PAPER
`
`www.rsc.org/loc | Lab on a Chip
`
`DEP actuated nanoliter droplet dispensing using feedback control†
`
`Kai-Liang Wang,a Thomas B. Jones*a and Alan Raisanenb
`
`Received 24th September 2008, Accepted 24th November 2008
`First published as an Advance Article on the web 24th December 2008
`DOI: 10.1039/b816438j
`
`Dielectrophoretic (DEP) droplet dispensing using dielectric-coated coplanar electrode structures
`provides an ideal platform for testing smart control systems for high-speed microfluidic devices. Open-
`loop control of DEP droplet dispensing is not sufficiently robust for precision droplet dispensing
`because unavoidable surface property variations of the substrates and other parameters such as liquid
`viscosity introduce uncertainty in the motion. Closed-loop systems employing distributed optical
`sensors and feedback provide flexibility, sensitivity, and reliability. In this new scheme, an array of
`distributed optical sensors detects fluid motion and, through a programmable control module, triggers
`application of AC voltage bursts of appropriate magnitude, duration, and frequency to control liquid
`motion and droplet formation. Reconfiguring the module connections and reprogramming the control
`module permits testing of a variety of control strategies.
`
`Introduction
`
`Lab-on-a-chip (LOC) technology integrates microfluidics for
`handling small
`liquid volumes with miniaturized analytical
`devices or diagnostic probes for the performance of chemical/
`biomedical protocols. Microfluidic functionalities essential to
`a workable lab-on-a-chip include droplet dispensing,1 mixing,2
`separation, routing,3 reacting4 and transport. Such systems
`promise broad application for analysis, diagnostics, and other
`routine laboratory processes where higher throughput, smaller
`required volumes of biological substances or reagents, and
`massively parallel processing are advantageous. Not as often
`acknowledged is that automation reduces human exposure to
`dangerous substances and frees up the time of laboratory tech-
`nicians for more productive labor.
`LOC schemes may be broadly categorized according to the
`microfluidic subsystems that drive them. One broad category
`relies on mechanical components such as microvalves, mini-
`pumps, or even syringes to move liquid through closed channels
`machined into substrates. The second category employs any of
`a diverse set of actuation schemes including electrically-, ther-
`mally- or optically-generated capillarity,5–8
`charge-induced
`surface wetting,9 electro-osmosis,10,11 electroconvection,12 and
`electromechanical actuation. Often, such systems do not employ
`channels at all, but instead use electrode arrays patterned on
`open substrates, and employ discrete droplets as fundamental
`operational elements for transport, processing, reacting and
`other operations.13,14 Electromechanical schemes, principally
`including electrowetting-on-dielectric (EWOD)15–18 and dielec-
`trophoresis (DEP),19,20 are particularly amenable to such droplet-
`based microfluidics.
`A high degree of integration enhances the capability of any
`lab-on-a-chip, but concomitantly increases the complexity and
`
`aUniversity of Rochester, Rochester, NY, 14627, USA. E-mail: jones@ece.
`rochester.edu
`bRochester Institute of Technology, Rochester, NY, 14623, USA
`† Electronic supplementary information (ESI) available: Supplementary
`videos S1–S3. See DOI: 10.1039/b816438j
`
`raises the technical challenges of how to monitor processes and
`how to operate systems intelligently. Attention is now turning to
`real-time feedback control because it offers the promise of smart,
`automated operation. The few examples of feedback-controlled
`microfluidics reported in the literature to date include flow-rate
`control,21–24 temperature-based chemical reaction control,25,26
`programmable processor27 and capacitance-sensing based feed-
`back control.28 It is clear that more effort in this area is needed.
`This paper describes a system using a distribution of optical
`sensors to control high-speed DEP actuation and droplet
`dispensing.
`
`DEP actuation and droplet dispensing
`
`The electrode structure for DEP droplet dispensing consists of
`parallel and coplanar, dielectric-coated electrode strips patterned
`on an insulating substrate,29,30 see Fig. 1(a). A microliter-sized
`parent drop is manually deposited at one end, as shown by the
`dashed circle. When AC voltage at sufficiently high frequency
`(100 kHz for DI water) is applied, a finger-like rivulet of semi-
`cylindrical cross-section forms and extends quickly to cover the
`electrodes. When this rivulet reaches the far end of the structure,
`it stops and establishes electrohydrostatic equilibrium. The liquid
`DEP force is responsible for the rivulet’s extension along the
`electrodes, but the cross-sectional profile is controlled by capil-
`larity, which completely dominates over gravity. When voltage is
`removed, the liquid finger breaks up into regularly spaced sessile
`droplets of fairly uniform size by hydrodynamic instability. In
`most respects, this instability is identical to that manifested by
`the cylindrical
`liquid jet analyzed by Lord Rayleigh over
`a century ago.31,32 Usually, one droplet forms per length l*, where
`l* ¼ 4.508D is the most unstable wavelength, D z 2w + g is the
`diameter of the cylindrical capillary jet, and w and g are electrode
`width and gap, respectively. The bumps are spaced at intervals of
`l*, which promotes regular droplet formation, and sized at radius
`Rb ¼ 0.946D, so that each bump can accommodate the semi-
`cylindrical liquid volume trapped per wavelength.33,34
`
`This journal is ª The Royal Society of Chemistry 2009
`
`Lab Chip, 2009, 9, 901–909 | 901
`
`1
`
`

`
`Fig. 1 DEP droplet dispenser with T-junction for liquid trapping and transparent diaphragms that serve as optical windows. (a) Top view showing the
`three-electrode coplanar device and optical sensor positioning; (b) Side view of structure showing details of optical fiber mounted to optical window at
`bottom of the etched pit. (Not to scale). Passage of the liquid finger alters the light intensity received by the optical fiber, and the sensing module detects
`the signal attenuation.
`
`The T-junction with transverse gap g0 overcomes the tendency
`of surface tension to draw some of the liquid back into the parent
`drop when the voltage is turned off,33 while imposing negligible
`impedance on the liquid motion. By first removing the voltage
`from E2, all the liquid along the adjacent sections of the elec-
`trodes E1 and E3 is trapped, preventing backflow and allowing
`the hydrodynamic instability to proceed undisturbed. The result
`is more regular and well-spaced droplets.29,30
`For adaptation as a platform to test closed-loop control
`schemes, the DEP droplet dispenser is coupled through trans-
`parent diaphragms to a set of optical fibers mounted under the
`electrode structure. These diaphragms, depicted as squares in
`Fig. 1(a), are at the bottom of pyramidal pits fabricated by
`anisotropic, backside etching of the <100> Si wafer. Optical
`fibers, from which the cladding has been stripped, are mounted
`into these etched pits, carefully aligned normal to the optical
`windows and secured with epoxy, see Fig. 1(b). The substrates
`are illuminated from above, so when the leading edge of the
`finger arrives at a window, it reduces the incident light. The
`sensing module detects this attenuation.
`
`Device fabrication and fiber assembly
`
`The DEP droplet dispenser with optical diaphragms is fabricated
`on a double-side polished, <100> Si wafer of thickness 550  50
`mm. The process, shown in Fig. 2, starts with a 400 A˚ thermal
`oxide layer, which improves the strength of subsequent 1800 A˚
`low-pressure chemical vapor deposition (LPCVD) nitride
`coating. Next, 8 mm of tetraethylorthosilicate (TEOS) glass is
`deposited on the device side by plasma-enhanced chemical vapor
`deposition (PECVD) for passivation. The first of two photoli-
`thography steps patterns optical windows on the back of the
`wafer. After dry etching, the patterned nitride layer serves as
`a pseudo mask for anisotropic silicon etching in hot 40 wt%
`KOH, creating the pyramidal pits for the fibers with square
`transparent diaphragms (140 by 140 mm) at the bottom. After
`deposition of 0.2 mm Al on the TEOS layer, a second lithography
`step patterns the electrode structures, properly aligning them
`with the optical windows. Then, 0.5 mm spin-on-glass (SOG,
`Futurrex IC1-200) is spin-coated and thermally cured, followed
`by a 0.2 mm amorphous fluoropolymer hydrophobic coating
`(Dupont Teflon-AFÔ or Asahi CytopÔ). The combination of
`SOG and fluorocarbon coating provides a robust layer with good
`dielectric strength and hydrophobicity for reliable and repeatable
`actuation.
`
`Fig. 2 Fabrication of DEP microdispenser with optical windows and
`fiber guides. (a) Thermally-oxidized wafers coated with TEOS deposition
`and nitride layer; (b) the first lithography patterns optical windows on the
`backside of wafer; (c) etched nitride as pseudo mask; (d) anisotropically
`etched pyramidal pits and transparent diaphragms; (e) Al deposition on
`the front side; (f) the second lithography step patterns the electrode
`structures; (g) the electrodes are aligned with the optical windows; and (h)
`spin-coated SOG and Teflon-AF layers.
`
`Commercial riser-rated fiber cables (Corning OFNR 50/
`125mm) are used for signal coupling from the optical windows to
`the sensing module, see Fig. 1(b). After stripping the jacket, the
`fiber is seated in the etched pit using a 3-axis micromanipulator
`and glued with two types of UV-cured epoxy adhesives: Dymax
`OP-52 with refractive index ng1 ¼ 1.52 and OP-4-20632-GEL
`with ng2 ¼ 1.554, respectively. The less viscous OP-52 (5000 cP)
`fills the gap between the diaphragm and the core and minimizes
`signal loss by matching the refractive indices at the interface. The
`more viscous OP-4-20632-GEL (50 000 cP) secures the fiber in
`the etched pit and improves assembly strength.
`The optical windows, composed of TEOS, SOG and Teflon
`layers, are transparent to visible light, but diaphragm thickness
`and any misalignment of the fiber adversely influence light
`transmission. The grating aperture of the optical window is
`
`902 | Lab Chip, 2009, 9, 901–909
`
`This journal is ª The Royal Society of Chemistry 2009
`
`2
`
`

`
`larger than the numerical aperture of the fiber,
`
`q
`ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
`¼ 0:2,
`2 n2
`n2
`1
`where n2, n1 are refractive indices of the fiber core and the
`cladding. Therefore, the numerical aperture determines the light
`incident on the optical fiber. Assuming ideal alignment and 50%
`attenuation due to dielectric absorption and interfacial reflection,
`we estimate the power received by the photodiode to be 2 nW.
`
`Closed-loop feedback control
`
`The block diagram in Fig. 3 describes the closed-loop system
`consisting of the DEP device, the optical-sensing elements, and
`the control module. The microcontroller executes a program
`directing the function generator to create an AC voltage signal,
`which is amplified and applied to the DEP chip for liquid actu-
`ation. The feedback system includes the optical fibers mounted to
`the transparent windows beneath the device, which detect the
`
`liquid motion. Trigger signals are generated by the sensing
`module and fed back to the control module, which, complying
`with programmed instructions, applies voltage bursts of specified
`magnitude, frequency and duration to control liquid motion.
`The control logic is programmed on a PC in PIC-C using a code
`editor, and then downloaded to the microcontroller (Microchip
`PICSTAR plus). A LabVIEWÔ macro triggers program initia-
`tion, camera recording, and video acquisition simultaneously.
`The system is very flexible; various control strategies and fluidic
`functionalities can be implemented easily by modifying and then
`downloading new programs to the PIC. Results of testing several
`control strategies are presented later in this paper.
`
`Sensing and control modules
`
`The diagram in Fig. 4(a) shows the optical signal sensing
`circuitry. These signals are detected by a PIN photodiode
`
`Fig. 3 Architecture of optical-sensing based feedback control system for DEP droplet dispensing. The feedback loop of the system is completed by
`optical signals produced by the motion of the rivulet at the sensor locations, which generate trigger signals that supply the amplified bursts of AC voltage
`to the electrodes. Control logic is coded externally and then downloaded to the microcontroller. High-speed video acquisition is synchronized to
`program initiation in a LabVIEW master program. The system is very flexible; different control strategies are readily implemented by modifying the
`hardware connections and the control logic.
`
`Fig. 4 Block diagrams of controller. (a) The sensing circuit detects the drop in the light intensity due to passage of liquid rivulet and generates a trigger
`signal. There is one of these circuits per fiber in the sensing array. (b) The control module is programmed to monitor the trigger signals and drive the
`function generator to create preset bursts of AC voltage.
`
`This journal is ª The Royal Society of Chemistry 2009
`
`Lab Chip, 2009, 9, 901–909 | 903
`
`3
`
`

`
`over a 5  5 cm2 area. Videos were processed using a MAT-
`LABÔ program to track the leading edge of the moving finger.
`A block diagram of the experimental implementation of the
`closed-loop feedback system is shown in Fig. 5. Amplified,
`bipolar voltage is supplied on the DEP microdispenser with
`negative polarity to the electrode E1 and positive polarity to E2
`and E3, respectively, as shown by the thin arrows. Up to four
`sensors can be implemented, shown by block arrows in feedback
`path II. One of the sensors is connected to the normally closed
`relay unit through feedback path I for operation of E2.
`
`Droplet dispensing results using a single sensor
`
`The flow chart in Fig. 6 outlines a control program implementing
`a single sensor and two voltage bursts applied in sequence. Upon
`initiation (a), the control module applies the first voltage burst
`(V1, f1, T1) between E1 and E2/E3 for liquid actuation (b), and
`then monitors the sensor S (c). If no signal is detected (that is, S
`¼ 0) within preset maximum time T1, the program stops, displays
`‘Failure’, and the voltage is removed. If the sensor is triggered
`within T1, (S ¼ 1), the feedback control directs the relay
`controller (feedback path I) to remove voltage for E2, thus
`trapping the liquid along E3 (d). Simultaneously, the feedback
`signal triggers the control module (feedback path II) to apply the
`second burst (V2, f2, T2) to maintain the finger profile and to
`prevent any further lengthening of the finger. After lapsed time
`T2 (e), the control module removes the voltage from E3 (f),
`allowing droplets to form, and reports ‘Success’ (g).
`
`(OPF482) operated in the photovoltaic mode to minimize
`background noise. For photodiode flux responsivity of 0.5 A/W,
`the optical signal is converted to a photocurrent of 1 nA, then
`amplified by a high transconductance amplifier (AD549) to an
`output level of 1 V. Cascaded with the low-pass filter (LPF) is
`a sample-and-hold device that stores a reference value of the
`optical signal. When this signal drops to <95% of the reference,
`the comparator generates a trigger signal. Several of these
`circuits, one for each mounted optical fiber, constitute the sensor
`array.
`Fig. 4(b) shows the diagram of the control module. The
`MicrochipÒ microcontroller
`(PIC16F877) monitors
`trigger
`signals and, through a D/A converter (MCP4492), directs the
`function generator (XR2206) to apply a sequence of AC voltage
`bursts with preset values for voltage magnitude V, frequency f,
`and maximum duration time T. A comparator guarantees that
`voltages are switched only at zero crossings and high-speed
`PhotoMosÔ relays are used for voltage on/off control. Program
`execution is monitored on a dedicated LCD display.
`Sensitivity, response speed and noise immunization are major
`concerns in the design. Dependent on illumination intensity, fiber
`orientation, electrode spacing, and finger profile, the voltage
`decrement due to optical attenuation may be expected to range
`from 50 to 200 mV. The time constant of the preamp, 1 ms,
`and the response of the PhotoMos relay, 0.2 ms, account for
`most of the circuit response delay, which is negligible compared
`to the time scale of DEP actuation, 10 to 100 ms. The circuit
`is housed in a cast metal chassis for EM shielding.
`
`Experiments
`The experimental electrodes had width w ¼ 30 mm, gap spacing g
`¼ 30 mm, length l  10 mm, and T-junction gap spacing of g0 ¼ 10
`mm. The 25 bumps, spaced at l* ¼ 410 mm, were of radius Rb ¼ 85
`mm, giving an estimated droplet volume v ¼ 1.3 nL. DI water
`(dielectric constant kl ¼ 80, conductivity sl z 1.5  104 S m1,
`and surface tension g ¼ 0.073 Nm1) was used exclusively.
`Bipolar AC voltage bursts of 250 to 400 V-rms in the
`frequency range of 70 to 100 kHz were applied to the electrode
`pairs.
`A high-speed camera (Photron FASTCAM-PCI) mounted on
`a stereomicroscope (Zeiss Stemi V6) recorded all experiments at
`500 fps. A 150 W tungsten-halogen light source was used as
`illumination. To increase the video contrast, the optics was set up
`for an output intensity of 0.1 W cm2. The light was coupled to
`an axial, diffuse beam-splitter to establish uniform illumination
`
`Fig. 5 Block diagram of the feedback control system with the voltage
`application path shown with thin arrows and two feedback paths with
`block arrows. Up to four sensors may be implemented, one of which is
`connected to the relay controller.
`
`Fig. 6 The flow chart shows the control strategy of single-sensing
`feedback control. (a) Initiation. (b) First voltage burst initiates liquid
`actuation. (c) The monitored sensor is designated S. If the leading edge of
`the rivulet is not detected within T1, execution stops. (d) If S ¼ 1, the
`voltage to E2 is removed to initiate liquid trapping, and simultaneously
`the second burst is applied to E3. (e) The timer counts down T2. (f) The
`voltage is removed from E3 for droplet dispensing. (g) The system reports
`‘Success’.
`
`904 | Lab Chip, 2009, 9, 901–909
`
`This journal is ª The Royal Society of Chemistry 2009
`
`4
`
`

`
`between E1 and E3. After T2 ¼ 30 ms, the finger broke into two
`droplets, instead of one as expected, due to a triggering delay
`inherent in the controller. Voltages of V1 ¼ 304 V-rms in Fig. 7(a-
`2) and 316 V-rms in Fig. 7(a-3) also produced an extra droplet.
`Droplet volumes were slightly larger than at 293 V-rms, probably
`due to a weak but evident dependence of the rivulet’s diameter
`upon voltage.
`For experiments conducted using S2 as the active sensor [see
`Fig. 7(b)], the feedback control performed similarly, yielding
`four droplets as predicted. For tests using S3 [Fig. 7(c)], the
`number of dispensed droplet was close to the prediction of 13
`with a maximum error of 2, possibly due to the formation of
`tiny satellite droplets. These experiments demonstrate that
`a control strategy based on a single sensor can control the
`trapped finger length and thus the number of dispensed droplets.
`Fig. 8 plots transient finger length data extracted from the
`experiments in Fig. 7 with z(t) measured from the T-junction gap.
`The data reveals smooth motion with little apparent retardation
`at the T-junction gap. The solid markers indicate the time when
`the optical sensor (S1, S2, or S3) detects arrival of the leading
`edge of the finger while the last plotted point for each set indi-
`cates when the voltage was removed to initiate droplet forma-
`tion.
`Because sensor S3 is much further away from the parent drop
`than S1 or S2, the amplitude of the first voltage burst strongly
`influences the arrival time of the finger. For example, changing
`the voltage from 293 to 316 V-rms decreases the trigger time from
`85 to 40 ms. Triggering delays lead to some overshoot at 316 V-
`rms when either S1 or S2 are active. On the other hand, no
`overshoot or length extension occurs for S3 active, probably
`because the rivulet is moving much slower by the time it reaches
`S3. Fig. 8 reveals that sensor location controls the number of
`droplets dispensed, irrespective of variations of parameters such
`as voltage, initial placement of the parent drop, liquid viscosity,
`and flow retardation at the T-junction. Fig. 9 is a histogram of
`
`Fig. 7 Experimental demonstration of feedback-controlled droplet
`dispensing for three different sensor locations: S1, S2, and S3 (marked by
`the arrows) for each of the three different initial voltage burst magnitudes
`(293, 304, 316 V-rms). The magnitude of the second burst is 325 V-rms for
`all experiments.
`
`The images in Fig. 7 show a series of experiments on a set of
`identical DEP structures with dimensions w/g/g0 ¼ 30/30/10 mm.
`Optical fibers are mounted at three locations S1, S2, and S3 along
`the electrodes as marked by arrows. Two voltage bursts, both at
`80 kHz, are applied sequentially. In separate experiments using
`S1, S2, or S3 as the active sensor, three different initial voltage
`magnitudes, 293, 304, and 316 V-rms, were tested. These voltages
`were chosen to be high enough to avoid perceptible retardation
`at the T-junction. The second burst, of duration T2 ¼ 30 ms and
`always at an amplitude 325 V-rms, equalized the distribution of
`trapped liquid along the length of the structure without further
`extension of the rivulet.
`At V1 ¼ 293 V-rms in Fig. 7(a-1), the leading edge triggered the
`sensor S1 and the feedback control removed the voltage from E2
`to trap the liquid mass; meanwhile, V2 ¼ 325 V-rms was applied
`
`Fig. 8 Composite plot of the position of the leading edge of the finger
`z(t) for the single-sensor feedback control scheme of Fig. 7. The data are
`obtained for three sensor locations: S1, S2, and S3, and for three different
`values of the amplitude of the first voltage burst: 293 V, 304 V, and 316 V,
`all in rms values. The solid points indicate the time when the finger was
`detected by the sensor and the last plotted points mark the time when the
`voltage was removed to form droplets.
`
`This journal is ª The Royal Society of Chemistry 2009
`
`Lab Chip, 2009, 9, 901–909 | 905
`
`5
`
`

`
`actuation voltages create wider liquid fingers, which, according
`to Rayleigh’s theory, produce fewer droplets of larger volume.
`The scatter of the volume data is accentuated because volume is
`proportional the third power of the measured droplet radii.
`
`Model predictive feedback control using multiple-
`sensors
`
`One means for control of distributed systems such as the DEP-
`based droplet dispenser is to implement model predictive feed-
`back control. The basis of this approach is to monitor the system,
`comparing its performance in real-time to a reference derived
`from an existing model and then to apply corrections on the fly to
`drive the system back toward the desired dynamic trajectory. For
`our system, we can use the set of optical sensors distributed along
`the structure. When a sensor detects passage of the leading edge
`of the rivulet, the signal is sent to the microcontroller, which
`compares the arrival time to the value predicted by the model.
`The voltage is then adjusted upward or downward to maintain
`z(t) as close as possible to the desired trajectory. See Fig. 11,
`which is illustrative.
`The first step to implement model predictive control is to
`develop a reduced-ordered, hydrodynamic model of DEP finger
`actuation dynamics. Assuming the rivulet cross-section is
`
`constant, the non-linear equation of motion is29,35
`
`
`w þ g
`þ ð2w þ gÞx
`þ 4m
`dz
`z
`z
`2
`c
`t
`dt
`¼ UV 2uðtÞ p
`w þ g
`2
`where m ¼ dynamic viscosity, x ¼ contact-line-friction coeffi-
`cient, g ¼ surface tension, r ¼ liquid density, and u(t) ¼ unit step
`function. The left-hand side of eqn (1) includes the time rate of
`change of momentum, a viscous drag term (obtained from
`a conformal mapping analysis of the laminar flow model of the
`finger36), and the contact line friction force. This last term is
`associated with energy dissipation caused by molecular
`kinetics.37 The coefficient x is determined from a curve-fitting
`exercise.38 On the right-hand side of eqn (1) appear the DEP force
`
`dz
`dt
`
`g
`
`dz
`dt
`
`(1)
`
`
`
`d d
`
`r
`
`
`
`2
`
`
`
`p 2
`
`Fig. 9 Data histogram showing number of droplets dispensed for active
`optical sensor located at three different positions: S1, S2, and S3, cor-
`responding to 1, 4 and 13 droplets expected. The numbers of individual
`trials for each sensor location were 17, 14, and 18, respectively.
`
`results for the structure shown in Fig. 7, for many trials per-
`formed with the structure of Fig. 7 using the three different active
`sensor
`locations. The time-based control
`strategy shows
`reasonable repeatability. In general, the number of droplets
`dispensed is within 1 of the expected value.
`The largest deviation from the expected number of droplets,
`encountered when S1 is active, is probably due to triggering
`delays and fluid momentum. For the active sensor located at S2,
`an ‘elastic’ response related to surface tension during the finger
`trapping stage may cause an observed, modest shortening of the
`rivulet. For location S3, satellite droplet formation may lead to
`fewer dispensed droplets.
`Fig. 10 plots another important performance measure of the
`feedback-controlled dispensing scheme,
`the volumes of
`the
`dispensed droplets. These values were calculated from measured
`radii based on the assumption of hemispherical shapes. Higher
`
`Fig. 10 Influence of actuation voltage on the dispensed droplet volume.
`The experimental results (symbols) are reasonably close to the theoretical
`predictions (solid line) for the actuation voltage range 290340 V.
`However, larger voltages (325340 V) result in a slightly wider finger,
`thus producing fewer, but larger droplets.
`
`Fig. 11 Representation of DEP-driven finger actuation using model
`predictive control with five spatially distributed sensors. The smooth
`curve is calculated from the reference model. After comparing measured
`arrival times of the moving rivulet at a set of fixed points to the reference
`times derived from the model, the system adjusts the voltage to accelerate
`or decelerate the finger. The dashed curve depicts the actual motion,
`which exhibits positive and negative excursions from the reference.
`
`906 | Lab Chip, 2009, 9, 901–909
`
`This journal is ª The Royal Society of Chemistry 2009
`
`6
`
`

`
`that drives the rivulet starting at t ¼ 0+ and the constant capillary
`force, which always tends to pull the finger back.
`A full test of the scheme, with the voltage recomputed and
`adjusted after comparison of the trajectory to the reference,
`could not be implemented because of the memory limits of the
`microprocessor. However, a realistic test was conducted by using
`simulations done in advance using SimuLinkÔ and with the
`magnitudes of a voltage sequence (316, 270, 293, and 283 V-rms)
`programmed into the control logic. Fig. 12 shows selected video
`frames from a test with three distributed sensors: S1, S2, S3. The
`first voltage burst of 316 V-rms was applied at t ¼ 0+. At 6 ms,
`the finger arrived at the sensor S1, triggering the second burst of
`
`270 V-rms, which decelerated the rivulet. When sensor S2 was
`triggered the controller at 18 ms, the third voltage burst (293 V-
`rms) was applied, accelerating the rivulet. Finally, when the
`rivulet reached S3 at 58 ms, the voltage on E2 was removed
`trapping the liquid finger and the fourth voltage burst of 283 V-
`rms was applied between E1 and E3. The frequency was fixed at
`80 kHz.
`The fourth and last voltage burst was set at a relatively low
`value to promote even distribution of the trapped liquid inven-
`tory along the length of electrode E3 before droplet formation.
`Note that, at 110 ms [see Fig. 12(e)], the left side of the finger has
`passed out of the field of view. The droplets that formed after
`voltage removal are irregular due to deterioration of the SOG/
`Teflon coating that occurred after more than twenty tests had
`been conducted with this particular substrate.
`Transient finger
`length data obtained using the three
`sensors, S1, S2, and S3, are plotted in Fig. 13. The continuous
`curve is a solution of eqn (1) at V ¼ 295 V-rms. The experi-
`mental trajectory remains fairly close to the reference; the
`rapid accelerations and decelerations evident when the finger
`reaches each sensor demonstrate the rivulet’s response to
`voltage-based control. Because momentum is negligible, each
`section of the data can be fitted by least-squared regression to
`the hydrodynamic model of eqn (1) with the contact line
`friction coefficient x ¼ 0.314 Ns m2. This experiment
`demonstrates that model predictive feedback control with
`distributed sensors is capable of error detection and correction,
`and should be a suitable real-time control strategy for high-
`speed microfluidic systems.
`
`Fig. 12 Selected images from video record of model predictive feedback
`control using three sensors, the locations of which are marked by arrows.
`(a) t ¼ 0+. (b) With voltage v ¼ V1 ¼ 316 V, the finger triggered S1 at 6 ms.
`(c) When the voltage was changed to V2 ¼ 270 V, the finger decelerated
`and reached S2 at 18 ms. (d) The rivulet again accelerated with V3 ¼ 293
`V-rms. At 58 ms, S3 was triggered and voltage was removed from E2
`trapping liquid along E3. (e) At the reduced voltage V4 ¼ 283 V-rms, the
`trapped liquid is redistributed and the rivulet extended out of the field of
`view at 110 ms. (f) After voltage removal, droplets were dispensed. These
`droplets are non-uniform due to deterioration of the coating after many
`experiments with the substrate.
`
`Fig. 13 Transient finger length date z(t) under model predictive feed-
`back control using three sensors (S1, S2, S3) and four voltage levels (V1 ¼
`316, V2 ¼ 270, V3 ¼ 293, V4 ¼ 283 V-rms). Experimental data (B) within
`each fixed voltage interval have been fitted to the hydrodynamic model.
`Overall, the z(t) trajectory exhibits positive and negative excursions but
`remains fairly close to the predictive model, shown as the solid black line,
`for V0 ¼ 295 V-rms.
`
`This journal is ª The Royal Society of Chemistry 2009
`
`Lab Chip, 2009, 9, 901–909 | 907
`
`7
`
`

`
`Conclusion
`
`Liquid DEP microactuation offers fast dispensing of droplets
`ranging in volume from 10 pL to 100 nL within 100 ms. The
`three-electrode microdispenser design, featuring the T-junction
`to trap liquid, facilitates droplet uniformity. Coplanar structures
`capable of dispensing as many as 30 droplets per structure have
`been demonstrated and larger numbers should be possible. In
`fact, scale-up to thousands of droplets should be possible using
`chips patterned with multiple structures in parallel on a single
`chip. Still, successful development of such complex, high-speed
`microfluidic systems will depend on a high level of controlla-
`bility. Some form of closed-loop process control will be essential.
`Another reason for considering feedback is to overcome inherent
`performance limits caused by irregularities in chip processing,
`surface contamination, and the need to accommodate liquids of
`varied viscosity.
`The feedback controlled microfluidic scheme reported here
`proves that high-speed DEP actuated droplet dispensing can be
`controlled effectively by modulating the AC voltage in response
`to sensor inputs. The distributed optical fibers along the length of
`the electrode structure detect the leading edge of the advancing
`liquid rivulet. These signals are used in real-time to modify the
`applied voltage according to a model predictive control strategy.
`The controller compares the arrival time of the liquid at each
`sensor location to a set of previously established reference values
`and then adjusts the voltage upward or downward according to
`a set of instructions to speed up or slow down the liquid,
`respectively.
`Two control schemes have been demonstrated. The first
`employs a single sensor and shows that a predetermined volume
`of liquid can be dispensed, then trapped and maintained stably
`by voltage. This scheme provides a simple means to improve the
`accuracy and reliability of DEP droplet dispensing. The second
`scheme employs three sensing elements, and uses the model
`predictive control strategy to control the liquid motion along its
`trajectory. By comparing the measured time with the reference
`time, the system generates a sequence of corrective voltage bursts
`to control the motion of the rivulet. But, while model predictive
`control offers great promise for real-time control this DEP
`droplet dispensing platform in LOC devices, one may envision
`a far wider variety of control strategies for automatic processing
`and intelligent handling of picoliter to nanoliter liquid volumes.
`This capability stems from the fact that both the magnitude and
`frequency of the voltage bursts can be modulated. For example,
`precise control of the onset of the Rayleigh instability that forms
`the droplets might be achieved by voltage modulation after the
`liquid finger has reached the end of an electrode structure.
`Assuming the liquid cont