In a microfluidic system, flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in a microchannel. The flow-electricity interaction in a complex microfluidic system subjected to...In a microfluidic system, flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in a microchannel. The flow-electricity interaction in a complex microfluidic system subjected to joint action of wall slip and electro-viscous effect is an important topic. This paper presents an analytic solution of pressuredriven liquid flow velocity and flow-induced electric field in a two-dimensional microchannel made of different materials with wall slip and electro-viscous effects. The Poisson- Boltzmann equation and the Navier-Stokes equation are solved for the analytic solutions. The analytic solutions agree well with the numerical solutions. It was found that the wall slip amplifies the fow-induced electric field and enhances the electro-viscous effect on flow. Thus the electro-viscous effect can be significant in a relatively wide microchannel with relatively large kh, the ratio of channel width to thickness of electric double layer, in comparison with the channel without wall slip.展开更多
This paper presents an analytical solution to periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in twodimensional uniform microchannel based on the Poisson-Bo...This paper presents an analytical solution to periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in twodimensional uniform microchannel based on the Poisson-Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow. Dimensional analysis indicates that electric-viscous force depends on three factors： （1） Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state, （2） profile function describing the distribution profile of electro-viscous force in channel section, and （3） coupling coefficient reflecting behavior of arnplitude damping and phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number （Re = wh^2/v）. Flow-induced electric field varies very slowly with Re when Re 〈 1, and rapidly decreases when Re 〉 1. Electro-viscous effect on flow-induced electric field and flow velocity are very significant when the rate of the channel width to the thickness of electric double layer is small.展开更多
In a microfluidic system, the flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in the microchannel. The flow-electricity interaction in a complex microfluidic system subjec...In a microfluidic system, the flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in the microchannel. The flow-electricity interaction in a complex microfluidic system subjected to a joint action of wall slip and electro-viscosity is an important topic. An analytical solution for the periodical pressure-driven flow in a two-dimensional uniform microchannel, with consideration of wall slip and electro-viscous effect is obtained based on the Poisson-Boltzmann equation for the Electric Double Layer （EDL） and the Navier-Stokes equations for the liquid flow. The analytic solutions agree well with the numerical solutions. The analytical results indicate that the periodical flow velocity and the Flow-Induced Electric Field （FIEF） strongly depend on the frequency Reynolds number （Re = （wh2/v ）, that is a function of the frequency, the channel size and the kinetic viscosity of fluids. For Re 〈 1, the flow velocity and the FIEF behave similarly to those in a steady flow, whereas they decrease rapidly with Re as Re 〉 1. In addition, the electro-viscous effect greatly influences the periodical flow velocity and the FIEF, particularly, when the electrokinetic radius kH is small. Furthermore, the wall slip velocity amplifies the FIEF and enhances the electro-viscous effect on the flow.展开更多
We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boun...We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boundary condition, for instance, the zero electrostatic potential in the middle of the channel. Using the similarity transformation, we employ the homotopy analysis method （HAM） to get the analytical solution of the model. In our approach, the unknown pressure constant and the integral constant related to the electric potential are solved spontaneously by using the proper boundary conditions on the channel walls, which makes our model consistent with the commonly accepted models in the field of fluid mechanics. It is expected that our model can offer a general and proper way to study the flow phenomena in microchannels.展开更多
基金supported by the National Natural Science Foundation of China(10872076)
文摘In a microfluidic system, flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in a microchannel. The flow-electricity interaction in a complex microfluidic system subjected to joint action of wall slip and electro-viscous effect is an important topic. This paper presents an analytic solution of pressuredriven liquid flow velocity and flow-induced electric field in a two-dimensional microchannel made of different materials with wall slip and electro-viscous effects. The Poisson- Boltzmann equation and the Navier-Stokes equation are solved for the analytic solutions. The analytic solutions agree well with the numerical solutions. It was found that the wall slip amplifies the fow-induced electric field and enhances the electro-viscous effect on flow. Thus the electro-viscous effect can be significant in a relatively wide microchannel with relatively large kh, the ratio of channel width to thickness of electric double layer, in comparison with the channel without wall slip.
基金Project supported by the National Natural Science Foundation of China (No.10472036)
文摘This paper presents an analytical solution to periodical streaming potential, flow-induced electric field and velocity of periodical pressure-driven flows in twodimensional uniform microchannel based on the Poisson-Boltzmann equations for electric double layer and Navier-Stokes equation for liquid flow. Dimensional analysis indicates that electric-viscous force depends on three factors： （1） Electric-viscous number representing a ratio between maximum of electric-viscous force and pressure gradient in a steady state, （2） profile function describing the distribution profile of electro-viscous force in channel section, and （3） coupling coefficient reflecting behavior of arnplitude damping and phase offset of electro-viscous force. Analytical results indicate that flow-induced electric field and flow velocity depend on frequency Reynolds number （Re = wh^2/v）. Flow-induced electric field varies very slowly with Re when Re 〈 1, and rapidly decreases when Re 〉 1. Electro-viscous effect on flow-induced electric field and flow velocity are very significant when the rate of the channel width to the thickness of electric double layer is small.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50805059)
文摘In a microfluidic system, the flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in the microchannel. The flow-electricity interaction in a complex microfluidic system subjected to a joint action of wall slip and electro-viscosity is an important topic. An analytical solution for the periodical pressure-driven flow in a two-dimensional uniform microchannel, with consideration of wall slip and electro-viscous effect is obtained based on the Poisson-Boltzmann equation for the Electric Double Layer （EDL） and the Navier-Stokes equations for the liquid flow. The analytic solutions agree well with the numerical solutions. The analytical results indicate that the periodical flow velocity and the Flow-Induced Electric Field （FIEF） strongly depend on the frequency Reynolds number （Re = （wh2/v ）, that is a function of the frequency, the channel size and the kinetic viscosity of fluids. For Re 〈 1, the flow velocity and the FIEF behave similarly to those in a steady flow, whereas they decrease rapidly with Re as Re 〉 1. In addition, the electro-viscous effect greatly influences the periodical flow velocity and the FIEF, particularly, when the electrokinetic radius kH is small. Furthermore, the wall slip velocity amplifies the FIEF and enhances the electro-viscous effect on the flow.
基金supported in part by the Australian Research Council through a Discovery Early Career Researcher Award to Qiang SUN
文摘We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boundary condition, for instance, the zero electrostatic potential in the middle of the channel. Using the similarity transformation, we employ the homotopy analysis method （HAM） to get the analytical solution of the model. In our approach, the unknown pressure constant and the integral constant related to the electric potential are solved spontaneously by using the proper boundary conditions on the channel walls, which makes our model consistent with the commonly accepted models in the field of fluid mechanics. It is expected that our model can offer a general and proper way to study the flow phenomena in microchannels.
