Using surface acoustic waves to drive thin film flow over an obstacle

Abstract

We study a new paradigm for ultrasonic driven object coating by using a model system where MHz-level surface acoustic waves (SAWs) drive the spreading of a silicone oil film atop topographical obstacles. We use experiments to show that nanometer-amplitude SAWs, propagating in the substrate of a piezoelectric actuator, propel macroscopic oil films to climb and traverse solid obstacles placed on the actuator. The oil dynamics reveal rich coupling between ultrasonic forcing, capillarity, and gravity; the balance of which determines coating success. We formulate a simplified two-dimensional theoretical model that incorporates obstacle geometry directly in the oil thin-film evolution equation, introducing a new representation of acoustic streaming in the presence of substrate height variations. Despite the simplifications inherent in the modeling, simulations show qualitative agreement with the experiments, providing evidence that the model captures the key physics.

Figures (16)

• Figure 1: (a) Top view of the SAW actuator used in the experiment (dimensions: 24.5 mm × 10.8 mm × 0.5 mm), comprising an inter-digital transducer to the left made from metal electrodes fabricated atop the piezoelectric lithium-niobate substrate of the actuator, and a PDMS obstacle placed atop the SAW actuator (to the right). (b) The SAW actuator, supporting a 3D printed PDMS obstacle viewed from above, attached to a power source (to the left) and (c) a side view of the same SAW actuator supporting the PDMS obstacle (to the right) and an oil film that spreads over the SAW actuator and toward the obstacle under the action (and in the direction) of the SAW in the solid substrate of the actuator.
• Figure 2: Side view snapshots of a typical experiment ($A_n$=1.43 nm), where oil climbs over a ramp-shaped obstacle, indicated by the sketch in (a). During the experiment, (b) initially, the oil film (highlighted using a thin, white curve) moves along the upper surface of the SAW transducer to make contact with the obstacle; the oil film then deforms and (c,d,e) climbs up the obstacle and (f) reaches the peak. Time $t$ is measured from the moment the oil comes in contact with the ramp. (Full experimental videos available upon request.)
• Figure 3: Time variation of the climbing height of the film atop the ramp for (a) $A_n$ = 0.52 nm to 1.69 nm and (b) the same results with a logarithmic time axis, indicating a change in the mechanism that drives the climb above a height of approximately 1 mm. Symbols are experimental data and the connecting curves are guides for the eye. The uncertainty in climb height is 5% based on the spatial resolution of the camera.
• Figure 4: Maximum climbing height, $H_\text{max}$, of the film on the ramp, vs SAW normal amplitude displacement ($A_n$), for 8 $\mu$l of silicone oil volume (blue dots) and for 8+8 $\mu$l of oil volume (red squares). The dashed line shows the top of the ramp. The uncertainty in climb height is 5% based on the spatial resolution of the camera.
• Figure 5: (a) A sketch of the oil covering bump obstacle and the (b1–e1) side view and (b2–e2) corresponding top view snapshots of a SAW driven silicone oil film climbing over and coating a bump; the oil film outline is marked by a dark, thin line. The snapshot sequence commences at $t=0$ (b1, b2) when the oil front reaches the rear of the bump. The oil then climbs over it under the influence of SAW (c1--d1; c2--d2), and ultimately reaches the bump front after 46 seconds (e1, e2). (Full experimental videos available upon request.)