Electrokinetic mixing of two fluids with equivalent conductivity

Fang Yang,Wei Zhao,Guiren Wang,3,*

1 Key Laboratory for Molecular Enzymology and Engineering of Ministry of Education,School of Life Sciences,Jilin University,Changchun 130012,China

2 Institute of Photonics and Photon-technology,International Scientific and Technological Cooperation Base of Photoelectric Technology and Functional Materials and Application,Northwest University,Xi’an 710127,China

3 Department of Mechanical Engineering,University of South Carolina,Columbia,USA

Keywords:Microfluidics Microchannels Mixing Electrokinetics Micromixer

ABSTRACT Electrokinetic (EK) micromixers have been widely studied in the past decade for biochemical applications,biological and chemical analysis,etc.Unfortunately,almost all EK mixers require different electrical conductivity between the two fluids to be mixed,which has greatly limited their wide applications,in cases where the two streams to be mixed have equivalent electrical conductivity.Here we show that mixing enhancement between two fluids with identical conductivity can be achieved in an EK micromixer with conductive sidewalls,where the electric field is in transverse direction of the flow.The results revealed that the mixing became stronger with increased conductivity value.This mixing method provides a novel and convenient strategy for mixing two liquids with the same or similar electrical conductivity in microfluidic systems,and could potentially serves as a powerful tool for sample preparation in applications such as liquid biopsy,and environmental monitoring, etc.

1.Introduction

Mixing of analytes and reagents is a critical step in many life science applications [1,2],such as enzymatic reaction [3],protein folding[4],DNA purification[5],etc[6,7].These processes’ performance,e.g.sensitivity and measurement of chemical kinetics depends strongly on the mixing effectiveness and rapidness of the samples and reagents[8].Fast mixing will generate stronger signals to improve the detection sensitivity and enable more accurate measurement of the kinetics.In the past decade,applications of the electrokinetic(EK)mixing in microfluidic devices have attracted a wide interest[9-15].EK mixers generally require no external mechanical moving parts and promise fast mixing even under the condition of low Reynolds numbers,which are the cases in most microfluidic devices [16].Electrical conductivity difference between the two streams to be mixed is an important condition required in most EK mixing strategies.This is because a net charge could be induced and accumulated at the fluid-fluid interface with an electrical conductivity gradient.By applying an electric field,electrical body force is subsequently induced on the streams,which destabilizes the interface and enhances the mixing[17-19].However,in many applications (dielectric fluids mixing,enzymatic reaction,for example),it’s inconvenient to require the fluids have different conductivities.Therefore,methods of mixing two fluids with equivalent conductivity have more practical meaning,yet such a technique needs to be developed for’lab-on-a-chip’devices[20].

In our previous study,we have discovered that there could be microelectrokinetic turbulence in a microchannel[21] and its corresponding ultrafast mixing[22]when a pressure driven flow with two streams of different electrical conductivity is forced electrokinetically at low Reynolds number.The same technique has been successfully applied to produce monodispersed polymer (core)and protein(shell)nanoparticles with much less bandwidth of particle size distribution compared with that produced in convectional mixer [23].Fortunately,it is further found that the same device could also be used to enhance mixing of two streams with the same conductivity although the flow is not turbulent,but chaotic.Here,we report this new design of active EK micromixer,which has electrically conductive sidewalls for mixing fluids with the same electrical conductivity by applying an alternating current (AC) electric field to create an externally time-dependent electric body force.

2.Materials and Methods

Conductive electrodes were used directly as the sidewalls of the presented new micromixer.In this way,since the distance between the electrodes is very short,we could more easily obtain a strong electric field at low voltage.The schematic of the micromixers is given in Fig.1(a).It is a quasi T-channel made of acrylic plates,gold(conductive)sheets.The two gold sheets between the acrylic plates formed the sidewalls of the microchannel.In this work,we used a parallel sidewall mixer that had a rectangular cross section of 120 μm in width (W) and 230 μm in height (h),with a length ofL=5 mm.There were two inlets and one outlet with diameter of 1 mm.

The mixing process began with each fluid entering the microchannel through an inlet.Electrical double layers(EDLs)were formed at the interface between the acrylic substrates and the electrolytes.When the electrodes were electrically activated,fluids were subjected to an electrical body force (as shown in Fig.1(c))induced by the electric field on both the net mobile electric charge in the EDL and non-zero charges due to the Joule heating.If the electric body force is sufficiently large,it will create a transversal convection (secondary flow) across the interface between the two fluids.By applying an AC electric field,Joule heating effect occurred both near the sharp edge of the entrance of the flow channel and on the imperfect surface of the electrodes and caused local temperature gradient(see red spots in Fig.1(c)).Then the conductivity gradient was generated locally near the electrode surfaces and consequently leads to electrically driven secondary flow.Those secondary flows destabilized the interface and promote the mixing process of the two fluids,when the electric field E is arranged to be perpendicular to the stream direction.Thus,one could expect to achieve good mixing between the two fluids without requirement of the conductivity difference between the initial two streams in this mixer.

In addition,the electroosmotic flows near the interface between acrylic and fluid could oscillate when AC electric field is applied.Such an oscillating EOF may also generate chaotic flow [24,25] to disturb the main flow and enhance the mixing as shown in Fig.1(c).

In the experiment,a syringe pump (Harvard,Model PHD2000)was used to inject two fluids to the micromixer.Rhodamine B(Sigma-Aldrich,Corp.) was used as the fluorescent dye trace for mixing visualization,as it is an electrically neutral dye which could minimize the possibility of conductivity difference between the two fluid streams.Phosphate buffer (VWR VW3345-1 pH 7.2)was diluted into de-ionised (DI) water as the streams to control the conductivity of the two streams.The micromixer was placed on the test bed of an inverted fluorescent microscope (Olympus-IX70).A function generator (Tektronix,Model AFG3102) was used to apply AC electric signal on electrodes.

A mercury lamp was used as the illumination source in the present study.Passing through an epi-fluorescent cube,the bright light from the mercury lamp went through a filter and was used to excite the dyed solution in the microchannel.Upon excitation(with the light of 532 nm in wavelength),the fluorescent solution would emit fluorescence light signal with a peak located at 568 nm.A 10X objective lens(NA=0.25)was used for the fluorescence imaging.The fluorescence signal was captured by a sensitive high-resolution CCD camera (SensiCam-QE,PCO).The concentration was quantitatively determined by measuring the fluorescence intensity within each pixel of the camera using the software analytical tools (MATLAB,MathWorks Inc.).Based on our measurement,the dye concentration and the fluorescence intensity had a linear relation in the current dye concentration range.Mixing enhancement results were compared based on concentration profiles of the fluorescent dye along a transverse line,which is perpendicular to the flow direction of the microchannel at a given streamwise position.The bulk flow Reynolds number is defined asReb=UD／ν,whereUis bulk flow velocity,Dis hydraulic diameter and ν is kinematic viscosity.In this investigation,Rebis in the range of 0.1-0.5.

Fig.1.(a)Schematic diagram of the micromixer with conductive sidewalls.The height and width of the microchannel were 230 μm and 120 μm,respectively.The length of microchannel was 5 mm.(b)The size of the chip is 25 mm×25 mm(not include electrodes).(c)Cross view of the micromixer:Mixing is achieved by the local Joule heating near the electrodes (red spots) and electroosmotic flow (EOF).Electrical conductivity gradient is generated locally,and consequently leads to electrically driven flow.

3.Results and Discussion

To investigate influence of conductivity value(σ)on the mixing,we kept voltage at 20 Vp-p,flow rate at 1 μl·min-1.The high frequency(1 MHz)was selected to ensure that no bubble will be generated for potential applications.Meanwhile,with the conductivity ratio kept at 1,mixing fluids with equivalent conductivity but different values have been investigated,i.e.σ=10,100 and 1000 μS·cm-1,respectively.Results are shown in Fig.2.

In Fig.2,it can be clearly seen that strong mixing was achieved in the conductive sidewall mixer,even though there was no conductivity difference between the two streams.Fig.2 indicates that,the mixing was weakest under σ=10 μS·cm-1,stronger under σ=100 μS·cm-1and became strongest under σ=1000 μS·cm-1respectively.Hence,the mixing was enhanced with the increasing of σ.

Furthermore,Fig.2(d) shows the quantitative measurement of the concentrationCdistribution in the transverse direction,at streamwise position of 1.5W(Wis the entrance width of the microchannel) downstream from the entrance.As we know,the stronger the mixing,the more uniform the concentration (i.e.the fluorescence intensity here).The curve should approach flat when the fluids are well mixed in the microchannel.In Fig.2(d),it shows that,Cdistribution with σ=1000μS·cm-1reached the most uniform profile atx/W=1.5,while at the samex-position,the profile of the concentration distribution with σ values of 100 μS·cm-1and 10 μS·cm-1were still far away from a flat profile.This quantitative result indicates that mixing is enhanced rapidly with increased conductivity value in the conductive sidewall micromixer.

The dependence of the mixing on the electrical conductivity value indicates that the local Joule heating could play an important role for the mixing enhancement [26],which is proportional to σE2,where σ is electrical conductivity of the fluid and E is the applied electric field[27].The larger σ,the stronger the Joule heating.Joule heating generates local temperature gradient which leads to the local gradients of electrical permittivity and conductivity,which then causes the thermal convection [28].The temperature change caused by the Joule heating is governed by [29]

where ρm,Cpandkare the density,specific heat (at constant pressure) and thermal conductivity respectively.Both electric permittivity ε=ε(T) and electric conductivity σ=σ(T) are functions of temperature.In water solutions,normally αε=(?ε／?T)=-0.004 and=0.02.In electrokinetic flows (including electrothermal flow),the electric body force can be generally described as

Where ρEis the net charge density.The first and second term on the right-hand side of Eq.(2) are the Coulomb force and the dielectric force respectively.Under AC electric field,the averaged electric body force 〈F〉 according to electrothermal effect can be expressed as [29,30]

In this equation,electrical conductivity is not simply a passive scalar because the electric body force,which relies on the electrical conductivity and permittivity distribution,will in turn cause change in the flow velocity field[18].The local hot spots were convected by the secondary flow from the near wall to the center region of the channel,which further induced entrainment of fluid with higher temperature into the region with lower temperature,and accordingly complicated ?Tdistribution in this microchannel.Consequently,a strong and highly nonuniform 〈F〉 can be generated spatially as results of ?T·Ecand ?Tdistributions.Intuitively,a larger absolute value of σ could induce stronger variation ofTand ?T.Therefore,a stronger mixing could be achieved due to the stronger 〈F〉.Besides,if the temperature variation is strong,the influence of buoyance (Fb=βgT,with β andgbeing thermal expansion coefficient and gravity respectively [31]) in vertical direction is also nonnegligible.It can also contribute to the mixing as a result of thermal convection.

To further understand the influence of flow condition on the mixing results,effect of Reynolds number (Reb) on mixing was investigated as well.In this experiment,we kept voltage,AC frequency and σ at 20 Vp-p,1 MHz and 1000 μS·cm-1respectively.The flow rate was changed in the range of 1-5 μl·min-1,and the correspondingRebnumber was 0.1,0.3 and 0.5 respectively.Results are shown in Fig.3.

Fig.2.Visualization of mixing in the micromixer with equivalent electrical conductivity of the two fluids and comparison of different conductivity values.(a)σ=10 μS·cm-1;(b)σ=100 μS·cm-1;(c)σ=1000 μS·cm-1.(d) Comparison of concentration profile in transverse direction at x/W=1.5 from the channel entrance.

Fig.3.Visualization and comparison of mixing in the micromixer with different Reb numbers,where σ=1000 μS·cm-1.(a) Without voltage,(b) Reb=0.1,(c) Reb=0.3,(d)Reb=0.5.(e) Comparison of concentration profile in transverse direction at x/W=1.5 from the channel entrance.

As visualized in Fig.3,the mixing is strongest when theRebis 0.1,compared with situations whereRebwere 0.3 and 0.5 respectively.In lowRebflow,much faster mixing could be achieved at a given downstream position than that at higherRebsituations.The reason could be (1) the lowRebnumber flow has longer time to mix the fluids at the same streamwise position;(2) the ratio of the EK force to the inertial force due to the hydrodynamic pressure in the streamwise direction is larger in theRebflow than in the highRebflow,and this EK force will generate relatively stronger transverse stirring to enhance mixing.Therefore,in a low flow rate situation,the mixing could be achieved closer to the entrance.On the other hand,in high flow rate situation,the same mixing will be achieved at further downstream position from the entrance.To achieve same mixing at higherRebnumber flow,higher voltage is needed,which is inconvenient in practical applications.However,with our conductive sidewall arrangement,high electric field could be easily generated with low voltage.Therefore,even our function generator can only provide the maximal voltage of 20 Vp-p,mixing could be enhanced for allRebnumber investigated in our micromixer.

These results could have very important practical applications in life science,where electrical conductivity difference among fluid samples is not always available or possible.With the conductive sidewall mixer,mixing could be achieved either with the same or different conductivity,which means the electrical conductivity gradient is no longer an indispensable requirement for mixing of different fluids.This achievement will be able to broaden the applications of micromixer in Lab-on-a-chip.

4.Conclusions

In the present investigation,by applying AC signals on conductive sidewalls,rapid mixing between two fluids with the same electrical conductivity has been achieved in the quasi-T-channel electrokinetic micromixer.As the values of the electrical conductivity of the two fluids was increased,the mixing became stronger.Future study could include more detailed parametric study,such as effect of voltage,frequency,electrodes arrangement and numerical simulation,etc..This mixing strategy provides a new and convenient method for enhancing mixing of two fluids with the same conductivity,which is the common situation in biomedical and biochemical analysis applications.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The work is partially supported by the North American Mixing Forum (NAMF),NSF CAREER (CBET-0954977),the National Natural Science Foundation of China(21705055),Science and Technology Development Planning Program of Jilin Province(20190201178JC),Jilin Province Industrial Technology Research and Development Project(2019C048-5).