Parametric Investigations On The Nonlinear Oscillating Electroosmotic Flow Of Insulating Wall Based On Laser Induced Fluorescence Photobleaching Anemometer(LIFPA)

Electroosmotic flow(EOF)is a basic physical phenomenon widely existing at the solidliquid interface,and widely present in micro/nanofluidics and electrochemical analysis systems.EOF can be generated by either DC or AC electric field.Oscillating electroosmotic flow(OEOF)is a branch of EOF induced by AC electric field.It can be further divided into linear and nonlinear OEOF briefly.When the external electric field is sufficiently strong,nonlinear OEOF caused by concentration polarization is critical for electrochemical analysis and micro/nanofluidics applications.However,due to the limitation of the flow diagnostic techniques,no experimental investigations on the flow field and velocity fluctuation of nonlinear OEOF have been reported.In this study,we used laser-induced fluorescence bleaching velocimetry(LIFPA)technology with high spatio-temporal resolution to study the velocity fluctuation of the OEOF in the electrical double layer of the insulating bottom wall away from the electrode.The influence of basic pressure-driven flow is also taken into account.First,we theoretically deduce the control equations of both velocity field and the internal electric field of the OEOF,and find the both fields can be described by an 1D inviscid Burgers equation with an external force term.The coefficients corresponding to the linear(Zl)and nonlinear(Znl)terms of the equation determine the state of OEOF.These two coefficients are further determined by five dimensionless parameters,including the Stokes number(St),the ratio of the macro-scale to the micro-scale(y),the Schmidt number(Sc),and the Peclet number of the basic flow(Pe,U)and electrophoretic Peclet number(Pe,EP).Subsequently,we experimentally investigated the effects of the electric field intensity EA,frequency ff and the flow rate Q on the nonlinear behavior of OEOF,by measuring velocity fluctuations of flow on the diffuse layer of insulated bottom wall.The results show that:(1)With the increasing of EA,OEOF evolves from linear state where the time series of velocity fluctuations is temporally symmetric to nonlinear state where the velocity fluctuations become temporally asymmetric.The time series of velocity fluctuations is further shown as flat or even reversed velocity fluctuations at the troughs of the waveform.The experiments again support the existence of "turn-over" phenomena.(2)The power spectra of velocity fluctuations are investigated.It can be seen under the linear OEOF state,the power spectra only have a single peak at the electric field frequency ff.With the increasing EA,when OEOF enters nonlinear state,multiple peaks appear at ff and its higher harmonic frequencies on the power spectra.(3)With the increase of Q,the nonlinear behavior of OEOF is inhibited,and accordingly,the linear behavior is relatively enhanced.The turn-over phenomena is inhibited.Accompanied is that the heights of the higher-order harmonic peaks are reduced,with the number of harmonic peaks reduced.Finally,we analyze the critical behavior of the state of linear-nonlinear oscillating electroosmotic flow—the critical electric field EC and its influencing factors.The results show:(1)EC will increase with the increase of frequency under the same flow.(2)With the same frequency,EC will increase with the increase of the flow.Subsequently,EC was also measured at different pH values.On the basis of linear term coefficient Zl=U/ff lo and nonlinear term coefficient Znl =z2EA?Di/(21?|?2?f ff2l0),the marginal curve between Zl and Znlc=z2Ec?Di/(2|?|?2?fff2l0)was obtained.It was found that Znlc increased with the increase of Zl by a power-law curve,with the exponent b determined by pH value of solution.b decreases first and then increases with increasing pH.At the same time,the difference between the experimental results and the fitting results was evaluated.It was found that the power-law relationship between Zl and Znlc can provide an acceptable accuracy on experimental results,especially when Zl is sufficiently large.The agreement between the experiments and the theory was sufficiently high.In this investigation,we systematically studied the nonlinear oscillating electroosmotic flow on the insulating wall from both experimental and theoretical aspects.The research reveals the transformation process of linear behavior to nonlinear behavior and its influencing factors.It provides an important experimental basis for future researches on the dynamics of OEOF.It has important reference value for improving the conversion efficiency in future practical applications,and also provides important reference value for the future development of electroosmotic flow in micro-nano flow control,energy,and electrochemical fields.