Head-on collision of unequal-size droplets on a wetting surface

Abstract

Impacts of liquid droplets with another stationary droplet resting on a surface are important basic processes in many applications such as agricultural sprays, spray cooling, and inkjet printing. We investigated the head-on collision of unequal-size droplets of the same liquid on wetting surfaces both experimentally and theoretically at different size ratios and low-impact Weber numbers ( We). A series of high-speed camera images showing representative sequences of collision processes for greatly different size ratios are analyzed. Different collision outcomes such as coalescence, bouncing, and partial-coalescence-partial-bouncing are analyzed thoroughly. Four different stages are identified for characterizing the complete bouncing process during the impact of unequal-size droplets on a solid surface. Subsequently, an analytical model based on energy balance is developed to calculate the maximum spread diameter and restitution coefficient of falling droplets and compared with experimental data, satisfactory qualitative agreements are obtained. Results show that the dimensionless maximum spread diameter of falling droplets depends weakly on We and it is small for a higher size ratio. The restitution coefficient does not change significantly at a higher size ratio at a fixed We despite more viscous dissipation in bigger sessile droplets and it scales with We-1/2.

New insights into head-on bouncing of unequal-size droplets on a wetting surface

“…The present problem for droplets bouncing on a solid surface is controlled by three parameters (We, Δ and θ ) with fixed gas-liquid density, viscosity ratios and ambient pressure. The falling droplet diameter is also fixed at 300 μm, based on the previously reported experiments from the authors' group (Ray et al 2023a). The 3-D computational domain is illustrated in figure 1.…”

“…The number of grid points inside the falling droplet corresponds to 100 uniformly spaced grid points. In the present study, water droplet collisions at one atmospheric pressure are considered, again, same as the experiments (Ray et al 2023a). The time is non-dimensionalized with the inertial-capillary time scale (i.e.…”

“…To validate the present numerical set-up, the head-on collision of droplets on a solid surface at different size ratios is simulated and the simulation results are compared against the experimental results from Ramírez-Soto et al (2020) and Ray et al (2023a). Two cases with greatly different size ratios and surface wettability are considered, in order to demonstrate the robustness of the DNS model.…”

“…coated glass that has a contact angle of 119 • ), whereas both coalescence and bouncing were seen for hydrophilic surfaces that depend on Weber number. Very recently, Ray et al (2023a) experimentally studied the collision of unequal-size droplets on a hydrophilic surface, and observed droplet coalescence, bouncing and partial coalesences after the impact. The experiments were performed at a large size ratio (i.e.…”

“…Δ = 1.4) from Abouelsoud & Bai (2021). Although the droplet size ratio adopted by Abouelsoud & Bai (2021) and Ray et al (2023a) differs considerably, the experiments seemingly corroborated a universal behaviour during head-on bouncing at different size ratios on wetting surfaces, where the restitution coefficient (defined as the ratio of bouncing velocity to impacting velocity of the falling droplet, and denoted as ε) is insensitive to the droplet size ratio at various Weber numbers (e.g. from 2-4.6).…”