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.

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.

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.

Multiscale Simulations of Polymer Flow Between Two Parallel Plates

2021 ◽  
Vol 143 (4) ◽  
Author(s):  
Hong-Ji Yan ◽  
Zhen-Hua Wan ◽  
Feng-Hua Qin ◽  
De-Jun Sun
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulations ◽  
Chain Length ◽  
Multiscale Method ◽  
Time Averaging ◽  
Parallel Plates ◽  
Large Spatial Scale ◽  
Dynamics Simulations ◽  
Pressure Driven Flow ◽  
Pressure Driven

Abstract A modified multiscale method without constitutive equation is proposed to investigate the microscopic information and macroscopic flow properties of polymeric fluid with the memory effect between parallel plates. In this method, the domain is entirely described by macromodel with isolated molecular dynamics simulations applied to calculate the necessary local stresses. The present method is first verified by the creep-recovery motion and pressure-driven flow, and all results are in excellent agreement with the available numerical solutions in literature. Then, the method is extended to simulate two typical problems of relatively large spatial scale in general beyond the capability of molecular dynamics simulations. In the planar Couette flow, the relationship between macroscopic properties and the time evolution of local molecular information is investigated in detail without long time averaging. All results that are consistent with nonequilibrium molecular dynamics and literature qualitatively or quantitatively demonstrate the validity of present multiscale method in simulating transient viscoelastic flows and the capacity to obtain the polymer information. In the pressure-driven flow, a general monotonically decreasing relationship between the maximum or average velocities and the polymer concentrations has been found regardless of the polymer chain length. Particularly, the reference concentration that satisfies a power law with chain length is closely related to the overlap concentration, and the reference velocity is exactly the relevant velocity of Newtonian fluid with corresponding zero shear rate viscosity.

Motion of a drop along the centreline of a capillary in a pressure-driven flow

2009 ◽  
Vol 640 ◽  
pp. 27-54 ◽  
Author(s):  
ETIENNE LAC ◽  
J. D. SHERWOOD
Keyword(s):  
Capillary Number ◽  
Streaming Potential ◽  
Companion Paper ◽  
Boundary Integral ◽  
Viscous Drops ◽  
Low Viscosity ◽  
Gravity Effects ◽  
Circular Capillary ◽  
Pressure Driven Flow ◽  
Pressure Driven

The deformation of a drop as it flows along the axis of a circular capillary in low Reynolds number pressure-driven flow is investigated numerically by means of boundary integral computations. If gravity effects are negligible, the drop motion is determined by three independent parameters: the size a of the undeformed drop relative to the radius R of the capillary, the viscosity ratio λ between the drop phase and the wetting phase and the capillary number Ca, which measures the relative importance of viscous and capillary forces. We investigate the drop behaviour in the parameter space (a/R, λ, Ca), at capillary numbers higher than those considered previously. If the fluid flow rate is maintained, the presence of the drop causes a change in the pressure difference between the ends of the capillary, and this too is investigated. Estimates for the drop deformation at high capillary number are based on a simple model for annular flow and, in most cases, agree well with full numerical results if λ ≥ 1/2, in which case the drop elongation increases without limit as Ca increases. If λ < 1/2, the drop elongates towards a limiting non-zero cylindrical radius. Low-viscosity drops (λ < 1) break up owing to a re-entrant jet at the rear, whereas a travelling capillary wave instability eventually develops on more viscous drops (λ > 1). A companion paper (Lac & Sherwood, J. Fluid Mech., doi:10.1017/S002211200999156X) uses these results in order to predict the change in electrical streaming potential caused by the presence of the drop when the capillary wall is charged.

Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows

1999 ◽  
Vol 383 ◽  
pp. 29-54 ◽  
Author(s):  
ANTHONY D. SCHLEIZER ◽  
ROGER T. BONNECAZE
Keyword(s):  
Capillary Number ◽  
Contact Angles ◽  
Fluid Viscosity ◽  
Diffusive Transport ◽  
Two Dimensional ◽  
Parallel Plates ◽  
Contact Lines ◽  
Critical Capillary Number ◽  
Pressure Driven Flow ◽  
Pressure Driven

The dynamic behaviour and stability of a two-dimensional immiscible droplet subject to shear or pressure-driven flow between parallel plates is studied under conditions of negligible inertial and gravitational forces. The droplet is attached to the lower plate and forms two contact lines that are either fixed or mobile. The boundary-integral method is used to numerically determine the flow along and dynamics of the free surface. For surfactant-free interfaces with fixed contact lines, the deformation of the interface is determined for a range of capillary numbers, droplet to displacing fluid viscosity ratios, droplet sizes and flow type. It is shown that as the capillary number or viscosity ratio or size of the droplet increases, the deformation of the interface increases and above critical values of the capillary number no steady shape exists. For small droplets, and at low capillary numbers, shear and pressure-driven flows are shown to yield similar steady droplet shapes. The effect of surfactants is studied assuming a fixed amount of surfactant that is subject to convective–diffusive transport along the interface and no transport to or from the bulk fluids. Increasing the surface Péclet number, the ratio of convective to diffusive transport, leads to an accumulation of surfactant at the downstream end of the droplet and creates Marangoni stresses that immobilize the interface and reduce deformation. The no-slip boundary condition is then relaxed and an integral form of the Navier-slip model is used to examine the effects of allowing the droplet to slip along the solid surface in a pressure-driven flow. For contact angles less than or equal to 90°, a stable droplet spreads along the wall until a steady shape is reached, when the droplet translates across the wall at a constant velocity. The critical capillary number is larger for these droplets compared to those with pinned contact lines. For contact angles greater than 90°, the wetted area between a stable droplet and the wall decreases until a steady shape is reached. The critical capillary number for these droplets is less than that for pinned droplets. Above the critical capillary number the droplet completely detaches for a contact angle of 120°, or part of it is pinched off leaving behind a smaller attached droplet for contact angles less than or equal to 90°.

The Study of Combined Electroosmotic and Pressure Driven Flow in Wavy Nanochannels

2010 ◽  
Author(s):  
Naga Siva Kumar Gunda ◽  
Suman Chakraborty ◽  
Sushanta Kumar Mitra
Keyword(s):  
Flow Pattern ◽  
Stokes Equations ◽  
Flow Direction ◽  
Debye Length ◽  
Surface Profile ◽  
Base Flow ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Pressure Driven Flow ◽  
Pressure Driven

Solid surfaces of micro/nanochannels exhibit a certain degree of roughness that is incurred during fabrication and/or adsorption of macromolecules. The presence of such roughness changes the flow pattern in electroosmotic flows (EOF). The present study investigates the effect of surface waviness on combined EOF and pressure driven flow (PDF) of an electrolyte solution, in a nanochannel having charged walls. The surface profile of the top and bottom walls vary either in a varicose or in a sinuous mode. The problem is solved by using the Perturbation model, a modified linearized disturbance Navier-Stokes equations, by assuming two-dimensional combined EOF and PDF between two parallel plates as base flow. By discretizing the linearized disturbance equations using the Chebyshev collocation method in the wall normal direction and Fourier transformation in the flow direction, the perturbed velocity components are calculated. The effects of electric double layer (EDL) and amplitude of wavy surface on the flow pattern are studied. The effects of overlapped EDL are also studied as one of the limiting case. The formation of circulation regions is observed in the varicose mode channel when the EOF and PDF are flowing in the opposite direction. The decrease in the number of circulation regions is ob served for the decrease in the value of average half height of the channel to debye length ratio (κ). Serpentine or triangular type waviness in the streamline velocity is observed in sinuous mode type channel when the EOF and PDF are in opposite directions. The increase in the waviness of the streamline velocity is observed for decrease in the value of κ and increase in the amplitude a when both EOF and PDF are flowing in the same direction.

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