Eiectrophoresis 2005, 26, 37 06—3?1 5
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`Analysis). The calculation assumes a relative permittivity
`
`of a
`ifor 56-40 at to the Teflon tubing and a ::: 3.3 for the
`poly(methyi methacrylate} (PMMA) housing. The elec—
`trodes are represented by cylindrical line elements placed
`inside the Plexiglas housing 1.5mm from the axis of
`symmetry, each extending 4mm from the edge of the
`computational boundary. A potential of 2600 V between
`the electrodes generates the field.
`
`The result of the calculation is depicted in Fig. 2. Bold
`lines represent parts of the device and the hin lines
`represent eduipo’lentials. The field is reiatively uniform in
`the gap between the electrodes, which should favor
`electrocoalescence forces over dielectrophoreiic forces
`in our apparatus. Nevertheless. field gradients exist near
`the electrodes. due to their close proximity to each other
`and the variable conductivities of the different materials.
`
`This may lead to a small dielectrcphcretic force opposing
`the droplet coalescence. Note that the magnitude of the
`electric field i
`i the Fills-4Q is significantly less than what
`might be ex ected from the applied voltage, owing to the
`voltage drop at the various interfaces. The field inside the
`
`Pic-40 is approxir ateiy SHOE) V/‘cm for an applied voltage
`of 2000 V on 2mm. Finally, we remark that the asymme~
`tries in the electric: field outside the gap are probably arti~
`facts of the calculation procedure arising from imprecise
`far—field conditions, as the actual device geometry i
`symmetric. This version of Quicktield only possesse
`minimal mesh refinement capabilities, so our computation
`resources did not allow us to elirriinate these asymmetries
`by systematically expanding the computational domain.
`in any event, the key elements of the calculation (the
`
`S S
`
`Capillary as Bill:
`.-
`\
`
`
`
`\x\_ \_ 1m
`like ~
`
`“
`
`Cylinclriml electrodes
`
`
`
`Figure 2. Finite-element calculation of the electric field in
`the gap between the electrodes. Dark lines correspond to
`parts of the device, light lines correspond to equipotential
`lines. Equipotentiai lines between the electrodes demon—
`strate the field uniformity therein, which favors electro—
`coalescence over dieiectrophoresis.
`
`33710
`
`M. Chabert et ai.
`
`camera (Hitachi) connected to a Sony GVDBQO Digital 8
`video recorder, and the data were analyzed using custom
`tracking software and Scion image. Some data were also
`collected from a 100i) frames per second high speed
`camera (PS 220 Photron Fastcam super 10 K).
`
`Static fluid coalescence experiments were performed by
`aspirating a pair of droplets into the gap between the
`electrodes (without applying the electric field) until the
`droplets were centere\
`in the gap. Once the system
`equilibrated, we applied the electric field at the desired
`frequency and strength.
`
`We determined the critical upper field strength for coales-
`cence at a given frequency by starting with a high field
`strength and gradually decreasing the voltage in 50 ‘v’
`steps until coalescence occurred. Each point is an average
`over about ten measurements. We attempted to use equal
`sized droplets with an undeformed diameter of approxi—
`
`mateiy 575 pm, corresponding to a voiume of about
`100 nl_. For these experiments at high field strengths, failed
`coalescence attempts usually resulted in some exchange
`of fluid (see Section 3). Thus, if the coalescence failed at a
`particular voltage, a new droplet pair was aspirated into the
`gap, the voltage was reduced by 50 V, and the experiment
`continued. The variance in field threshold between differ—
`
`ent droplet pairs was less than the 50V step size, so we
`use the latter as our error estimate.
`
`The lower bound for coalescence was also determined
`
`using two droplets of about 575 lil’l‘l undeformed diameter
`with an initial separation of 25E) pm. For a given frequency,
`we increased the applied potential until
`the droplets
`began to move toward each other. Once the droplets
`were animated, they always coalesced. Again, each data
`point
`is an average over at
`least ten rrieasurerrients.
`However, the value of the lower bound depends strongly
`on the droplet size, resulting in uncertainties greater than
`the 50V step size between droplet pairs possessing
`slightly different volume .
`
`For flowing fluid coalescence experiments, we aspirated
`the droplet pair into the gap between the electrodes while
`applying the electric field. For the mixing experiments, we
`seeded one of the drops with lviica Rheoscopic tracer
`particles (Kalliroscope, Groton, MA) and followed the
`procedure for coaiesoence in static fluids.
`
`3 Results and discussion
`
`3.1 Calculation of the electric field
`
`The electric field generated by the coaxial cylinder elec—
`trode design was calculated using the Poisson equation
`finite—element solver Quickfield (Version 5.0.3.539, Tera
`
`© 2005 WlLEY-‘v'Ci—l Verlag GmbH & Co. KGaA, Weinheim
`
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