Search Results (6)

This study analyzes the combined effects of non-Newtonian rheology and electrostatics on the transient electroosmotic flow of Maxwell fluids in soft channels. The walls of the rigid channels are hydrophobic, ionically charged, and coated with a polyelectrolyte layer (PEL). This design is intended to regulate both the surface electric potential and the flow velocity. The mathematical model is based on modified Poisson–Boltzmann and momentum equations, which are solved numerically using a one-dimensional (1D) approach. The results indicate that high potentials, exceeding the Debye–Hückel limit, are achieved under conditions of thick polyelectrolyte layers, high surface charge density, and a higher concentration of fixed charges compared to the electrolyte ionic concentration. In this regime, steric effects increase the electric potential; however, this potential increase is limited by the formation of a Donnan potential. The hydrodynamic analysis demonstrates that the velocity magnitude is influenced not only by the wall potential but also by the spatial distribution of free charge density and electroosmotic force, which, in turn, are affected by steric effects. Additionally, changing the polarity and concentration of fixed charge in the PEL produces asymmetric flows, and while hydrodynamic slip enhances velocity, the drag parameter reduces it. Finally, the dimensionless parameters that control the time required to dampen the oscillatory flow induced by viscoelastic effects and reach steady-state are mainly the relaxation time, the drag parameter, the PEL thickness, and the electrokinetic parameter of the PEL, while the surface charge density and the external pressure gradient exert a comparatively minor influence. Full article

This study investigates the time-periodic electroosmotic flow and solute transport of Maxwell fluid in a parallel microchannel with modulated surface charges. The Poisson–Boltzmann equation and the linearized momentum equations are solved using a superposition-based analytical approach. The influences of oscillation intensity, fluid elasticity, and electrokinetic parameters on the velocity and concentration distributions are examined. The results show that wall-potential modulation combined with a time-periodic electric field generates recirculating motion and oscillatory velocity patterns. Moderate oscillation strengthens both flow and solute transport, whereas stronger oscillation weakens transport efficiency. This work provides a quantitative analysis the interplay between oscillatory electroosmotic flow and solute transport in Maxwell fluid and clarifies the role of oscillation strength in controlling solute dispersion. Full article

The present investigation analyzes the transient multilayer electro-osmotic flow through an annular microchannel with hydrophobic walls. The fluids are considered immiscible and viscoelastic, following the Maxwell rheological model. In the problem examined, the linearized Poisson–Boltzmann and Cauchy momentum equations are used to determine the electric potential distribution and the flow field, respectively. Here, different interfacial phenomena are studied through the imposed boundary conditions, such as the hydrodynamic slip and specified zeta potentials at solid–liquid interfaces, the velocity continuity, the electroviscous stresses balance, the potential difference, and the continuity of electrical displacements at the interfaces between fluids. The semi-analytic solution uses the Laplace transform theory. In the results, the velocity profiles and velocity tracking show the oscillatory behavior of flow, which strongly depends on the dimensionless relaxation time. Furthermore, the hydrodynamic slip on the channel walls contributes to the release of energy stored in the fluids due to elastic effects at the start-up of the flow. Similarly, other dimensionless parameters are also investigated. This research aims to predict the parallel flow behavior in microfluidic devices under electro-osmotic effects. Full article

This work investigates the transient multilayer electro-osmotic flow of viscoelastic fluids through an annular microchannel. The dimensionless mathematical model of multilayer flow is integrated by the linearized Poisson-Boltzmann equation, the Cauchy momentum equation, the rheological Maxwell model, initial conditions, and the electrostatic and hydrodynamic boundary conditions at liquid-liquid and solid-liquid interfaces. Although the main force that drives the movement of fluids is due to electrokinetic effects, a pressure gradient can also be added to the flow. The semi-analytical solution for the electric potential distribution and velocity profiles considers analytical techniques as the Laplace transform method, with numerical procedures using the inverse matrix method for linear algebraic equations and the concentrated matrix exponential method for the inversion of the Laplace transform. The results presented for velocity profiles and velocity tracking at the transient regime reveal an interesting oscillatory behavior that depends on elastic fluid properties via relaxation times. The time required for the flow to reach steady-state is highly dependent on the viscosity ratios and the dimensionless relaxation times. In addition, the influence of other dimensionless parameters on the flow as the electrokinetic parameters, zeta potentials at the walls, permittivity ratios, ratio of pressure forces to electro-osmotic forces, number of fluid layers, and annular thickness are investigated. The findings of this study have significant implications for the precise control of parallel fluid transport in microfluidic devices for flow-focusing applications. Full article

In this paper, the combined effect of the fluid rheology, finite-sized ions, and slippage toward augmenting a non-reacting solute’s mass transport due to an oscillatory electroosmotic flow (OEOF) is determined. Bikerman’s model is used to include the finite-sized ions (steric effects) in the original Poisson-Boltzmann (PB) equation. The volume fraction of ions quantifies the steric effects in the modified Poisson-Boltzmann (MPB) equation to predict the electrical potential and the ion concentration close to the charged microchannel walls. The hydrodynamics is affected by slippage, in which the slip length was used as an index for wall hydrophobicity. A conventional finite difference scheme was used to solve the momentum and species transport equations in the lubrication limit together with the MPB equation. The results suggest that the combined slippage and steric effects promote the best conditions to enhance the mass transport of species in about 90% compared with no steric effect with proper choices of the Debye length, Navier length, steric factor, Womersley number, and the tidal displacement. Full article

In this investigation, the transient electroosmotic flow of multi-layer immiscible viscoelastic fluids in a slit microchannel is studied. Through an appropriate combination of the momentum equation with the rheological model for Maxwell fluids, an hyperbolic partial differential equation is obtained and semi-analytically solved by using the Laplace transform method to describe the velocity field. In the solution process, different electrostatic conditions and electro-viscous stresses have to be considered in the liquid-liquid interfaces due to the transported fluids content buffer solutions based on symmetrical electrolytes. By adopting a dimensionless mathematical model for the governing and constitutive equations, certain dimensionless parameters that control the start-up of electroosmotic flow appear, as the viscosity ratios, dielectric permittivity ratios, the density ratios, the relaxation times, the electrokinetic parameters and the potential differences. In the results, it is shown that the velocity exhibits an oscillatory behavior in the transient regime as a consequence of the competition between the viscous and elastic forces; also, the flow field is affected by the electrostatic conditions at the liquid-liquid interfaces, producing steep velocity gradients, and finally, the time to reach the steady-state is strongly dependent on the relaxation times, viscosity ratios and the number of fluid layers. Full article