(a) The asymptotic behavior of a bouncing droplet on a vibrating liquid bath is categorized and sketched as a function of the Ohnesorge parameters Oh d of the droplet and Oh b of the bath. These parameters represent the relative damping of the oscillations on the droplet and on the bath. (b) A selection of relevant works on bouncing droplets is plotted on the Ohnesorge diagram revealing the importance of the deformation of the droplet and/or of the bath in each experiment. 35,36
(a) Silicone oil droplets (20 ) are made using a droplet dispenser which consists in a small container with a hole at the bottom and a piezoelectric chip at the top. A short electric impulse is injected to the piezoelectric chip which produces a shock wave in the container that ejects a droplet through the hole at the bottom. (b) These droplets were laid on the surface of a highly viscous silicone oil bath (1000 ) that is vertically vibrated using an electromagnetic shaker. A high speed camera (1000 frames/s) recorded the motion and deformation of the drop from the side which were enhanced by a well positioned backlight.
Experimental trajectories of a 20 cSt silicone oil droplet of diameter D = 890 μm bouncing on a bath oscillating at a frequency of 50 Hz for various accelerations . The bouncing mode (p, q) and the forcing acceleration are indicated in each figure. The time interval between two successive bounces and the bouncing heights h that are measured on each trajectory are illustrated on graph (e).
Trajectories characterization of the experiments and of the simulations (k = 0.072 N/m, ) for a droplet of diameter 890 μm bouncing on a rigid liquid bath oscillating at 50 Hz for various forcing accelerations . (a) Experimental measurements of the time intervals , normalized by the oscillation period T of the bath, between two successive bounces; and (b) experimental measurements of the bouncing heights (cf. Fig. 3(e) ). (c) Simulation measurements of the time intervals ; and (d) simulation measurements of the bouncing heights h. The different bouncing modes (p, q) are indicated in each diagram.
Spatio-temporal diagram of a 20 cSt silicone oil droplet of diameter D = 740 μm falling on a static highly viscous 1000 cSt silicone oil bath. Time elapses from left to right. The droplet experiences several bounces of heights h 1, h 2 that are measured from the center of mass of the droplet when it is floating (white dotted line). The impact speeds of the first bounce are about 0.15 m/s (We ≈ 0.8). A snapshot illustrates the shape of the droplet when its deformation D + X is maximal during the bounce. Successive dots (green) represent the center of mass of the droplet detected on the successive snapshots. The simulated trajectory of a falling mass-spring-damper system, from a height of h 1 = 1.1 mm, with parameters k = 0.072 N/m and , is superposed using 3 solid lines on the spatio-temporal diagram. The central solid line (red) is the trajectory of the center of mass of the system and both outer, upper and lower, solid lines (blue) are the trajectories of the point masses m 1 and m 2, respectively.
The bouncing droplet is modeled by two masses m 1, 2 linked by a spring of stiffness k in parallel to a dashpot with a damping coefficient c. The spring system is in contact with the plate oscillating sinusoidally at a frequency f and amplitude A. As m 2 is in contact with the plate, a normal force acts from the plate on m 2. In this case the spring is compressed ( ), both masses feel outwards spring forces and in addition to the gravity forces and .
Article metrics loading...
Full text loading...