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.

Pressure-driven flow of a thin viscous sheet

1995 ◽  
Vol 292 ◽  
pp. 359-376 ◽  
Author(s):  
B. W. Van De Fliert ◽  
P. D. Howell ◽  
J. R. Ockenden
Keyword(s):  
Shell Theory ◽  
Stokes Equations ◽  
Thin Sheet ◽  
Theory Model ◽  
Navier Stokes ◽  
Coordinate Frame ◽  
Leading Order ◽  
Navier Stokes Equations ◽  
Pressure Driven Flow ◽  
Pressure Driven

Systematic asymptotic expansions are used to find the leading-order equations for the pressure-driven flow of a thin sheet of viscous fluid. Assuming the fluid geometry to be slender with non-negligible curvatures, the Navier–Stokes equations with appropriate free-surface conditions are simplified to give a ‘shell-theory’ model. The fluid geometry is not known in advance and a time-dependent coordinate frame has to be employed. The effects of surface tension, gravity and inertia can also be incorporated in the model.

Electrokinetic Flow and Measure Method in Microfluidic

2013 ◽  
Vol 275-277 ◽  
pp. 649-653 ◽  
Author(s):  
Lei Gong ◽  
Jian Kang Wu ◽  
Bo Chen
Keyword(s):  
Stokes Equations ◽  
Solid Wall ◽  
Streaming Potential ◽  
Navier Stokes ◽  
Electrokinetic Flow ◽  
Navier Stokes Equations ◽  
Electroviscous Effect ◽  
Poisson Boltzmann Equation ◽  
Electrokinetic Flows ◽  
Pressure Driven

An analytical solution for pressure-driven electrokinetic flows in a narrow capillary is presented based on the Poisson–Boltzmann equation for electrical double layer and the Navier–Stokes equations for incompressible viscous fluid. The analytical solutions indicate that pressure-driven flow of an electrolyte solution in microchannel with charged solid wall induces a streaming potential, which is proportional to the flowrate and induces an electroviscous effect on flow. A device for measuring the electrokinetic flow rate and streaming potential is proposed.

Vortex Flow Driven by Electroosmosis in Microchannels

2008 ◽  
Author(s):  
Wu Zhong ◽  
Yunfei Chen
Keyword(s):  
Electroosmotic Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Channel Surface ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation ◽  
Set Up ◽  
Rotational Direction

The governing equations of electroosmotic flow, including the Navier-Stokes (N-S) equations, Laplace equation and Poisson-Boltzmann equation, are set up in a straight microchannel. The meshless method is employed as a discrete scheme for the solution domain. The semi-implicit multistep (SIMS) method is used to solve the Navier-Stokes equations. The simulation results demonstrated that different patterns of the zeta potential over the channel surface could induce different flow profiles for the vortex. The rotational direction of the vortex is determined by the electroosmotic driving force.

Internal laminar flow

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Poiseuille Flow ◽  
Stokes Equations ◽  
Circular Cross Section ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Concentric Cylinder ◽  
Navier Stokes Equations ◽  
Concentric Cylinders ◽  
Constant Viscosity ◽  
Pressure Driven Flow

In this chapter it is shown that solutions to the Navier-Stokes equations can be derived for steady, fully developed flow of a constant-viscosity Newtonian fluid through a cylindrical duct. Such a flow is known as a Poiseuille flow. For a pipe of circular cross section, the term Hagen-Poiseuille flow is used. Solutions are also derived for shear-driven flow within the annular space between two concentric cylinders or in the space between two parallel plates when there is relative tangential movement between the wetted surfaces, termed Couette flows. The concepts of wetted perimeter and hydraulic diameter are introduced. It is shown how the viscometer equations result from the concentric-cylinder solutions. The pressure-driven flow of generalised Newtonian fluids is also discussed.

Nanofluidic transport and formation of nano-emulsions

2008 ◽  
Vol 2 (1) ◽  
Author(s):  
P.A. Chando ◽  
S.S. Ray ◽  
A.L. Yarin
Keyword(s):  
Stokes Equations ◽  
Theoretical Calculations ◽  
Ccd Camera ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Fluid Layers ◽  
Pressure Driven Flow ◽  
Two Fluid

The focus of this research is to study fluidic transport through carbon nanotubes. The nanotubes studied were formed by electrospinning Polycaplrolactone (PCL) nanofibers and then using them as channel templates in colyacrylamide blocks which were carbonized. A pressure driven flow is initiated through the nanochannels and the rate of emulsion formation is recorded with a CCD camera. Theoretical calculations are conducted for nanochannels because in many experiments, the nanochannels studied have two-phase flows, which make direct application of Poiseuille law impossible. The model used for the calculations is a slit with two fluid layers in between. In particular, in many experiments, decane-air system is of interest. The calculations are carried out using the Navier-Stokes equations. The results of the model are used to evaluate experimental volumetric flow rates and find the distribution of air and decane in the nanochannels.

Double diffusive effects on pressure-driven miscible displacement flows in a channel

2012 ◽  
Vol 712 ◽  
pp. 579-597 ◽  
Author(s):  
Manoranjan Mishra ◽  
A. De Wit ◽  
Kirti Chandra Sahu
Keyword(s):  
Stokes Equations ◽  
Miscible Displacement ◽  
Interfacial Instability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Volume Approach ◽  
Diffusive Effects ◽  
The Moment ◽  
Double Diffusive ◽  
Pressure Driven

AbstractThe pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.

Electro-osmotic flow in microchannels

2008 ◽  
Vol 222 (5) ◽  
pp. 753-759 ◽  
Author(s):  
A K Arnold ◽  
P Nithiarasu ◽  
P F Eng
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Driven Systems ◽  
Osmotic Flow ◽  
Poisson Boltzmann ◽  
Wafer Surfaces ◽  
Flow Experiments ◽  
Complex Eof ◽  
Electro Osmotic Flow

In the current study, the modified Navier—Stokes equations together with the Poisson—Boltzmann and Laplace equations have been used to numerically model electro-osmotic flow (EOF) in straight microchannels. Flow experiments have been carried out using microchannels etched into silicon wafer surfaces. The numerical results from the present study have been compared against experimental data and an analytical solution. The results indicate that the numerical simulations are an accurate representation of EOF and that this model could be used as a tool in the design and analysis of complex EOF driven systems.

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.

Cosserat Modeling of Turbulent Plane-Couette and Pressure-Driven Channel Flows

2007 ◽  
Vol 129 (6) ◽  
pp. 806-810 ◽  
Author(s):  
Amin Moosaie ◽  
Gholamali Atefi
Keyword(s):  
Stokes Equations ◽  
Irreversible Thermodynamics ◽  
Channel Flows ◽  
Navier Stokes ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Micropolar Fluids ◽  
Cosserat Model ◽  
Dissipative Boundary ◽  
Pressure Driven

The theory of micropolar fluids based on a Cosserat continuum model is utilized for analysis of two benchmarks, namely, plane-Couette and pressure-driven channel flows. In the obtained theoretical velocity distributions, some new terms have appeared in addition to linear and parabolic distributions of classical fluid mechanics based on the Navier-Stokes equations. Utilizing the principles of irreversible thermodynamics, a new dissipative boundary condition is developed for angular velocity at flat plates by taking the couple-stress vector into account. The obtained results for the velocity profiles have been compared to results of recent and classical experiments. This paper demonstrates that continuum mechanical theories of higher orders, for instance Cosserat model, are able to describe a complex phenomenon, such as hydrodynamic turbulence, more precisely.

Frequency Dependent Velocity and Vorticity Fields of Electroosmotic Flow in a Closed-End Rectangular Microchannel

2004 ◽  
Author(s):  
Marcos
Keyword(s):  
Electroosmotic Flow ◽  
Navier Stokes ◽  
Vorticity Field ◽  
Navier Stokes Equation ◽  
Rectangular Microchannel ◽  
Layer Potential ◽  
Frequency Dependent ◽  
Variable Approach ◽  
Poisson Boltzmann ◽  
Poisson Boltzmann Equation

The frequency dependent electroosmotic flow in a closed-end rectangular microchannel is analyzed in this study. Dynamic AC electroosmotic flow field is obtained analytically by solving the Navier-Stokes equation using the Green’s function formulation in combination with a complex variable approach. With the Debye-Hu¨ckel approximation, the electrical double layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Additionally, the Onsager’s principle of reciprocity is demonstrated to be valid for AC electroosmotic flow. The effects of frequency-dependent AC electric field on the oscillating electroosmotic flow and the induced backpressure gradient are studied. Furthermore, the expression for the electroosmotic vorticity field is derived, and the characteristic of the vorticity field in AC electroosmotic flow is discussed. Based on the Stokes second problem, the solution of the slip velocity approximation is also presented for comparison with the results obtained from the analytical solution developed in this study.

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