor or against, depending of the positions of each fluid layer; in addition, the flow raises or diminishes by applying an external pressure gradient.

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 ].…”

“…To complement the research of Liu et al [ 36 ], Li et al [ 48 ], Afonso et al [ 38 ], Huang et al [ 39 ], Jian et al [ 46 ], Matías et al [ 42 ], Escandón et al [ 49 ] about parallel flows with non-Newtonian fluids under electroosmotic effects, and considering that many of handled fluids in microsystems have complex rheological behavior, the present investigation aims to realize a parametric study on the start-up of the electroosmotic flow of multi-layer immiscible Maxwell fluids in a microchannel. The semi-analytical solution for the velocity field that is based on the Laplace transform method, obtains the description of new liquid-liquid interfacial phenomena as well as combined effects from the physical, rheological and electrical properties of fluids, over the velocity profiles and on the tracking of the velocity magnitude in the time.…”

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

“…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. Escandón et al 18 discussed the transient electroosmotic flow of multilayer Maxwell fluids in a slit microchannel.…”

Multilayer analysis of immiscible power-law fluids under magnetohydrodynamic and pressure-driven effects in a microchannel

“…Here, the micropump that uses pressure-driven forces requires mobile parts and can drive fluids over a broad range of velocities and pressures. Another control method for multiphase flows is the electroosmotic flow [61][62][63][64][65][66][67][68][69][70][71][72][73]. The driving force is caused by the interaction between the net charged density in the electric double layer and an applied electric field in the flow domain.…”