Experimental investigation on flow characteristics of deionized water in microtubes

Chinese Science Bulletin◎2007》 Science in China Press包SningrVvetagExperimental investigation on flow characteristics ofdeionized water in microtubesXU ShaoLiang', YUE XiangAn & HOU JiRuiEnhanced 0il Recovery Research Center, China University of Petroleum, Beiing 102249, ChinaThe flow characteristics of deionized water in microtubes with diameters ranging from 2 to 30 μm areinvestigated. The experimental results show that the flow characteristics in microtubes with diametersof 16 μm and larger ones are in agreement with the classical theory. However, as the diameters are de-creased to 5 and 2 μm, the nonlinear flow characteristics prevail and the results indicate significantdeparture of flow characteristics from the predictions of the conventional theory, and the smaller thediameters, the larger the departure. As the Reynolds number increases, the degree of nonlinear flowcharacteristics decrease gradually and the experimental results are approximately equal to the theo-retical expectation. The minimum Reynolds number in this study is only 2.46x10-.microtubes, flow characteristics, microscale efect, fiction factor ratio, boundany layer fluidOver the past years, significant atention has been given toavailable experimental results are broken into two majorliquid flow on the microscale due to the incessant devel- groups: one is in agreement with conventional theoryopment of micro-electro-mechanical systems (MEMS).and the other deviates from it. Some experimental re-As the characteristic lengths are reduced to the same or-sults which are in agreement with classical theory arder of magnitude as the hydrodynamic boundary layershown as follows: Jiang et al.4l studied the variation ofthickness, the equations from the conventional theorythe Darcy friction factor with Reynolds number in mi-are not applicable any longer. Several effects such as thecrotubes with diameters ranging from 8 to 42 μm. Thesize effect and surface effect, which are normally ne-experimental results were in general agreement with theglected on the macroscale, become more and more im-predictions from conventional equations with range ofportant, and even become the dominant influencing fac-Reynolds number being 0.032- 26.1. Li et al.!3I studiedtors. The experiments on microscale flow of gases areexperimentally the flow characteristics of water andvery reproducible and consistent with the theoreticalseveral organic liquids in microtube which was about 25explanation. However, the microscale flow characteris-μm in diameter. They reported that the flow approxi-tics of liquids are much more complicated' because themately followed the Hagen-Poiseuille theory and theliquid is incompressible and the resistance caused byReynolds number was less than 8. Bucci et al!+ investi-viscosity is obvious. In addition, a number of influenc-gated the flow characteristics of water in microtubes5ing factors such as the intense momentum exchange, thewith diameters ranging from 172 to 520 um. Gan et al.5Tmolecular attraction and intermolecular interaction, andstudied the flow of water and methanol in microchannelthe liquid-solid interaction and adhesion also play im-with hydraulic diameter of 155.3 μm. Celata et al!6lportant roles in the microscale flow of liquids.Many researchers have conducted experiments on theRccived Seplember 13, 2006; aceped November 14, 2006flow of single-phase fluid in microchannels. The ex-doi: 10.1中国煤化工、tCorspperiments involved different test fluids and microchan-SuporedHC NMH Granof Chia (Grant No.ation of China (Grant No.50574060nels with different cross-sectional shapes. The current2002CCA00700)Www. scichina. com www.springerink. comChinese Science Bulletin I March 2007 1 vol, 52 Ino. 61 849-854studied the flow characteristics of water in microtubesmicroflow at low velocity, the liquid-solid interaction iswith diameters of 30- 326 μum. All these experimentalmuch stronger, which maybe enhances the microscaleresults were in rough agreement with the conventionaleffect. In this study, we carried out an experiment on thetheory.flow characteristics of deionized water in quartz micro-Some experimental results that deviate from the con-tubes with minimum diameter as small as 2 μm. Theventional theory are shown as follows: Pfahler et al.7minimum Reynolds number in this study was onlyconducted experimental studies on isopropanol in rec-2.46x10~, which enriches the experimental results. Thetangular microchannels which were approximately 100microscale flow effects are obtained and some newμm wide with depth less than 40 μum, finding the viscos-findings have been achieved.ity of liquid decrease. Mala and Lilsl investigated waterflow in microtubes made of fused silica and stainless1 Experimental apparatus and methodsteel, with the maximum Reynolds number reaching.1 Materials2500 and their results indicated that the relationship be-tween Reynolds number and pressure gradient deviatedThe microtubes used in this study are naturally fusedfrom predictions of conventional theory when the di-quartz microtubes (Polymicro Technology Company,ameter was less than 150 μm. Hao et al.'" investigatedUSA) with internal diameters of 30, 20, 16, 5 and 2 μm,water flow in trapezoidal silicon microchannel with arespectively. The working fluid is deionized water.hydraulic diameter of 237 μm, with the relationship be-1.2 Experimental apparatustween Reynolds number and pressure gradient deviatingThe experimental apparatus is shown in Figure 1. Thefrom the linear behavior and the deviation depending onapparatus consists of three parts: the power system, thethe Reynolds number.filter system and the measurement system. N2 from theAs can be seen from the experimental results men-compressed nitrogen gas tank flows through the flowtioned above, the conclusions are inconsistent under dif-control valve and enters the pressure-buffering reservoirferent experimental conditions. The size of micro-where it drives the deionized water to pass through thechannles and the Reynolds numbers in previous publica-thee-way pipe to the microtube. The measuring pipe istions are large, because the researchers mainly focusedconnected to the test microtube on the other end.on the early transition from laminar flow to turbulentflow, and on the different critical Reynolds numbers on1.3 Experimental methodthe microscale from that on the macroscale. But in the1.3.1 Pressure measurement. The inlet pressure is08十!312g|0 00中Measurement systemFilter systemPower system中国煤化工Figure 1 Experimental aparatus. 1, Compressed nitrogen gas tank; 2, flow control valve_g reservoir; 5, gas flter;6, liquid reservoir; 7, liquid filter; 8, three-way pipe; 9, pressure and temperature sensor;I.MYHCNMH( -hicroscope; 13, real-timeimage acquition system; 14, computer.850XU ShaoLiang et al. Chinese Science Blltinl March 2007 Ivol. 52 Ino. 61 849-854measured by the pressure sensor with a precision of 0.01viscosity.kPa, and is recorded via PC data acquisition system. The2.2 Error of flow rateflow control valve is turned on slowly to ensure that theThe measuring displacement in this study is longer thanpressure rises gradually. For each measurement, it is1 mm with a precision of 1 um, so the error is 0.1%. Theconsidered that the flow has reached a steady state whenmeasuring time is longer than 1 minute with a precisionthe pressure value does not change any further.of 0.01 s, so the error is about 0.167%. The length of1.3.2 Flow rate measurement. Flow rate is measuredmicrotubes is measured by a vernier caliper with a pre-by the displacement method. A PC image acquisitioncision of 0.02 mm, and the microtubes used in this studysystem is employed to transmit the interfacial image intoare 20- 40 mm in length, so the error is 0.05%-0.1%.a computer to record the displacement. The experimental2.3 Error due to capillary pressureflow rate is calculated using the displacement and thetime. Given the small flow rate, and the effect of liquidThe calculation of microscale flow rate is influenced byevaporation, the end of measuring pipe is sealed withthe self- adsorption phenomena, which is caused by theunvoltile white oil to keep the interface away from thecapillary pressure in tubes. The capillary pressure isgiven byatmosphere.△P。= 2σcosθ/r,1.3.3 Viscosity measurement. As a function of tem-perature, viscosity changes with temperature. In thiswhere σ is surface tension, θ is contact angle be-study, the viscosity of deionized water under standardtween microtube wall and liquid, and r is the radius oftemperature is obtained from the Handbook of Chemis-microtube.try. The viscosities under other temperatures are meas-It is assumed that the contact angle between micro-tube wall and liquid is zero. The surface tension of whiteured by a HAAKE-RS600 rheometer.oil is 36.7x10 2 mN/m. The capillary pressure is calcu-2 Error analysislated to be about 0.459 kPa with eq. (1). The lowestpressure in this study is 4 kPa, which leads the uncer-2.1 Error of viscosity due to temperature and pres-tainty of pressure to be up to 11%. Thus, the errorsurecaused by capillary pressure cannot be neglected. TheDue to the high specific area of the microtube and abil-error is minimized in the process of data analysis.ity of heat exchange, viscosity is highly sensitive to2.4 Error due to inlet and outlet lossestemperature variation. The integrated temperature con-Figure 2 shows schematic diagram of pipe junction withtrolling method is adopted to reduce the error caused bydifferent diameters from the pressure and temperaturelocal temperature contolling. The viscosity variation issensor to the test microtube and the measuring pipe. It+2.4% as the temperature varies by 1C at 25"C. Dur-can be seen that the pipeline diameter varies from theing the course of the experiment, the temperature varia-pressure and temperature sensor to the measuring pipe.tion is +0.5C. Thus, the uncertainty of viscosity causedTherefore, the inlet and outlet losses possibly influenceby temperature variation is about 1.2%.the flow rate. In order to account for the error due toUnder atmospheric pressure, the viscosity of waterinlet and outlet losses, the experiments are conducted byincreases by about 0.1%一0.3% as pressure increases byusing the tubes which are the same in diameter (16 um)every 0.1 MPa. The measuring pressure range in thisbut different in length (20, 40, 60 mm).study is 0- 1 MPa, which results in 1%一3% increase inOn the macroscale, the frictional pressure drop inPSP20P,P.D中国煤化工4MYHCNMHGFigure 2 The schematic diagram of pipe junction with dfferent diameters.XU ShaoL iang et al. Chinese Science BlletinI March 2007 1vol. 52 Ino. 61 849-854351laminar tube flow is expressed asFigures 4 and 5 show the variation of pressure gradi-P=f台号叩i=1,2,3.4.(2)ent with Reynolds number for deionized water in mi-The local pressure drop due to a sudden contraction iscrotubes with diameters of 5 and 2 μm, respectively. Asshown in these two figures, the experimental data devi-s:=s(-唱，i=l,2.(3) .ate from the theoretical expectation. Furthermore, theD22deviation in the microtube with a diameter of 2 um isThe local pressure drop due to a sudden enlargement islarger than that of 5 μm. The variation of pressure gra-dient with Reynolds number shows apparent non-linearAP:=0.51-DD.v2, i=3.(4)flow characteristics, and the flow characteristics deviatefrom that of the conventional theory. In addition, for theThe error due to inlet loss, outlet loss and pipe junc-microtube with a diameter of 5 μm, the experimentaltion pressure drop isresults are close to the theoretical curve as ReynoldsError=P+R+P +SP + OR +△P .x100%. (5)number increases. But when the diameter is decreased toP2 μm, the experimental results deviate from theoreticalBased on the experimental data, the maximum errorvalues as Reynolds number reaches 0.0245. It impliesdue to inlet and outlet losses calculated by eq. (5) isthat the smaller the diameter, the stronger the microscale0.12%. It implies that the error caused by inlet and outleteffect.losses can be neglected.Due to the microscale efect, the Darcy frction factor3 Results and discussion30rThe flow characteristics of deionized water in micro-25-tubes (30, 20, 16, 5, 2 μm) are investigated, and the re-20-sults are shown as follows.Figure 3 shows the variation of pressure gradient with5|.:;"Reynolds number for deionized water in different mi-■Exp-5 umcrotubes (30, 20, 16 μm). The spots represent experi-0叶Theorymental data and the lines are theoretical values calcu-lated by the Poiseuille equation. Obviously, the experi-mental results are consistent with theoretical values. It0.000.020.040.060.080.100.120.140.16shows that the flow characteristics in microtubes withReynolds numberdiameters of 16 μm and larger ones are still in agree-Figure 4 Variation of pressure gradient with Re (5 μum).ment with the conventional theory.3.Sp80r0-3.(of2.01.5|Exp-30 um0f.■Exp-2 umEXn-200m-TheoryExp-16 um墓20f- Theory0.510-0.0.0051.01.5320253.035 . 4.0中国煤化工20 0.025 0.030.YHC N M H GihReQum).Figure 3 Variation of pressure gradient with Re (30, 20, 16 μum).852XU ShaoL iang et al. Chinese Science Blletinl March 2007 1vol. 52 Ino.61 849-854in microflow deviates from that of conventional theory20% higher than the theoretical expectation.when single-phase fluid flows in microchannels. In or-In conclusion, the flow characteristics in microtubesder to account for this discrepancy, the friction factorwith diameters of 16 μum or larger are in agreement withratio C* is defined asthe classical theory. As the diameters decrease to 5 and 2fexpμm, the experimental results show significant departure6)from the predictions of conventional theory. Moreover, itJHPwhere fexp is the friction factor obtained from experi-implies that the smaller the diameter, the stronger themental data, and fup is the friction factor calculated bymicroscale effect. As Reynolds number increases, thefriction factor ration C* decreases, and is approximatelythe Hagen-Poiseuille equation.As is evident in Figures 6 and 7, the friction factor ra-equal to the theoretical expectation.The micoflow is affected by a number of factors,tio C* for all the data is greater than 1, and the value ofC* changes as Reynolds number increases. This indi-such as the surface roughness, the electronic doublecates that the friction is higher than that predicted bylayer effect and the micropolar effect of fluid molecules.macroscale theory. The maximum C* in the microtubeAccording to laminar fluid theory, the flow charactertis-with a diameter of 2 μm is about 4.21 while the maxi-tics on the macrosacle are independent of wall surfaceroughness which only afects the transition from laminarmum C* in the microtube with a diameter of 5 μm isflow to turbulent flow. However, studies from Mala etmerely 1.93. As the pressure gradient increases, the C*al.81 and Li et al."0] showed that the early transitionvalues in the microtube with a diameter of 5 μum begin tofrom laminar flow to turbulent flow resulted from wallaccord with the conventional theory, whereas the C*surface roughness. Thus, it remains unclear whether thevalues in the microtube with a diameter of 2 μm are stilllaminar flow characteristics are affected by tube wallsurface roughness. In addition, as the thickness of elec-tronic double layer reaches the same order of magnitude1.6■Exp-5 μumas characteristic length of the microflow, the ions and一-Theorypotential distribution also influence liquid microflow.1.4-Besides, the solid surface property, liquid property and飞1.2-their interaction also contribute to such a process be-1.cause they largely determine the ions and potential dis-tribution. Ye et al." obtained velocity profiles and mi-0.8cro-rotation gyrations in microchannels by a procedure0.6 tbased on numerical method. The results showed that there0.00 : 0.02 0.040.060.080.100.120.14was an obvious decrease in the flow rate when the Cou-Reynolds numberpling between velocity vector and micro-rotation gyration2Figure 6 Varation of C* with Re (5 um),vector was strengthened. As concluded above, the elec-tronic double layer effect and micropolar effect of fluidmolecules are the factors that influence microflow.4.0When liquid flows in a microtube, due to such influ-3.5encing factors as the electronic double layer effect and3.■Exp-2 μumthe micropolar effect of fluid molecules, intensive inter-actions occur between the liquid and tube wall. There-fore, evident property difference is shown between the乙2.0liquid layer adjacent to the solid wall and body fluid.1.5-.....Alexander et al.proved theoretically that water den-1.0sity profiles existed in interfacial water layer near to0.cylinder solid surface, and that the closer to the wall, the0.000 0.0050.010 0.0150.020 0.025higher中国煤化工1 that the thicknessof adsdYHCNMH G surfacc was notaFigure7 Variation of C* with Re (2 um).constan, oul a Tuncuun UI uIe ulviug pressure gradient.XU ShaoLiang et al. Chinese Science Blletin I March 2007 lvol. 52 Ino. 6| 849-854853Moreover, it became thinner as pressure gradient in-Reynolds number is approximately equal to the theo-creased. Rene et al."4 investigated the meniscusretical expectation.thickness of pure water on fused quartz surface by usingan image analyzing interferometer. The results showed4 Conclusionsthat the thickness was larger than 0.1 um. All thesestudies clearly showed that the boundary layer fluid(i) The flow characteristics of deionized water in mi-played an important role in the microflow.crotubes with diameters of 16 μm or larger are inSince there is a difference between the boundary layeragreement with the conventional theory.fluid and the body fluid, a small portion of the boundary(i) As the diameters are decreased to 5 and 2 μm, thelayer fluid cannot be regarded as the body fluid. Con-nonlinear flow characteristics prevail and the resultssidering the influence of the boundary layer fluid, whenindicate significant departure of flow characteristicsthe liquids flow in microchannels, the effective flowfrom the predictions of conventional theory. The frictionradius diminishes while the flow resistance increases,factor ratio C* for the flow in microtubes with diameterswhich gives rise to the microscale effect and theof 5 and 2 μm is greater than 1, and the maximum val-non-linear flow characteristics. As pressure gradient andues are 1.93 and 4.21, respectively.wall shear stress increase, the electric double layer effect(ii) The values of C* for the flow in the microtubeand the micropolar effect of fluid molecules becomewith diameter of 2 μm are larger than that of 5 um at theweaker. More boundary layer fluid graduates into bodysame Reynolds number. As Reynolds number increases,fluid and the boundary layer becomes thinner. The ef-the degree of nonlinear flow characteristics and the fric-fective flow radius increases and the degree oftion factor ratio C* decrease. Moreover, the experimen-non-linear flow characteristics decreases, which leads to tal values are approximately equal to the theoretical ex-the result that the variation of pressure gradient withpectation. .1 Liu J. Heat Transfer on Micro/Nano Scale (in Chinese). Beijing:ASME Proc, 1991, 32: 49-60Science Pess, 20018 Mala G M, LiD Q. Flow characteristics of water in microtubes. Interm2 Jiang X N, Zhou Z Y, Huang X Y, e al. Laminar flow hrough mi-J Heat Fluid Flow, 1999 20(2): 142 - 148crochannels used for microscale cooling systerms. In: Proeedings of9 Hao PF He F, Zhu K Q. Flow caraceristis in a trapezoidal silionthe Electronic Packaging Technology Conference, Singapore, 1997.microchannel. J Micromech Microeng, 2005, 15: 1362- 1368119-12210 LiZX, Du D x, Guo z Y. Experimental study on flow charactestics3 LiZ H, Zhou X B, Zhu s N. 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Experimental study of adsorbed6 Celata G P, Cumo M. Mcphail S, et al. Characterization of fluid dy-water layer on solid particle suface. Acta Miner Sin (in Chinese),namic behavior and channel wall efects in microtubes. Interm J Heat2005, 25(): 15-19Fluid Flow, 2006, 27: 135-14314 Rene R M, Wayner PC. Aqueous wetting films on fused quartz. J Coll7 Pfahler J, Harley J, Bau H. Gas and liquid flow in small channels.Interf Sci, 199, 214(2): 156- 169中国煤化工MYHCNMHG854XU Shaoliang et al. Chinese Science Buletin1 March 2007 1vol. 52 Ino.61849-854