Electric generation and ratcheted transport of contact-charged drops

Charles A. Cartier, Jason R. Graybill, and Kyle J. M. Bishop

Phys. Rev. E 96, 043101 – Published 2 October 2017

Abstract

We describe a simple microfluidic system that enables the steady generation and efficient transport of aqueous drops using only a constant voltage input. Drop generation is achieved through an electrohydrodynamic dripping mechanism by which conductive drops grow and detach from a grounded nozzle in response to an electric field. The now-charged drops are transported down a ratcheted channel by contact charge electrophoresis powered by the same voltage input used for drop generation. We investigate how the drop size, generation frequency, and transport velocity depend on system parameters such as the liquid viscosity, interfacial tension, applied voltage, and channel dimensions. The observed trends are well explained by a series of scaling analyses that provide insight into the dominant physical mechanisms underlying drop generation and ratcheted transport. We identify the conditions necessary for achieving reliable operation and discuss the various modes of failure that can arise when these conditions are violated. Our results demonstrate that simple electric inputs can power increasingly complex droplet operations with potential opportunities for inexpensive and portable microfluidic systems.

Received 9 May 2017
Revised 15 August 2017

DOI:https://doi.org/10.1103/PhysRevE.96.043101

Physics Subject Headings (PhySH)

Electrokinetic flows Microfluidic devices Multiphase flows

Drop & bubble phenomena

Fluid Dynamics

Authors & Affiliations

Charles A. Cartier and Jason R. Graybill

Department of Chemical Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, USA

Kyle J. M. Bishop^*

Department of Chemical Engineering, Columbia University, New York, New York 10027, USA

^*kyle.bishop@columbia.edu

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Issue

Vol. 96, Iss. 4 — October 2017

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Images

Figure 1
(a) Schematic illustration of a microfluidic device for the electric generation and ratcheted transport of aqueous drops. The relevant dimensions of each device are listed in Table 1; an additional gallium electrode (not shown) was used to ground the water channel upstream (Fig. S1) [29]. Application of a positive voltage $V$ induces the formation of negatively charged water drops (blue) at the nozzle, which move toward the lower electrode under the influence of the field. On contact with the lower electrode, the drop acquires a net positive charge (red) and moves back toward the opposite electrode. The PDMS ramps rectify this oscillatory motion to transport the drop down the channel. Note that gravity is directed into the page. (b) Overlaid experimental images (Experiment 6, $V = 400 V, p_{w}^{'} = 0.12 psi$ ) showing the generation and transport of a single water drop at consecutive time points. The solid curve shows the trajectory of the drop down the channel (see Supplemental Video 1) [29].
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Figure 2
(a) Drop diameter (red squares) and time interval between successive drops (blue circles) as a function of time for a single experiment under ideal conditions (Experiment 6, $V = 400 V, p_{w}^{'} = 0.12 psi$ ). The black curve is an exponential fit with a characteristic time scale of 3 s. (b) Average drop diameter vs. applied voltage for experiments 1–5 (see Table 1). In each experiment, the inlet water pressure was set just below that required to flood the central channel. (c) Data from (b) collapse onto a single line when scaled according to Eq. (1). The black line is a linear fit to the data for small drops ( $D < H$ ) with slope 0.46 and $R^{2} = 0.98$ .
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Figure 3
(a) Average drop generation frequency $f$ vs. voltage $V$ for two different water viscosities. Data are from experiments 4 and 5 in Table 1. The solid curves show fits of the form $f = A [{(V / V^{*})}^{2} - 1]$ . The dashed curve shows the predicted frequency for CCEP oscillations $f = U_{0} / W$ . (b) Drop volume vs. time during the generation of the second drop. For each voltage, the time range starts at pinch-off of the first drop and continues until pinch-off of the second drop. Data are from experiment 5. The solid lines are linear fits showing a constant volumetric flow rate of $Q = 3.7 nL / s$ . (c) Schematic illustration of the different stages of drop generation.
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Figure 4
(a) Drop velocity $U$ scaled by the predicted value $U_{0}$ as a function of drop size $D$ scaled by the channel height $H$ for the experimental systems summarized in Table 1. Colored markers denote the mean of ca. 10 measurements made on each drop; error bars represent one standard deviation above and below the mean. The dashed curve represent the predicted drop velocity when accounting for the increased hydrodynamic resistance due to the channel walls (see Supplemental Material). (b) Characteristic images of charged droplets approaching an oppositely biased electrode immediately prior to reversing direction. The capillary number $C a_{D} = ɛ D E^{2} / η$ increase from left to right as 0.11, 0.13, 0.29, and 0.48.
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Figure 5
(a) Phase diagram of drop generation and transport as a function of applied voltage $V$ and water pressure $p_{w}^{'}$ for experiment 4. Markers representing individual experiments are colored based on the qualitative behaviors listed in the legend. The colored regions are only to guide the eye. The upper and lower pressure limits correspond to the flooding and receding pressures, respectively. (b) Representative images of droplet generation (left) and transport behavior (right) illustrating the qualitative behaviors in (a). Representative videos for regions I–IV are provided in the Supplemental Material [29].
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Figure 6
Schematic illustration of the model geometry for a spherical drop moving in a cubic channel.
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