Micro-imbibition electro-magneto-hydrodynamics of viscoelastic fluids with interactive streaming potential

Abstract

• Imbibition electro-magneto-hydrodynamics of ionic viscoelastic fluid explored • Capillarity of a sPTT fluid with induced streaming potential solved semi-analytically • Roles of Hartmann number, Electroviscous number, and Deborah number investigated • The critical Hartmann number decreases with increase in Deborah number • Capillarity with rheology independent ( x ¯ ∼ t ¯ ), and later, rheology modulated regime ( x ¯ ∼ t ¯ ). Conjugated surface tension and electro-magneto-hydrodynamics driven micro-capillary imbibition of an ionic viscoelastic fluid, in presence of interacting streaming potential, has been investigated in this article. The rheology of the fluid is modelled by appealing to the linearized simplified Phan-Thien Tanner (sPTT) model. By taking into account the electrolytic nature of the fluid, additional electroviscous forces due to induced streaming potential is also considered in the model. Transverse electric and magnetic fields are applied externally to the fluid to investigate the possibility of achieving volumetric flow gain and/or fluidic control using body force manipulation. Considering all the participating mechanisms, we deduce a semi-analytical formalism and present a comprehensive picture on the dependence of various parameters on capillary imbibition dynamics. We explore the roles played by the governing non-dimensional parameters, viz. Hartmann number, Electroviscous number, and Deborah number. For low Hartmann number regimes, there is evidence of augmented imbibition, while at higher values the flow is suppressed. We also show that the critical Hartmann number decreases with increase in Deborah number, allowing for such viscoelastic fluids to achieve more efficient imbibition velocity with less strength of applied fields. The flow regime is noted to consist of two parts – a rheology independent regime ( x ¯ ∼ t ¯ ), and later, a rheology modulated regime ( x ¯ ∼ t ¯ ). These findings are expected to provide a significant understanding of the imbibition hydrodynamics of such complex fluids, and at the same time, provide means for flow augmentation and control in microfluidic devices.