FIG. 1: Droplet behaviour with increasing excitation power.

Transcription

1 5 th Autralaian Congre on Applied Mechanic, ACAM December 27, Bribane, Autralia SAW Driven Microchannel Flow M. K. Tan 1, J. R. Friend, and L. Y. Yeo 1 Department of Mechanical Engineering, Monah Univerity, Autralia In thi paper a new method for urface acoutic wave (SAW) driven microchannel flow i introduced. Thi method employ a laer ablation ytem to create a groove type microchannel on the 128 rotated Y-cut X-propagating Lithium Niobate (LiNbO 3, LN), to provide two wall a the driving ource that radiate acoutic energy into the fluid. Thi new configuration allow the fluid to flow in the microchannel without generate vortice for a channel width le than 5 m at a driving frequency of 3 MHz. Numerical analyi wa performed and the reult agreed with the experimental finding. The potential application of thi new configuration for SAW driven microchannel flow i to propel fluid in Lab-on-a-chip device. Keyword: acoutic treaming, urface acoutic wave. 1 Introduction The direct generation urface acoutic wave on a piezoelectric ubtrate uing interdigital electrode wa firt reported by White and Volter [1]. The device were fabricated uing photolithography technique to produce an interdigital pattern on a metallic coating that puttered on the piezoelectric ubtrate. Acoutic wave wa generated along the urface of the piezoelectric ubtrate by applying a high-frequency i gnal to the interdigital tranducer (IDT). If the ubtrate conit of Y-cut, X- propagating LiNbO 3, Rayleigh wave can be generated. Upon placing a water droplet upon the urface of the ubtrate to interact with the urface acoutic wave (SAW), the axially-polarized compreional diplacement component i diffracted at the Rayleigh angle into the droplet, generating o-called Leaky SAW [2]. The leaky component of the SAW induce an acoutic preure gradient inide the droplet, giving rie to acoutic treaming. For high-power ultraonic excitation, the induced treaming motion impart inertia to the fluid, giving rie to acoutic teaming jet [3] or atomization [4], below which the droplet vibrate and tranlate along the direction of the SAW propagation [5-7], Figure 1. Vibrating Excitation power Moving Jetting Atomizing FIG. 1: Droplet behaviour with increaing excitation power. Teng et al [8] and Sritharan et al [9] extended thi SAW-treaming actuation mechanim from the free urface droplet manipulation to the encloed microchannel flow, particularly for the micromixing application. In Teng experiment [8], the micro-mixer ued a 9.6 MHz SAW device. The channel were fabricated directly on top of the ubtrate forming the ingle radiator configuration. Their microchannel wa 2 m wide and 1 m high. Flow circulation were oberved in the channel and the fluid mixing wa greatly enhanced when the channel wa oriented tranverely to the SAW direction. On the other hand, Sritharan [9] placed a 146 MHz SAW device directly underneath a ubtrate which had a microchannel fabricated on, to form a hybrid ytem. The channel wa 75 m wide and 1 m high. Similarly, the SAW device wa oriented uch that the urface wave propagate

2 tranverely to the flow direction to induce vortex-flow in the channel. Vortexe are critical for micromixing application but it hinder the SAW-actuation for microchannel pump application. Vortex caue the local flow circulation and thu reult in t he low net flow through the channel. In thi paper, we propoe a new configuration that enable the SAW induced microchannel flow without vortice. By utilizing the configuration of SAW propagate in parallel to the fluid flow direction, together with the propoe dual-radiator configuration, the formation of vortice i uppreed. Thi traight flow i highly deirable for the micropump application. 2 Numerical analyi A Carteian coordinate ytem x i (i =1, 2, 3) i choen with x 3 defining the tranvere direction, and x 1 defining the direction of wave propagation. Conider a fluid-olid half-pace ytem a hown in Fig. 2(a), the olid half-pace i given by x 3 >, and the fluid by x 3 <. The partial differential equation governed the diplacement and electric field potential in the piezoelectric crytal are [1, 11]: C ξ ξ ϕ ρ t 2 j ijkl k, li + ekij, ki = 2 (1) e ξ ikl k, li εikϕ, ki = (2) where ρ, ϕ,ki, C ijkl, e ikl, ε ik, and ξ k, li are the component of ma denity, electrical potential, elatic tiffne contant, piezoelectric contant, dielectric contant, and mechanical diplacement, repectively. An index preceded by a comma denote differentiation with repect to a pace coordinate, and the dot notation for differentiation with repect to time. In the crytal medium (x 3 > ), the traveling wave ha the olution of the form [11]: [ ] ( ) ξi = βi exp α ωx3 / v exp jω t x1 / v, i = 1,2, 3 (3) [ x v ] j ( t x v ) ϕ = β4 exp α ω 3 / exp ω 1 / (4) The olution are then ubtituted into the differential equation (1) and (2), leading to a linear homogeneou ytem of four equation. For the non-trivial olution to exit, the determinant of the coefficient mut be zero. Upon obtaining the four appropriate value ofα, the correponding value of β can be found from eachα. The coupled field in the crytal i expreed a the linear i combination of the partial field, equation (5) and (6). The amplitude coefficient B ( 1), ( 4) B are determined by the olid-liquid boundary condition [11]. ( 2) B, ( 3) B and 4 ( l) ( l ) ( l) i = B exp i x3 / v exp j ( t x1 / v ), i = 1,2, 3 (5) l = 1 ξ β α ω ω 4 ( ) ( ) ( ) B l l 4 exp l x3 / v exp j ( t x1 / v ) (6) l= 1 ϕ = β α ω ω In the fluid mediu m (x 3 < ), the equation of motion i decribed by: u 4 = + + u t 3 2 ρ f p η µ u µ (7) where ρ f, η, µ i the fluid denity, fluid bulk modulu, and fluid vicoity repectively. The above equation can be uniquely decompoed into a longitudinal part of u l, atified the condition, u l

3 and a tranvere part of u t, which atified the condition g u t [12]. Thu, the firt-order Navier- Stoke equation can be divided into two eparate equation; one decribed acoutic wave propagation in which relate preure to the longitudinal part of u, the other expreed hear vicou wave which give the behavior of the tranvere part of u. In the fluid medium, the decompoed particle diplacement and electric potential have the form [11]: ( ) ξ = γ exp / exp /, 1,2 i i α ωx v jω t x v i f 3 = 1 (8) ( ) ϕ = C exp α ωx / v exp jω t x / v f 3 1 and for the hear vicou wave, the tranvere wave ha velocity of the form [13]: ( j 1) ut = A exp jωt x3 d v where d ( 2µ ) ( ρω ) v = i the vicou boundary layer thickne. The amplitude coefficient of A in equation (1) i determined by the boundary condition for velocity continuou acro the interface at x 3 =, between the crytal and fluid hear vicou velocitie. Subtituting olution for particle diplacement and potential waveform, equation (8) and (9), into the partial differential equation decribed the motion in fluid medium give the equation for α f in term of the velocity v. (9) (1) (a) (b) FIG. 2: SAW on the emi-infinite LN ubtrate coupled with the half-pace water. (a) The motion of the olid particle element of the LN ubtrate. (b) The diplacement and tre ditribution in the LN ubtrate when coupled with water. The boundary condition are employed to find the amplitude coefficient for the coupled-field thee are: continuity of fluid velocity at the interface between boundary layer and bulk fluid medium, continuity of electric potential at x 3 = between olid and liquid, continuity of the normal component of electric diplacement at x 3 = between olid and liquid, continuity of normal tre component, and continuity of hear at x 3 =. Subtituting the coupled field olution (5), (6), (8), (9), and (1) to the boundary condition to obtain the ix homogeneou equation in the ix unknown amplitude coefficient B ( 1) ( 2) ( 3) ( 4), B, B, B, C, and γ. In order to obtain the urface wave velocity v 3, the determinant of the matrix coefficient mut be zero for the nontrivial olution to exit. The econd-order ytem of equation for the fluid motion conit of the teady tate and the time ocillating harmonic field. Acoutic treaming i obtained from the time independent component of the fluid motion, thu the econd-order time dependent term have to be filtered out from the econd-order ytem of equation by time averaging. Thi derive a pair of treaming equation a follow [12, 14]: 1 u1 F = p1 ρ f ( u1g ) u1 (11) c t 2

4 2 1 = p µ η + µ F u u 3 g (12) where F i the body force denity (N/m 3 ), p i the econd-order preure, u i the econdorder treaming velocity, p 1 i the firt-order acoutic preure, and u 1 i the firt-order acoutic velocity. The firt-order fluid velocity field i obtained from the coupled-field equation between the piezoelectric crytal and the fluid and reult i then ubtituted into equation (11) to get the body force ditribution. Once the body force i obtained, equation (12) i olved for the treaming velocity, u. For the free treaming cae, channel with open end, the differential of econd-order preure i aumed to be zero, :, and taking the aumption that the fluid i incompreible, p g u =, equation (12) reduced to elliptical partial differential equation. Eq. (11) and (12) are then olved numerically uing the finite-volume method. FIG. 2: The ingle and dual-radiator configuration for microchannel flow. (a) The channel build on top of the LN ubtrate that provide a ingle wall a the radiator. Under the pecified boundary condition a labelled, the calculated flow field i howed in the inet. (b) The propoe configuration provide two radiator. Thi configuration i achievable experimentally uing laer ablation technique to create the groove type channel on the LN ubtrate. (a) Streaming velocity (m/ (c) Streaming velocity (m/ (b).25 (d) -.35 Streaming velocity (m/).2.1 Streaming velocity (m/).25 - FIG. 3: Profile of the x 1 (olid line) and x 3 (dahed line) component of the treaming velocity for travelling SAW in channel with different width. (a) and (b) how the profile for the ingle radiator configuration for channel of width 5 m and 1 m repectively. (c) and (d) how the profile for the dual-radiator configuration for channel of width 5 m and 1 m, repectively.

5 Fig. 2(a) how the velocity vector plot for treaming flow in microchannel. In the numerical analyi, no lip boundarie condition wa aumed on the wall urface. Reult indicate that the dominant actuation mechanim for aco utic treaming uing a 128 Y-X LN i due to the radiated acoutic energy into the fluid and that induce the econd-order fluid motion. A the channel height increae, treaming velocitie magnitude perpendicular to the radiator urface increae dramatically, give rie to the development of vortice, agreed with the Teng experiment. The new configuration i depicted in Fig. 2(b). Thi method ha two important factor to achieve fluid flow without vortice. Firtly, a the wave propagate at nearly equal amplitude along two parallel radiator urface that faced oppoite to one another, the radiated acoutic energy along x3 direction will tend to balance out if the channel width i ufficiently mall. Secondly, the treaming flow along the x1 direction enhance ignificantly for the two parallel aligned radiator configuration. Fig. 3 how the numerical reult for the ingle radiator and the two radiator configuration. The calculation wa baed on the aumption that no reflection from the ide wall and wave propagate on the two radiator have equal amplitude. Fig. 3(a) and 3(b) how the calculated flow profile for ingle radiator configuration for 5 m wide and 1 m wide channel. Reult indicate that the net flow along the x1-direction i poible only for a ufficiently narrow channel; u3-velocitie begin to exceed the u1-velocitie when the channel ize increae and thu allowing the formation of vortice. In contrat, dual-radiator configuration uppree the influence of u3-velocitie and permit a more contant flow velocitie acro the channel width along the x1-direction for the 5 m channel, Fig. 3(c). A the channel width increae, the u3-velocitie begin to develop and have magnitude ymmetric with repect to the center of the channel, Fig. 3(d). Thi ugget that a the channel width increae further, vortice would till be induced under thi dual-radiator configuration. 3 Microchannel fabrication and preliminary experimental reult (a) (b) 2 MHz IDT Laer ablated groove type microchannel 28 m SAW direction Top view (c) 5 m (d) 28 m FIG. 4: (a) Laer ablated microchannel on a 2 MHz SAW device. (b) The meaured intantaneou particle diplacement amplitude on the LN ubtrate uing laer doppler vibrometer. The reult indicate that the channel wall were vibrating pe rpendicular to the SAW propagation direction, caue the ditorted wavefront on the IN urface (indicated by the green line). The flow viualization uing fluorecent microparticle for treaming in the groove type microchannel of 5 m wide channel (c), and 28 m wide channel. Preliminary experiment were carried out to verify the numerical finding for the groove type microchannel. The ubtrate wa 128 rotated Y-cut X-propagating LN with thickne of 5 m. A

6 pair of bidirectional interdigital tranducer wa fabricated on the ubtrate to launch the urface wave at 2 MHz frequency. The laer ablated microchannel ha a rectangular cro ection. Figure 4(a) how the laer ablated channel on a 2 MHz SAW device. Thi channel wa 28 m in width, 2 m in depth, and 1 mm in length. During the experiment, an aborbing material (-gel, Geltec Ltd., Yokohama, Japan) wa attached on the ubtrate edge to prevent wave reflection. Meauring the diplacement perpendicular to the ubtrate urface with a canning laer doppler vibrometer (MSA4, Polytec PI, Waldbrunn, Germany) howed that the vibration amplitude were higher along the edge between the ablated region than the ubtrate urface under the free boundarie condition, ince there wa no coverlip. The reult alo revealed that along thee channel wall the vibration wa eentially in 3-dimenion; the channel wall were vibrating at the direction perpendicular to the urface wave that propagate along the ubtrate urface. Thi vibration mode i important a it i the main driving ource to actuate fluid in thi groove type channel. Figure 4(c) and (d) how the fluid flow inide the groove type microchannel of width 5 m and 28 m, repectively, under 5 time magnification. Fluorecent microphere (BioScientific, Gymea NSW) of diameter 1 m were ued to viualize the type of induced flow and the fluid motion wa recorded uing a high peed video camera (MotionBLITZ HSC-kit, Mikrotron, Germany) recording at the peed of 5 frame per econd. The flow velocitie inide the 5 m groove type channel appeared to be contant cro the channel width, wherea vortice were oberved a the channel width increaed to 28 m. Thi finding i conitent with our prediction and thu our model i verified. 4 Concluion A promiing cheme for new SAW driven microchannel flow ha been outlined, from the concept to the fabrication and preliminary experimental reult. The experimental reult how that SAW driven flow in a microchannel without vortice i poible. Significant advantage of uing SAW treaming i the high body force actuation and the implification to fabricate the device. Flow velocitie in the order of 1 mm/ were oberved in the initial trial. The numerical reult agreed with the experimental reult. Reference [1] R. M. White and F. W. Voltmer. Direct piezoelectric coupling to urface elatic wave, Applied Phyic Letter, 7 (1965) [2] T. Uchida, T. Suzuki and S. Shiokawa, Invetigation of acoutic treaming excited by urface acoutic wave, 1995 IEEE Ultraonic Sympoium, 1995, pp [3] Sir J. Lighthill, Acoutic treaming, Journal of Sound and Vibration, 61 (1978) [4] K. Chono, N. Shimizu, Y. Matui, J. Kondoh and S. Shiokawa, Development of noval atomozation ytem baed on SAW treaming, Japanee Journal of Applied Phyic, 43 (24) [5] A. Wixforth. Acoutically driven planar microfluidic, Superlattice and Microtructure, 33 (23) [6] C. J. Strobl, Z. v. Guttenberg and A. Wixforth. Nano- and pico -dipening of fluid on planar ubtrate uing SAW, IEEE Tranaction on Ultraonic, Ferroelectric and Frequency Control, 51 (24) [7] A. Renaudin, P. Tabourier, V. Zhang, J. C. Camart and C. Druon. SAW nanopump for handling droplet in view of biological application, Senor and Actuator B, 113 (26) [8] W. K. Teng, J. L. Lin, W. C. Sung, S. H. Chen, and G. B. Lee. Active micro-mixer uing urface acoutic wave on Y-cut 128 LiNbO 3, Journal of Micromechanic and Microengineering, 16 (26) [9] K. Sritharan, C. J. Strobl, M. F. Schneider, A. Wixforth, and Z. Guttenberg. Acoutic mixing at low Reynold number, Applied Phyic Letter, 88 (26) [1] H. F. Tieren. Wave propagation in an infinite piezoelectric plate. Journal of Acoutical Society of America, 35 (1963) [11] J. J. Campbell and W. R. Jone. A method for etimating optimal crytal cut and propagation direction for excitation of piezoelectric urface wave. IEEE Tranaction on Sonic and Ultraonic, 15 (1968) [12] W. L. Nyborg. Acoutic treaming. San Diego: Academic Pre Inc, 1965, [13] P. More and K. Ingard. Theoretical acoutic (MacGraw-Hill, 1968). [14] C. E. Bradley. Acoutic treaming field tructure: the influence of the radiator. Journal of Aco utical Society of America, 1 (1996)