# A control method for steering individual particles inside liquid droplets actuated by electrowetting

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TECHNICAL NOTE www rsc org loc Lab on a Chip A control method for steering individual particles inside liquid droplets actuated by electrowetting Shawn Walker a and Benjamin Shapirob Received 20th September 2005 Accepted 10th October 2005 First published as an Advance Article on the web 27th October 2005 DOI 10 1039 b513373b An algorithm is developed that allows steering of individual particles inside electrowetting systems by control of actuators already present in these systems Particles are steered by creating time varying flow fields that carry the particles along their desired trajectories Results are demonstrated using an experimentally validated model developed in ref 1 We show that the current UCLA electro wetting on dielectric EWOD system2 contains enough control authority to steer a single particle along arbitrary trajectories and to steer two particles at once along simple paths Particle steering is limited by contact angle saturation and by the small number of actuators that are available to actuate the flow in practical electrowetting systems Introduction In this paper we demonstrate the possibility of using the available electrodes in an electro wetting on dielectric EWOD device to actuate a single droplet in such a way that the resulting fluid flow inside the drop will carry a particle around a figure 8 path or carry two particles along separating trajectories Steering particles inside droplets introduces another level of functionality into electro wetting systems For example cells can be precisely placed over local sensors or moved from one location to another at rates much faster than those created by diffusion see Fig 1 In addition particles can be sorted inside a droplet and then separated by controlled splitting of the droplet Our steering results are demonstrated using an experimentally validated numerical model1 of droplet motion inside a Aerospace Engineering Research Assistant University of Maryland at College Park MD 20852 USA E mail swalker wam umd edu Tel 1 301 405 1998 b Aerospace Engineering Joint appointment with Bio Engineering graduate program and Institute of Systems Research University of Maryland at College Park MD 20852 USA E mail benshap eng umd edu Tel 1 301 405 4191 the UCLA electrowetting system 2 3 This model of EWOD fluid dynamics includes surface tension and electrowetting interface forces viscous low Reynolds 2 phase fluid flow and the essential loss mechanisms due to contact angle saturation triple point line pinning and the related mechanism of contact angle hysteresis To experimentally demonstrate particle steering in the UCLA EWOD device would require integration of a real time implementation of our least squares based control algorithm with a real time vision system to find the locations of particles and track droplet shapes In this paper we only show simulations that assume the visual feedback and ignore the real time implementation issues Steering control algorithm The electrode voltages in an EWOD device directly influence the pressure gradient field inside a droplet which in turn controls the velocity field 1 10 11 This allows us to steer multiple particles inside droplets by manipulating the fluid flow field through the voltages Therefore the control problem is to find an electrode voltage sequence that creates a temporally and spatially varying flow field that will carry all the particles along their desired trajectories Fig 1 The EWOD system manipulates fluids by charging a dielectric layer underneath the liquid that effectively changes the local surface tension properties of the liquid gas interface creating liquid motion Existing move split join and mix capabilities of electrowetting devices are shown schematically 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 of the 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 enhanced by the fluid dynamics created inside the droplet due to its imposed motion 1404 Lab Chip 2005 5 1404 1407 This journal is The Royal Society of Chemistry 2005 However the particle motion depends on the droplet shape and the number of electrodes that the droplet overlays at any given moment Since this is not known a priori we use local estimation and control at each time step of our simulation to compute the pressure boundary conditions needed to realize the desired flow field At each instant in time the control algorithm is provided with the droplet shape and particle locations as would be available through a vision sensing system Any deviation of the particles from their desired trajectories that may arise from thermal fluctuations external disturbances and actuation errors is corrected using feedback of the particle positions We now give an overview of our algorithm 1 Initialization Represent the desired trajectory of each particle as a set of points connected by straight line segments 2 Sensing Feedback the particle position data and the location of the droplet boundary to the control algorithm as would be provided by the vision sensing system 3 Control algorithm part A Choose the desired velocity directions of each particle so that the particles will move towards and then along the desired trajectories 4 Control algorithm part B Solve a least squares problem for the necessary voltage actuations to induce a pressure gradient field that will create a flow field that will carry the particles along the desired directions obtained in step 3 5 Actuate Apply the computed control voltages at the current time step of our simulation and advance the simulation to the next time step This updates the droplet shape and particle positions Then go back to step 2 and repeat the feedback control loop Step 4 of the algorithm requires more elaboration Since the pressure field obeys Laplace s equation which is linear we can consider linear combinations of pressure boundary conditions due to voltage actuation at the electrodes see Fig 2 Hence the problem of computing the necessary boundary conditions to create a pressure gradient field to move the particles in the directions we want leads to a least squares problem which is given by the following First knowing the current droplet configuration we solve Laplace s equation