A control method for steering individual particles inside liquid dropletsactuated by electrowettingShawn Walker*aand Benjamin ShapirobReceived 20th September 2005, Accepted 10th October 2005First published as an Advance Article on the web 27th October 2005DOI: 10.1039/b513373bAn algorithm is developed that allows steering of individual particles inside electrowetting systemsby control of actuators already present in these systems. Particles are steered by creating timevarying flow fields that carry the particles along their desired trajectories. Results aredemonstrated using an experimentally validated model developed in ref. 1. We show that thecurrent UCLA electro-wetting-on-dielectric (EWOD) system2contains enough control authorityto steer a single particle along arbitrary trajectories and to steer two particles, at once, alongsimple paths. Particle steering is limited by contact angle saturation and by the small number ofactuators that are available to actuate the flow in practical electrowetting systems.IntroductionIn this paper, we demonstrate the possibility of usingthe available electrodes in an electro-wetting-on-dielectric(EWOD) device to actuate a single droplet in such a way thatthe resulting fluid flow inside the drop will carry a particlearound a figure 8 path or carry two particles along separatingtrajectories. Steering particles inside droplets introducesanother level of functionality into electro-wetting systems.For example, cells can be precisely placed over local sensors ormoved from one location to another at rates much faster thanthose created by diffusion (see Fig. 1). In addition, particlescan be sorted inside a droplet and then separated by controlledsplitting of the droplet.Our steering results are demonstrated using an experi-mentally validated numerical model1of droplet motion insidethe UCLA electrowetting system.2,3This model of EWODfluid dynamics includes surface tension and electrowettinginterface forces, viscous low Reynolds 2-phase fluid flow, andthe essential loss mechanisms due to contact angle saturation,triple point line pinning, and the related mechanism of contactangle hysteresis. To experimentally demonstrate particlesteering in the UCLA EWOD device would require integrationof a real-time implementation of our least squares basedcontrol algorithm with a real-time vision system to find thelocations of particles and track droplet shapes. In this paper,we only show simulations that assume the visual feedback andignore the real-time implementation issues.Steering control algorithmThe electrode voltages in an EWOD device directly influencethe pressure gradient field inside a droplet which, in turn,controls the velocity field.1,10,11This allows us to steer multipleparticles inside droplets by manipulating the fluid flow fieldthrough the voltages. Therefore, the control problem is to findan electrode voltage sequence that creates a temporally andspatially varying flow field that will carry all the particles alongtheir desired trajectories.aAerospace Engineering, Research Assistant, University of Maryland atCollege Park, MD 20852, USA. E-mail: [email protected];Tel: +1 (301) 405-1998bAerospace Engineering, Joint appointment with Bio-Engineeringgraduate program and Institute of Systems Research, University ofMaryland at College Park, MD 20852, USA.E-mail: [email protected]; Tel: +1 (301) 405-4191Fig. 1 The EWOD system manipulates fluids by charging a dielectric layer underneath the liquid that effectively changes the local surface tensionproperties of the liquid/gas interface creating liquid motion. Existing (move, split, join, and mix) capabilities of electrowetting devices are shownschematically above (see ref. 3, 4, 5, 6, 7, 8 and 9) alongside the new particle steering capability developed in this paper. The view is from the top ofthe EWOD device. Shaded circles represent droplets of liquid. Squares are electrodes where the dotted hatching indicates the electrode is on.Directed lines specify the direction of motion. The multi-shaded droplet shows the diffusion and mixing of two chemicals, here mixing is enhancedby the fluid dynamics created inside the droplet due to its imposed motion.TECHNICAL NOTE www.rsc.org/loc | Lab on a Chip1404 |Lab Chip, 2005, 5, 1404–1407 This journal isßThe Royal Society of Chemistry 2005However, the particle motion depends on the droplet shapeand the number of electrodes that the droplet overlays atany given moment. Since this is not known a priori,weuse local estimation and control at each time step of oursimulation to compute the pressure boundary conditionsneeded to realize the desired flow field. At each instant intime, the control algorithm is provided with the droplet shapeand particle locations, as would be available through a visionsensing system. Any deviation of the particles from theirdesired trajectories that may arise from thermal fluctuations,external disturbances, and actuation errors is corrected usingfeedback of the particle positions. We now give an overview ofour algorithm.(1) Initialization: Represent the desired trajectory of eachparticle as a set of points connected by straight line segments.(2) Sensing: Feedback the particle position data and thelocation of the droplet boundary to the control algorithm (aswould be provided by the vision sensing system).(3) Control algorithm part A: Choose the desired velocitydirections of each particle so that the particles will movetowards and then along the desired trajectories.(4) Control algorithm part B: Solve a least squares problemfor the necessary voltage actuations to induce a pressuregradient field that will create a flow field that will carry theparticles along the desired directions obtained in step 3.(5) Actuate: Apply the computed control voltages at thecurrent time step of our simulation and advance the simulationto the next time step. This updates the droplet shape andparticle positions. Then go back to step 2 and repeat thefeedback control loop.Step 4 of the algorithm requires more elaboration. Since thepressure field obeys Laplace’s equation, which is linear, we canconsider linear combinations of pressure boundary conditionsdue to voltage actuation at the electrodes (see Fig. 2). Hence,the problem of computing the necessary boundary conditionsto create a pressure gradient field to move the particles in thedirections we want, leads to a least squares problem which isgiven by the following.First, knowing the current droplet configuration,