Droplet Ejection at Controlled Angles via Acoustofluidic Jetting

William Connacher, Jeremy Orosco, and James Friend

Phys. Rev. Lett. 125, 184504 – Published 30 October 2020

Abstract

We study the nozzle-free ejection of liquid droplets at controlled angles from a sessile drop actuated from two, mutually opposed directions by focused surface acoustic waves with dissimilar parameters. Previous researchers assumed that jets formed in this way are limited by the Rayleigh angle. However, when we carefully account for surface tension in addition to the driving force, acoustic streaming, we find a quantitative model that reduces to the Rayleigh angle only when inertia is dominant, and suggests larger ejection angles are possible in many practical situations. We confirm this in demonstrating ejection at more than double the Rayleigh angle. Our model explains the effects of both fluid and input parameters on experiments with a range of liquids. We extract, from this model, a dimensionless number that serves as an analog for the typical Weber number for predicting single droplet events.

Received 16 April 2020
Revised 22 July 2020
Accepted 11 September 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.184504

Physics Subject Headings (PhySH)

Acoustic interactions Interactions in fluids Interfacial flows Microfluidics Nonlinear acoustics

Drops & bubbles Microfluidic devices

Surface acoustic wave

Fluid DynamicsInterdisciplinary PhysicsNonlinear DynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

William Connacher , Jeremy Orosco , and James Friend ^*

Medically Advanced Devices Laboratory, in the Center for Medical Devices Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, Department of Surgery, School of Medicine University of California San Diego, La Jolla, California 92093, USA

^*Corresponding author. jfriend@eng.ucsd.edu

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Vol. 125, Iss. 18 — 30 October 2020

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Images

Figure 1
(a) Typical acoustofluidic jetting devices consist of two focused IDTs (FIDTs), which produce focusing SAW (FSAW). A sessile drop with a given volume is confined to the SAW focal region by a hydrophobic coating that is applied everywhere except this region. The resulting contact angle, $θ_{c}$ , depends on the size of the region. A voltage, $V_{i}$ , signal with burst duration $t$ is delivered to each FIDT. (b) A stationary sessile drop is deformed by acoustic streaming when SAW leaks in at the Rayleigh angle, $θ_{R}$ , while (c) surface tension resists deformation according to Eq. (3) resulting in an ejected droplet at $θ_{e}$ .
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Figure 2
As vibrational velocity, $\dot{ξ}$ , due to one FIDT is increased, $θ_{e}$ approaches $θ_{R}$ from larger angles. This result is at odds with the assumption in the literature that $θ_{R}$ is the upper limit. Instead, it appears to be the lower limit in the case of a single IDT SAW source. Our proposed model (see text) provides a fuller understanding of these physical trends when two SAW sources are considered.
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Figure 3
In order to control $θ_{e}$ to $\approx 45 °$ with the vibrational velocity ratio, the average vibrational velocity, $\bar{\dot{ξ}}$ , and average duration, $\bar{t}$ , must be adjusted. Our proposed model, Eq. (5), explains the experimental results with greater fidelity than the conventional model, Eq. (2), and also indicates which parameter values will produce the desired angles. Notice that greater inertia (increasing $\bar{t}$ or $\bar{\dot{ξ}}$ ) moves the proposed model closer to the conventional model, confirming as in Fig. 2 that inertia-dominated ejection is limited to $θ_{R}$ , but $θ_{e}$ can be much greater with substantial surface tension. Thick lines indicate droplet ejection is predicted via Eq. (6), while thin lines indicate no ejection is predicted.
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Figure 4
The duration ratio method achieves ejection control to $\approx 45 °$ with a fixed parameter set. Our proposed model, Eq. (5), explains the experimental data better than the conventional model, Eq. (2), by accounting for surface tension and gravity. Notably, ejection angle is nearly a linear function of duration ratio, an attractive feature in the context of potential applications, and in distinct contrast to the highly nonlinear relationship present between vibration velocity ratio and ejection angle observed in Fig. 3.
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Figure 5
Aqueous mixtures of glycerol ( $G$ ) and propylene glycol (PG) were jetted using the vibrational velocity ratio method. As in Fig. 3, $\bar{t}$ and $\bar{\dot{ξ}}$ were adjusted as needed to obtain desired angles. For clarity, we only plot model points necessary for comparison with experiments. Equation (5) takes fluid parameters into account, predicting ejection angle without need for ad hoc empirical fitting parameters.
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Figure 6
Adjusting both the vibrational velocity and the burst duration from each FIDT produces a four-dimensional space; (a), (b), (c), and (d) represent four different cross sections of this parameter space. Experiments reveal the single droplet regime in these sectional plots as circles amid either zero or multiple droplet ejections. Equation (6) generates the contours in the background. In all four spaces, the emboldened line indicating $ϒ = 1$ coincides with the onset of single droplet events in the experiments.
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