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.

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.

The present work analyzes the combined viscoelectric and steric effects on electroosmotic flow in a soft channel with polyelectrolyte coating. The structured channel surface, which controls the electric potential, creates two different flow regions: the electrolyte flow within the permeable polyelectrolyte layer (PEL) and the bulk electrolyte. Thus, this study discusses the interaction of various electrostatic effects to predict the electroosmotic flow field. The nonlinear governing equations describing the fluid flow are the modified Poisson–Boltzmann equation for the electric potential distribution, the mass conservation equation, and the modified Navier–Stokes equations for the flow field, which are solved numerically using a one-dimensional (1D) scheme. The results indicate that the flow enhances when increasing the electric potential magnitude across the channel cross-section via the rise in different dimensionless parameters, such as the PEL thickness, the steric factor, and the ratio of the electrokinetic parameter of the PEL to that of the electrolyte layer. This research demonstrates that the PEL significantly enhances control over electroosmotic flow. However, it is crucial to consider that viscoelectric effects at high electric fields and the friction generated by the grafted polymer brushes of the PEL can reduce these benefits.

This work analyzes the hydrodynamic behavior of a magnetorheological valve, considering the microscopic fluid characteristics to generate a damper force. The magnetorheological fluid is composed of ferromagnetic particles dispersed in a non-magnetic carrier fluid, whose mechanical resistance depends on the magnetic field intensity. In the absence of a magnetic field, the magnetorheological fluid behaves as a liquid whose viscosity depends on the particle volume fraction. Conversely, the presence of a magnetic field generates particle chain-like structures that inhibit fluid motion, thereby regulating flow in the control valve. The mathematical model employs the continuity and momentum equations, the Bingham model, and the boundary conditions at the solid–liquid interfaces to determine the flow field. The results show the fluid hydrodynamic response under different flow conditions depending on dimensionless parameters such as the pressure gradient, the field-independent viscosity, the yield stress, the particle volume fraction, the Bingham number, the Mason number, and the critical Mason number. For a pressure gradient of $\Gamma =-10$, the flow rate inside the valve (with particle volume fraction $\varphi =0.2$) results in ${\overline{Q}}_{T,x}=0.34$, $0.06$, and 0 when the magnetic field is 80, 120, and 160 kA m⁻¹, respectively. Likewise, when the magnetic field increases from 80 to 160 kA m⁻¹, the damping capacity increases by $88\%$ when $\varphi =0.2$ and $128\%$ when $\varphi =0.3$ compared to the Newtonian viscous damping. This work contributes to our understanding of semi-active damping devices for flow control.

This study analyzes the hydrodynamic characteristics of a short magnetorheological squeeze film damper, with emphasis on the fluid microstructure responsible for generating damping forces. The magnetorheological fluid contains non-Brownian spherical particles suspended in a non-magnetic Newtonian fluid. When exposed to a magnetic field, these particles form chain-like structures that restrict fluid motion. In this context, the Mason number characterizes the fluid microstructure and establishes the ratio of viscous to magnetic forces. The mathematical model for solving the flow field, which depends on the continuity and momentum laws, the Bingham rheological model, and boundary conditions at the interfaces, is solved analytically. The Reynolds equation determines the fluid pressure distribution and follows the Sommerfeld boundary condition. Mass imbalance induces chaotic rotor motion, resulting in lateral vibrations. As the journal squeezes the fluid, positive pressure develops, generating damping forces that dissipate vibration energy. The results in this research show that the Mason number significantly affects fluid pressure, which increases as magnetostatic forces exceed viscous forces. This increase in pressure produces damping forces that reduce rotor displacement. Additionally, both radial and tangential forces increase with particle volume fraction, in contrast to classical Newtonian behavior. These findings are relevant to the handling of magnetorheological fluids in vibration control mechanisms.

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.