Role of extensional rheology on droplet bouncing

Recent experiments and theories have dismissed the role of increased extensional viscosity during impact of viscoelastic droplets. Here we show that for relatively low Weber numbers, $\mathrm{We}=\rho U_0^2{D}_0/\gamma =O\left({10}^0–{10}^1\right)$, where $\rho$ is the density, $U_0^{}$ the impact velocity, $D_0$ the droplet diameter, and $\gamma$ the surface tension, droplets tend to bounce on an air film with a thickness, $h$, which sets off capillary waves that eventually focus into a single wave. This focusing causes rapid deformation of the droplet thus producing high strain rates, which we verified using a particle-tracking method. Without the addition of polymers, the capillary wave focusing generates droplet contact with the substrate; however, with the addition of polymers, contact is inhibited even for relatively small polymer concentrations (10 ppm). We attribute the inhibition of contact to the large increase in the extensional viscosity near the center of the droplet, which dissipates the kinetic energy of the droplet during impact and deformation.

Figure 1

Experimental schematic of the total internal reflection microscopy (TIRM) technique for studying droplet impact on a substrate.

Figure 2

Thinning dynamics of the droplet neck radius using the dripping-onto-substrate method [38]. Inset images show the minimum filament thickness at different times for 500 ppm PEO. The time origin ($t=0$) is set at the boundary between the inertia-capillary and elasto-capillary regime, e.g., E.C. boundary. The error bars were determined from three independent experiments. The scale bar represents 1 mm.

Figure 3

(a) Droplet impact showing capillary wave propagation as a function of time. The red arrow indicates the final wave prior to the inversion of the droplet top surface, which occurs between 4 and 4.5 ms; $\mathrm{We}\approx 5$ and the scale bar represents 1 mm. (b) The distance of the top surface from the substrate, normalized by the droplet diameter, as a function of time. The open circles represent data from 100 ppm PEO droplets and the filled circles represent 10 ppm PEO droplets. Both droplets have $\mathrm{We}\approx 5$. (c) The change in the top surface velocity, $U_{\mathrm{T}}$, with respect to time. (d) Schematic representation of the instantaneous droplet shape before impact and (e) the droplet shape after spreading on a thin film of air.

Figure 4

Air film shapes for various PEO concentrations at $\mathrm{t}\approx 3\mathrm{ms}$ from impact using TIRM for $\mathrm{We}\approx 9$. The error bars were obtained from three experiments.

Figure 5

Particle-tracking velocimetry (PTV) data showing the strain rate as a function of time for 200 ppm and water droplets for $\mathrm{We}\approx 6$. The time $t=0$ is set as the beginning of the apparent impact with the surface and the start of the spreading phase of the droplet. The error bars were obtained from three experiments.

Figure 6

(a) The TIRM image sequence of a droplet with 50 ppm PEO. (b) The change in the averaged normalized intensity (across five separate droplet impacts, where the shaded areas are the error bars of one standard deviation), $I/I_0$, at the droplet dimple center as a function of time for various PEO concentrations for $\mathrm{We}\approx 9$. The dotted arrow connects the TIRM image sequence to the processed data where $I_0$ is the average grayscale intensity at $t=0$ and I is the average grayscale intensity for each sequential frame. The scale bar represents 0.5 mm.

Figure 7

Phase diagram for droplet bouncing. The dotted lines indicate the inertia-capillary dominant regime for air film failure for pure water droplets. Beyond We > 20, the contact is initiated by disjoining pressure [19]. Empty symbols represent no bouncing, and solid symbols represent droplet bouncing for >80% of the tests. Half-filled symbols represent <50% of the droplets bounced. At least 100 impact tests were conducted for the solid symbols and the transitional data points below We < 20.