Interface Analysis of a Combined Electroosmotic/Pressure Driven Flow of Three Viscoelastic Immiscible Fluids in a Microchannel

2017 ◽  
Author(s):  
Juan P. Escandón ◽  
Juan R. Gómez ◽  
Clara G. Hernández
Keyword(s):  
Surface Charge ◽  
Slip Surface ◽  
Flow Behavior ◽  
External Pressure ◽  
Immiscible Fluids ◽  
Charge Densities ◽  
Poisson Boltzmann Equation ◽  
Pressure Driven Flow ◽  
Viscous Stresses ◽  
Pressure Driven

This paper presents the analytical solution of a combined electroosmotic/pressure driven flow of three viscoelastic immiscible fluids in a parallel flat plate microchannel. The mathematical model is based in the Poisson-Boltzmann equation and Cauchy momentum conservation equation. In the steady state analysis, we consider that the three fluids are electric conductors and obey to the simplified Phan-Thien-Tanner rheological model; therefore, different conditions at the interface between the fluids as electric slip, surface charge density and electro-viscous stresses balance are discussed in detail. Results show the transport phenomena coupled in the description of the velocity profiles, by the analyzing of the dimensionless parameters obtained, such as: the electric slips, the electric permittivities ratios, the surface charge densities, the zeta potentials at the walls, the interfaces positions, the viscosity ratios, the viscoelastic and electrokinetic parameters, and the term involving the external pressure gradient. Here, the presence of a net electric charges balance at the interface, breaks the continuity of shear viscous stresses, modifying the flow field; hence, for the established electric conditions at the interface through the values of the electric slips and the surface charge densities, play a role like a switch on the flow behavior. This investigation extends the knowledge about the techniques on the control of immiscible non-Newtonian fluids in microescale.

Analysis of Combined Electroosmotic and Pressure Driven Flow of Multilayer Immiscible Fluids in a Narrow Capillary

2019 ◽  
Author(s):  
Juan P. Escandón ◽  
David A. Torres
Keyword(s):  
Surface Charge ◽  
Stokes Equations ◽  
Flow Behavior ◽  
Immiscible Fluids ◽  
Shear Stresses ◽  
Charge Densities ◽  
Narrow Capillary ◽  
Viscous Shear ◽  
Pressure Driven Flow ◽  
Pressure Driven

Abstract This paper presents the analytical solution of a combined electroosmotic and pressure driven flow of multilayer immiscible fluids in a narrow capillary. The mathematical model is based in the Poisson-Boltzmann equation and the modified Navier-Stokes equations. In the steady-state analysis, we consider different conditions at the interfaces between the fluids as potential differences, surface charge densities and electro-viscous stresses balances, which are discussed in detail. Results show the transport phenomena coupled in the description of velocity distribution, by the analyzing of the dimensionless parameters obtained, such as: potential differences, surface charge densities, electrokinetic parameters, term involving the external pressure gradient, ratios of viscosity and of dielectric permittivity. Here, the presence of a net electric charges balance at the interfaces breaks the continuity of the electric potential distributions and viscous shear stresses, modifying the flow field; thus, the electrical conditions established at the interfaces play an important role on the flow behavior. The present work, in which the velocity field is described, aims to be an important contribution in the development of theoretical models that provide a better understanding about labs-on-a-chip design.

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

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Juan P. Escandón ◽  
Juan R. Gómez ◽  
Clara G. Hernández
Keyword(s):  
Flow Field ◽  
Fluid Layer ◽  
Mathematical Formulation ◽  
Velocity Profiles ◽  
External Pressure ◽  
Immiscible Fluids ◽  
Double Layers ◽  
Viscous Drag ◽  
Poisson Boltzmann Equation ◽  
Pressure Driven

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.

Combined Magnetohydrodynamic/Pressure Driven Flow of Multi-Layer Pseudoplastic Fluids Through a Parallel Flat Plates Microchannel

2018 ◽  
Author(s):  
Juan R. Gómez ◽  
Juan P. Escandón
Keyword(s):  
Flow Behavior ◽  
Immiscible Fluids ◽  
Liquid Interfaces ◽  
Flat Plates ◽  
Power Requirement ◽  
Electrically Conducting ◽  
Pseudoplastic Fluids ◽  
Solid Liquid ◽  
Pressure Driven Flow ◽  
Pressure Driven

With the advance of microfluidic platforms and due to the need to solve different implications that still exist on the transport of electrically conducting fluids, the analysis on strategies in micropumps that involve a simplicity in its structure, absence of mechanical moving parts, flow reversibility and low power requirement is current. Therefore, the present investigation contributes with the analysis of the combined magnetohydrodynamic/pressure driven flow of multilayer immiscible fluids in a microchannel formed by two parallel flat plates. The mathematical model is based in a steady fully developed flow and the pumped fluids follow the power law model to describe the pseudoplastic fluids rheology, while magnetic effects on the flow are given from the Lorentz forces. The velocity profiles and flow rate are obtained in the limit of small Hartmann numbers by solving analytically a closed system of ordinary differential equations, together to the corresponding boundary conditions at the solid-liquid interfaces in the channel walls and at the liquid-liquid interfaces between the fluid layers. The results show that the flow field is controlled by the dimensionless parameters that arise from the mathematical modeling being a parameter that indicates the competition between pressure to the magnetic forces, magnetic parameters related to Hartmann numbers, viscosities ratios between the fluids, flow behavior indexes and the dimensionless position of the liquid-liquid interfaces.

scholarly journals Analytical Solution of Mixed Electroosmotic/Pressure Driven Flow of Viscoelastic Fluids between a Parallel Flat Plates Micro-Channel: The Maxwell Model Using the Oldroyd and Jaumann Time Derivatives

Micromachines ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 986
Author(s):  
Laura Casas ◽  
José A. Ortega ◽  
Aldo Gómez ◽  
Juan Escandón ◽  
René O. Vargas
Keyword(s):  
Flow Behavior ◽  
Viscoelastic Fluids ◽  
Volumetric Flow Rate ◽  
Maxwell Model ◽  
Parallel Plates ◽  
Flat Plates ◽  
Practical Applications ◽  
Low Viscosity ◽  
Pressure Driven Flow ◽  
Pressure Driven

In the present work, an analytical approximate solution of mixed electroosmotic/pressure driven flow of viscoelastic fluids between a parallel plates microchannel is reported. Inserting the Oldroyd, Jaumann, or both time derivatives into the Maxwell model, important differences in the velocity profiles were found. The presence of the shear and normal stresses is only close to the wall. This model can be used as a tool to understand the flow behavior of low viscosity fluids, as most of them experiment on translation, deformation and rotation of the flow. For practical applications, the volumetric flow rate can be controlled with two parameters, namely the gradient pressure and the electrokinetic parameter, once the fluid has been rheologically characterized.

Electro-osmotic and Pressure-Driven Flow in an Eccentric Microannulus

2019 ◽  
Vol 74 (6) ◽  
pp. 513-521
Author(s):  
F. Talay Akyildiz ◽  
Abeer F.A. AlSohaim ◽  
Nurhan Kaplan
Keyword(s):  
Boltzmann Equation ◽  
Velocity Field ◽  
Analytical Solution ◽  
Pressure Gradient ◽  
Bipolar Coordinates ◽  
Closed Form Analytical Solution ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Pressure Driven Flow ◽  
Pressure Driven

AbstractConsideration is given to steady, fully developed mixed electro-osmotic/pressure-driven flow of Newtonian fluid in an eccentric microannulus. The governing Poisson–Boltzmann and momentum equations are solved numerically in bipolar coordinates. It is shown that for a fixed aspect ratio, fully eccentric channels sustain the maximum average viscosity (i.e. flow rate) under the same dimensionless pressure gradient and electro kinetic radius. For the Debye–Hückel approximation (linearised Poisson–Boltzmann equation), we show that closed-form analytical solution can be derived for velocity field. Finally, the effect of the electrokinetic radius, pressure gradient, and eccentricity on the flow field was investigated in detail.

Analytical Solution of Mixed Electroosmotic and Pressure-Driven Flow in Rectangular Microchannels

2011 ◽  
Vol 483 ◽  
pp. 679-683 ◽  
Author(s):  
Da Yong Yang
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Microfluidic Chips ◽  
Layer Potential ◽  
Rectangular Microchannels ◽  
Navier Stokes Equations ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Pressure Driven Flow ◽  
Pressure Driven

Analytical solutions for potential distributions, velocity distributions of the mixed electroosmotic and pressure-driven flow in rectangular microchannels are discussed. To simulate the flow, a mathematical model, which includes the Poisson-Boltzmann equation and the modified Navier-Stokes equations, is presented and solved using the finite element method based on the Matlab software. The results show that the velocity distribution of mixed flow is compound of the “plug-like” and paraboloid at the steady state, and the pure electroosmotic flow is “plug-like”, which is similar with the electric double layer potential profile. The results provide the guidelines for the application of mix driven flow in microfluidic chips.

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