Microwave-induced Water Flows in Microsystems

Microwave-induced water flows in microsystems A. Ramos,a兲A. Robles, P. García-Sánchez, and M. J. Freire Departamento de Electrónica y Electromagnetismo, Universidad de Sevilla, Avda. Reina Mercedes s/n, Sevilla 41012, Spain 共Received 3 December 2008; accepted 21 December 2008; published online 14 January 2009兲 Alternating current electric fields are of increasing importance for the development of microfluidic pumps. We report how microwave fields can induce water flow in microsystems, irrespective of saline concentration. A drop of water is placed on two parallel coplanar microelectrodes that are energized by a microwave generator. Fluid flow is observed and the fluid velocity is about the same for two electrolytes with very different saline concentrations. Electrically induced gradients of temperature produce spatial variations in mass density and dielectric permittivity leading, respectively, to buoyancy and dielectric forces in the liquid. The observed fluid flow patterns demonstrate that both effects are taking place at different length scales: the dielectric forces dominate at lengths of the order of 100 ␮ m or smaller, while buoyancy dominates around 1 mm. ©2009 American Institute of Physics.关DOI: 10.1063/1.3070521兴 Control and manipulation of water is an important requirement for the lab-on-chip technology.1Among the most promising techniques to handle small amounts of liquid are those that employ electrical forces directly applied to the liquid. Electrohydrodynamic 共EHD兲actuation presents the advantages of voltage-based control, dominance of electrical forces at the micrometer scale, and absence of moving parts. Therefore, several possible ways of EHD actuation in microsystems have been explored such as electro-osmosis,2ac electro-osmosis,3electrothermal induction pumping,4and ion-drag pumping.5 Microwave electric fields have recently been used in microsystems for controlled dielectric heating6or for reagent detection within microchannels.7In this letter, we experimentally demonstrate the use of microwave fields for electrothermal actuation of water in microsystems. The microwave fields heat the fluid generating gradients in mass density and dielectric permittivity. The fluid is then set into motion due to buoyancy fg=⌬ ␳ gand dielectric forces fE=−1 2E2ⵜ␧. The main advantage of this kind of EHD actuation is that water saline solutions can be pumped with almost no dependence on saline concentration since the heating is based on water dielectric loss at microwave frequencies.8Other kinds of EHD pumping of water are suitable for certain ranges of conductivity: ac electro-osmosis is suitable for electrolytes with low ionic strength 共 ␴ ⱕ0.01 S/m兲, while ac electrothermal induction pumping is suitable for higher ionic strength 共 ␴ ⬎0.01 S/m兲. The latter can be used for liquids with smaller conductivity but using external heating. In addition, the frequency of the signal must be changed depending on conductivity to achieve the best pumping performance in both kinds of actuation. The power density dissipated as heat for an ac field Eof angular frequency ␻ due to dielectric loss is Pdiel =1 2␧⬙ ␻ E2, and due to Ohmic currents is POhm=1 2 ␴ E2, where ␧⬙is the imaginary part of the complex dielectric permittivity and ␴ is the electrical conductivity. Therefore, dielectric heating dominates over Joule heating for ␧⬙ ␻ ⬎ ␴ . For instance, the dielectric loss factor ␧⬙ ␻ at 3 GHz and 20 °C results in an equivalent conductivity of 2.2 S/m. 共The equivalent conductivity is 0.24 S/m for a frequency of 1 GHz at 20 °C.兲The heating and the expected flow induced by ac electric fields at 3 GHz are about the same for water solutions with conductivities smaller than 2.2 S/m. Therefore, most biological fluids could be pumped with the same behavior using the same applied signal. For higher conductivity, the heating will increase but the effect would be similar. We propose that microwave water actuation can be of use for the lab-on-chip technology. The experimental setup is shown in Fig. 1. A square fluid chamber was built with polydimethylsiloxane 共soft polymer used in microfluidics兲. The bottom of the chamber is a planar glass substrate with two parallel platinum microelectrodes fabricated on it. The lid is a glass coverslip. The electrodes are 100 nm thick and 500 ␮ m wide separated by a 10 ␮ m a兲Electronic mail: [email protected]. FIG. 1. Scheme of the experimental setup for the observation of microwave induced flows. Fluid flow is generated on top of two coplanar microelectrodes. The device is connected to a microwave generator through a transmission line. APPLIED PHYSICS LETTERS 94, 024104 共2009兲 0003-6951/2009/94共2兲/024104/3/$23.00 © 2009 American Institute of Physics94, 024104-1 09 June 2025 13:40:47 gap. KCl water solutions were pipetted into the chamber. Fluorescent latex particles 共500 nm diameter兲were suspended in the solution and used as flow tracers. Fluid flow was observed after application of ac electric fields from 1 to 4 GHz. The microwave source comprises an Agilent PNA E8363B automatic vector network analyzer used as a microwave generator and connected to a microwave amplifier AR 5S164. The device was connected to the amplifier through a coaxial transmission line. Figure 2共a兲presents the measured velocity against frequency for constant power Pin =0.16 W of the incident wave for two saline solutions. The height of the chamber is 737 ␮ m, sufficiently high to consider that the fluid motion is mainly due to buoyancy 共see below兲. Typically, two symmetric rolls were observed on top of electrodes. For f ⬎1.5 GHz, the velocity is roughly the same for the two water solutions. At frequencies from 1 to 4 GHz, microwave wavelengths are of the order of 10 cm, much greater than the dimensions of the device 共⬃2mm兲. Therefore, simple circuit theory is valid for the analysis of the microdevice and a voltage difference can be assumed to be applied between the parallel electrodes. The variation in fluid velocity with frequency can be understood from the frequency variation of the voltage between electrodes. Our device will behave as a load impedance Zconnected to the end of the transmission line, which has a characteristic impedance of Z0=50 ⍀.At microwave frequencies the connection pads behave mainly as an inductor 共of inductance L兲, which is connected to the two coplanar microelectrodes that, with the water drop on top, behave as a leaky capacitor 共with resistance Rand capacitance Cin parallel兲. The resistance Ris not a constant 共it is inversely proportional to ␴ +␧⬙ ␻ 兲. The device impedance is given by Z=i ␻ L+R/共1+i ␻ CR兲. The voltage V=V++V− and the electrical current I=共V+−V−兲/Z0at the end of the transmission line are related by V=ZI, where V+is the amplitude of the incident wave provided by the source and V−is the amplitude of the wave reflected by the device. The voltage at the electrodes relative to V+is then VCR/V+ =2ZCR/共Z+Z0兲, with ZCR=R/共1+i ␻ CR兲the impedance of the leaky capacitor. Figure 2共b兲shows the voltage at the electrodes as a function of frequency for reasonable values of L,R, and C, computed with finite elements for the actual device. It also shows the theoretical voltage required to generate the measured velocities by buoyancy. The agreement is satisfactory. Figure 2can be used as a calibration curve to infer the voltage at the electrodes as a function of frequency for a given incident power Pin=V+ 2/2Z0. Figure 3shows the experimental fluid velocity as a function of estimated dissipated power Pdis=共PinVCR/V+兲2共Z0/R兲for two channels with different heights 共287 and 737 ␮ m兲. The experimental velocities were obtained varying the incident power 共0–3 W兲 for given frequencies 共1, 2, and 3 GHz兲and saline concentrations 共de-ionized water and KCl solution of conductivity 128 mS/m兲. We can see that the experimental velocities have collapsed into a single curve, independent of frequency. Computations for the velocity using finite elements are also shown.9The difference between experimental and numerical results at low powers for the 287 ␮ m channel height can be attributed to the fact that the calibration curve was obtained from the 737 ␮ m channel height measurements. For the computations, we have solved the electric, temperature, and velocity fields in the chamber. Because the wavelength is much greater than microdevice dimensions, the electric potential is solved. Complex permittivity in different domains 共water, glass兲are used in order to account for the dielectric response at microwaves, ⵜ·关共 ␴ +i ␻ ␧ ˜ 兲ⵜ ␾ 兴=0 ␧ ˜ 共 ␻ 兲=␧⬘共 ␻ 兲−i␧⬙共 ␻ 兲.共1兲 At 20 °C, the real part ␧⬘is approximately 80␧0for frequencies below 5 GHz 共relative variation ⬍5%兲. On the other hand, the imaginary part ␧⬙depends on frequency in the range of our experiments 共1–4 GHz兲. The temperature field is governed by kⵜ2T+1 2共 ␴ + ␻ ␧⬙兲E2=0, 共2兲 neglecting convection of heat. Finally, the fluid velocity is obtained from Stokes equations for an incompressible fluid, ␩ ⵜ2u−ⵜp+fg+具fE典=0 ⵜ·u=0, 共3兲 where pis the pressure and ␩ is the viscosity. The dielectric force expression is usually obtained from thermodynamic arguments with static fields. We have assumed that the dielectric force expression is valid with ␧=␧⬘since 1 2␧⬘E2accounts for the electrical energy stored in the dielectric. For simplicFIG. 2. 共Color online兲共a兲Velocity measured at a given point 共x=200 ␮ m, z=100 ␮ m兲as a function of frequency for two water solutions 共incident microwave power is 0.16 W兲.共b兲Estimated voltages at electrodes as functions of frequency for generation of the observed fluid velocities by buoyancy and expected voltage at the electrodes from the circuit analysis 关L=2.3⫻10−8 H, C=10−12 F, and R=885/共␧⬙ ␻ 兲⍀兴Rand Care computed with COMSOL MULTIPHYSICS for the actual device. Lis estimated from analytical solution of the induction per unit length for two infinitely long strips. FIG. 3. 共Color online兲Velocity as a function of estimated dissipated power in the device for different frequencies and water solutions: 共a兲channel with height equal to 287 ␮ m and 共b兲to 737 ␮ m. Continuous lines: computed velocity as a function of dissipated power for ␧⬙ ␻ + ␴ =0.4 S/m. 024104-2 Ramos et al. Appl. Phys. Lett. 94, 024104 共2009兲 09 June 2025 13:40:47 ity, in the computations we have assumed that increments of temperature are small. Therefore, physical properties are considered constant, independent of temperature, except for the force terms in Stokes equations 共Boussinesq approximation兲:fg=共d ␳ /dT兲⌬Tgand fE=−1 2E2共d␧/dT兲ⵜT, where for water at 20 °C 共1/ ␳ 兲d ␳ /dT=−2.6⫻10−4 K−1 and 共1/␧兲d␧/dT=−4⫻10−3 K−1. The ratio between gravitational and dielectric forces is of the order of fg/fE⬃gl3⌬ ␳ /0.5V2⌬␧ 共with las the typical length兲,10 and this ratio decreases rapidly with decreasing l. Figure 4shows experimental particle paths for the two devices with channel heights of 287 and 737 ␮ m at a plane 90 ␮ m high from the level of electrodes. The fluid motion parallel to the gap between the electrodes is mainly originated by the dielectric force, while the motion perpendicular to the gap is mainly due to buoyancy.11 When the chamber is small the motion due to dielectric forces starts to dominate. The theory for small temperature increments predicts that fluid velocity due to buoyancy should be proportional to the dissipated power, while the velocity due to the dielectric force should be proportional to the dissipated power squared. For a channel with height 287 ␮ m, Fig. 3shows that the velocity increases more than linearly with dissipated power for Pdis⬎0.02 W. In conclusion, we have demonstrated the pumping of water in a microdevice by the electrothermal action of microwave electric fields. Buoyancy and dielectric forces set the liquid into motion. We have shown semiquantitative agreement between experiment and theory in terms of frequency and voltage dependence. The ability to pump water solutions with different conductivities 共including biofluids兲 in a microsystem has many potential applications in the labon-chip technology. We acknowledge the financial support of the Spanish government agency DGCyT 共Contract No. FIS2006-03645兲 and Junta de Andalucía 共Contract No. FQM-241兲. A. Robles acknowledges financial support of MIT-Spain Program Internship. 1H. Stone, A. Stroock, and A. Ajdari, Annu. Rev. Fluid Mech. 36,381 共2004兲. 2V. Pretorius, B. Hopkins, and J. Schieke, J. Chromatogr. A 99,23共1974兲. 3A. B. D. Brown, C. G. Smith, and A. R. Rennie, Phys. Rev. E 63, 016305 共2000兲. 4G. Fuhr, R. Hagedorn, T. Muller, W. Benecke, and B. J. Wagner, J. Microelectromech. Syst. 1,141共1992兲. 5A. Richter and H. Sandmaier, An Investigation of Micro Structures, Sensors, Actuators, Machines and Robots, Proceedings of the Micro Electro Mechanical Systems, 1990 共IEEE, New York, 1990兲, pp. 99–104. 6J. J. Shah, S. G. Sundaresan, J. Geist, D. R. Reyes, J. C. Booth, M. V. Rao, and M. Gaitan, J. Micromech. Microeng. 17, 2224 共2007兲. 7H. Lee and J. Yook, Appl. Phys. Lett. 92, 254103 共2008兲. 8R. Buchner, J. Barthel, and J. Stauber, Chem. Phys. Lett. 306,57共1999兲. 9A. Ramos, P. Garcia-Sanchez, A. Robles, and M. J. Freire, J. Electrost. 共unpublished兲. 10A. Ramos, H. Morgan, N. G. Green, and A. Castellanos, J. Phys. D 31, 2338 共1998兲. 11See EPAPS Document No. E-APPLAB-94-006903 for a video showing the fluid motion at two different heights above the electrodes. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html. FIG. 4. 共Color online兲Particle paths and computed velocities at a plane 90 ␮ m high from electrode level. Channel with heights of 287 ␮ m共up兲 and with 737 ␮ m共down兲. 024104-3 Ramos et al. Appl. Phys. Lett. 94, 024104 共2009兲 09 June 2025 13:40:47