Abstract
In this work, a non-isothermal electroosmotic flow of two immiscible fluids within a uniform microcapillary is theoretically studied. It is considered that there is an annular layer of a non-Newtonian liquid, whose behavior follows the power-law model, adjacent to the inside wall of the capillary, which in turn surrounds an inner flow of a second conducting liquid that is driven by electroosmosis. The inner fluid flow exerts an interfacial force, dragging the annular fluid due to shear and Maxwell stresses at the interface between the two fluids. Because the Joule heating effect may be present in electroosmotic flow (EOF), temperature gradients can appear along the microcapillary, making the viscosity coefficients of both fluids and the electrical conductivity of the inner fluid temperature dependent. The above makes the variables of the flow field in both fluids, velocity, pressure, temperature and electric fields, coupled. An additional complexity of the mathematical model that describes the electroosmotic flow is the nonlinear character due to the rheological behavior of the surrounding fluid. Therefore, based on the lubrication theory approximation, the governing equations are nondimensionalized and simplified, and an asymptotic solution is determined using a regular perturbation technique by considering that the perturbation parameter is associated with changes in the viscosity by temperature effects. The principal results showed that the parameters that notably influence the flow field are the power-law index, an electrokinetic parameter (the ratio between the radius of the microchannel and the Debye length) and the competition between the consistency index of the non-Newtonian fluid and the viscosity of the conducting fluid. Additionally, the heat that is dissipated trough the external surface of the microchannel and the sensitivity of the viscosity to temperature changes play important roles, which modify the flow field.
Highlights
Fluid transport is an essential task in microfluidic devices, where electroosmotic pumping (EOP) can be used [1,2] as an effective tool for displacing fluids and suspended particles in microchannels
Gao et al [6] analyzed the transient aspects of two-liquid electroosmotic flow (EOF), in which a low EO mobility liquid is delivered by the interfacial viscous force of a high EO mobility liquid driven by electroosmosis
We delineate the effects of considering temperature-dependent physical properties due to Joule heating in an EOF in a microcapillary with two immiscible fluids
Summary
Fluid transport is an essential task in microfluidic devices, where electroosmotic pumping (EOP) can be used [1,2] as an effective tool for displacing fluids and suspended particles in microchannels. In [12], the analytical solution for a coaxial two-phase electroosmotic flow in a circular microchannel was studied and solved in analytical fashion, but isothermal conditions were assumed In this last reference, non-Newtonian fluids were considered; for such cases, viscous stresses at the interface between both fluids were included, and Maxwell stresses were neglected. In the Micromachines 2017, 8, 232 case of Newtonian fluids, viscous and Maxwell stresses were considered in a simultaneous manner Another important aspect to consider from the present work is that we found an approximate solution, based on a regular perturbation technique [18], of the the non-linear and coupled partial differential equations (mass, momentum, energy, charge and electric field) that describe this EOF. The boundary conditions at the interface between both fluids take into account viscous and Maxwell stresses, continuity of velocity, temperature and heat flux, which couple the field variables between the Newtonian and non-Newtonian fluids
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