Electroosmotic Flow In A Microchannel With Wall Roughness

Electroosmotic flow(EOF)was widely applied to chemical and biomedical fields with the development of microfluidic technology,such as DNA separation,cell sorting and ion transportation,separation and mixing of samples in microfluidic chips,etc.As a special electrodynamic phenomenon,EOF can induce fluid motion in micro-or nanochannels.Many characteristics of this flow phenomenon,such as no external mechanical force,simple operation,and low energy consumption,are advantages over mechanically driven flows.The manufacturing process of the device or the precipitation of other substances(such as macromolecules)on the wall can cause roughness on the microchannel wall.On the other hand,the wall roughness may be designed purposely on the channel wall to improve the mixing efficiency of the fluidic system in practical problems.Therefore,the mechanism of the wall roughness effect in microchannel should be analyzed,and its specific influence should be identified unequivocally.In this context,this paper studies EOF in microchannels with wall roughness.By establishing a mathematical model,the effects of wall roughness and electric field strength on the velocity and average velocity(volume flow rate)of EOF were investigated.The results prove that wall roughness reduces the velocity of EOF and has a significant impact on the velocity amplitude and mean flow rate.This study provides new theoretical support for the practical application of EOF and is also of great significance to the manufacturing of microfluidic devices.Firstly,based on the boundary perturbation expansion method and the separation of variables method,the EOF in circular/annular microchannel with sinusoidal roughness have been investigated under the Debye-Hückel approximation.The perturbation solutions of potential distribution,velocity and average velocity,as well as the relationship between average velocity and roughness are obtained.The theoretical results show that,the flow rate in the rough microchannel is smaller than that in the smooth microchannel;the pressure gradient G promotes(when G>0)or hinders(when G<0)EOF;in the annular microchannel,the EOF velocity decreases with the increase of the ratio of inner radius to outer radius α;for any G and phase difference β,the increment of the average velocity(u2m)in the rough microchannel obviously changes with the increase of the roughness wavenumber λ.When G≥ 0,u2m increases with β,while the result is opposite when pressure gradient is inverse,i.e.G<0.However,β can barely influence u2m when λ crosses a critical value(λ=4).Moreover,(?) and u2m in rough microchannels enhance with the strengthening of G andβ for given inner and outer cylinder zeta potential ratio ζ.Based on the boundary perturbation expansion method and the separation of variables method,the EOF of viscoelastic fluid(including Maxwell and Jeffrey fluids)driven by alternating electric field in parallel plate microchannel with sinusoidal roughness have been investigated under the Debye-Hückel approximation.The perturbation solutions of potential distribution,velocity and average velocity,as well as the relationship between average velocity and roughness are obtained.There exist significant differences in velocity amplitudes of the Newtonian,Maxwell and Jeffrey fluids.The velocity distribution of viscoelastic fluid is significantly affected by the roughness of the wall,which causes a fluctuation phenomenon appearing in the fluid.And the velocity is strongly dependent on the phase difference θ of the roughness of the upper and lower plates.As the oscillation Reynolds number ReΩ increase,the velocity profile and the average velocity um(t)of AC EOF oscillate rapidly but the velocity amplitude decreases.The Deborah number De plays a similar role to ReΩ,which makes AC EOF velocity profile more likely to oscillate.The amplitude |Um| of the AC EOF average velocity and AC EOF velocity profile reduced with the enhancement of λ2ω;For given ReΩ,phase lag χ(representing the phase difference between the electric field and the mean velocity)also increases or decreases significantly with θ.Meanwhile,χ decreases with G,λ2ω and θ increased.However,for larger λ(e.g.λ>3.4),it almost has no phase lagχ.By the boundary perturbation expansion method and the separation of variables method,the EOF of two layers Newtonian fluid with conductive upper fluid and nonconductive lower fluid in parallel plate microchannel with sinusoidal roughness have been investigated under the Debye-Hückel approximation.The perturbation solutions of potential distribution,velocity and average velocity,as well as the relationship between average velocity and roughness are obtained.The velocity w(0,y)and the average velocity (?)(or called flow rate per unit volume)is increased as G,interface and upper zeta potential ratio C,electric width K,height ratio hr and λ increase,but (?) decreased as the viscosity ratio of the lower and upper fluid μr enhance.On the contrary,u2m increases with the decrease of G,C,K,hr,λ and the increase of μr.The w(0,y)and (?) with interface considering no Maxwell stress are smaller than that with a Maxwell stress interface.The effect of roughness on velocity u2m shows the opposite result.Finally,through the boundary perturbation expansion method and the separation of variables method,the EOF of two layers conductive Newtonian fluid in parallel plate microchannel with sinusoidal roughness have been investigated under the DebyeHückel approximation.The perturbation solutions of potential distribution,velocity and average velocity,as well as the relationship between average velocity and roughness are obtained.The velocity w(0,y)and the average velocity(or called flow rate per unit volume)(?) is increased as dielectric constant ratio εr,the interfacial charge density Qs,the jump in interfacial potential Z,lower and upper wall zeta potential ratio C and hr,G increase,but as μr decrease.The u2m decreases with the strengthening of εr,hr,G,ζ and μr for given parameters.The wⅠ(0,y),(?)Ⅰ,u2mⅡ and wⅡ(0,y),(?)Ⅱ,u2mⅠ increases as the Z increases and decreases respectively for fixed parameters;The maxwell electrical stress has no influece on fluid flows when Qs=Z=0.EOF velocity increases significantly at the case of ζ>0;the adverse local electrostatic force will reduce the pumping action and the corresponding velocity at the opposite case of ζ<0.The fluid velocity w(0,y)and (?) have been significantly weakened by considering Maxwell stress effect of interface.