Electroosmotic Flow And Electrokinetic Energy Conversion Efficiency In Soft Nanochannels

Along with the development of science and technology,the system miniaturization is an important feature of the development of natural science and engineering technology.The micro electro mechanical system(MEMS)and nano electro mechanical system(NEMS)are typical examples.In micro-nano electro mechanical system,under the micro-nano scale,the flow of fluid and electrokinetic energy conversion(EKEC)efficiency are widely used in biological science,pharmacology,medical diagnosis,chemistry and environmental monitoring,for example,biochip,drug delivery and the flow of body fluid,etc.The usual nanochannel is called rigid nanochannel,and the soft nanochannel,also called polyelectrolyte-grafted(PE-grafted)nanochannel in some literatures,is represented by the rigid surface covered by a polyelectrolyte layer(PEL)in a brush-like configuration.PEL is also called fixed charge layer(FCL)due to containing fixed charge density of ions.Electrolyte ions can penetrate into the PEL,and the interface of PEL can be seen as a semi-penetrable membrane.PEL has some influences on the flow of electrolyte solution in the nanochannel,thus it can control the movement of fluid.Therefore,soft nanochannel has an important significance in the realization of intelligent microchannel.In recent years,electroosmotic flow(EOF)and EKEC efficiency in the rigid nanochannel have drawn extensive attention and research from international and domestic academics,and obtained a lot of meaningful research findings.However,little research on the EOF and EKEC in the soft nanochannel.Based on above situation,we make some theoretical research about EOF and EKEC efficiency through a soft nanochannel in this paper.Under applied alternating current(AC)electrical field,the time periodic electroosmotic flow of Newtonian fluid and viscoelastic Jeffreys fluid through a slit soft nanochannel filled with electrolyte solution is discussed.Based on Debye-Hiickel approximation,by solving linearized Poisson-Boltzmann equations,we obtain analytical solutions of electrical potential in decoupled regime of soft nanochannel,where the thickness of PEL is independent of the electrostatic effects triggered by polyelectrolyte charges.Based upon the electrical potential obtained above,by modifying momentum equations we calculate EOF velocities of Newtonian fluid and viscoelastic Jeffreys fluid for soft nanochannel.The effects of pertinent dimensionless parameters on EOF velocity are discussed in detail.We compare the distributions of EOF velocity between soft and rigid nanochannels.The results indicate that a good agreement with each other is found when the thickness of PEL is very small.However,for both Newtonian fluid and Jeffreys fluid,the velocities for soft nanochannel are larger than those for rigid one when the thickness of PEL is large.The amplitudes of EOF velocity for soft nanochannel increase with the thickness of PEL.Furthermore,the increase of oscillating Reynolds number(Re)results in more obvious oscillating phenomenon of EOF velocity,together with the weakening amplitude of oscillation.In the case of high oscillating frequency,the oscillation of velocity is restricted within the region near the interface of PEL-electrolyte.In addation,for Jeffreys fluid,the increasing of relaxation time enhances the oscillation of EOF velocity profiles,yet the increasing of the retardation time dampens the oscillation.For viscoelastic Maxwell fliud,the streaming potential and EKEC efficiency generated by a pressure driven flow in a soft nanochannel are studied in the present paper.Based on the solution of the linearized Poisson-Boltzmann equation for small electrostatic potential and the Navier-Stokes equations for incompressible viscoelastic fluids,we provide analytical solutions for streaming potential and EKEC efficiency of Maxwell fluid through soft nanochannel combining with viscoelastic effect.We compare the streaming potential and EKEC efficiency for soft nanochannel with those for rigid nanochannel.Within the present selected parameter ranges,it is shown that the different peaks of maximal streaming potential and EKEC efficiency for the rigid nanochannel are larger than those for the soft nanochannel when forcing frequencies of the driving pressure gradient close to resonating frequencies(relative to the characteristic natural frequency of the viscoelastic fluid).However,more enhanced streaming potential and EKEC efficiency for a soft nanochannel can be found in most of the regions away from these resonant frequencies.Moreover,the influence of several dimensionless parameters such as drag coefficient,thickness of surface charge layer and inverse of Deborah number on EKEC efficiency is discussed in detail.In the present paper,we also investigate the streaming potential and EKEC efficiency generated by pressure gradient and vertical magnetic field combined driven flow in a soft nanochannel filled with incompressible Newtonian fluid.Debye-Huckel linearization is applied to obtain the analytical solutions of electrostatic potential,and the analytical expressions of streaming potential and EKEC efficiency are also obtained.under the interaction between electric field,flow field and magnetic field,the variations of streaming potential and EKEC efficiency are discussed in detail.We compare the streaming potential and EKEC efficiency with those in the rigid nanochannel.It is demonstrated that streaming potential and velocity decrease with Hartmann number(Ha).However,EKEC efficiency(?)increases with the increase of Hartmann number.Meanwhile,the influence of several pertinent dimensionless parameters on EKEC efficiency is discussed.These results provide broader physical insight associated with the electrokinetic phenomenon in soft nanochannel.The conclusions have theoretical significance for microfluidic transport system.The results obtained in the present paper can provide a basis for the design,optimization and development of the microfluidic devices.