PIV measurement inside single and double droplet interaction on a solid surface
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RESEARCH ARTICLE
PIV measurement inside single and double droplet interaction on a solid surface Ahmet Gultekin1,2 · Nejdet Erkan2 · Uner Colak1 · Shunichi Suzuki2 Received: 7 July 2020 / Revised: 8 September 2020 / Accepted: 10 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this study, the spreading velocities within the droplet impact on a sapphire glass surface is investigated with the aid of particle image velocimetry (PIV) method. Experiments are performed for unheated and heated surfaces and droplets with impact velocities ranging from 1.12 to 2.40 m/s which correspond to Weber numbers in the range 40–190. It was observed that the radial velocity is linear throughout a relatively large range of spreading radius. However, the velocity profiles show a non-linear shape outside radial positions owing to the capillary and viscous forces over time. For high-Weber numbers, the linearity of radial velocity profile is more evident due to the viscosity effects in the lamella which are insignificantly relative to the inertia forces. Also, the spreading velocities within the droplet pair are investigated at room temperature using the same methods. Another stagnation point formation was observed in the interaction area. In the last part, radial velocity measurements within the liquid lamellas were compared with analytical and computational models for the temperature of unheated surface. For high-Weber case, the analytical model quite agrees with the linear parts of the radial velocity profiles in the interior radial positions. For moderate Weber case, the predicted radial velocity profile only agrees well with the linear parts of experimental data during early spreading process, but the inconsistency between the analytical model and PIV results rises in the later spreading and receding phases. Comparing the results with the computational simulation show that there is a good agreement for both linear and non-linear parts in radial velocity profiles. Graphic abstract
* Ahmet Gultekin [email protected] Extended author information available on the last page of the article
List of symbols c Constant non-dimensional parameter Do Initial droplet diameter (mm) Ds Spreading diameter (mm) D Non-dimensional spreading diameter
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dh Horizontal distance (mm) dh Non-dimensional horizontal distance dv Vertical distance (mm) dv Non-dimensional vertical distance E Energy hl Thickness of lamella (mm) hl Non-dimensional thickness of lamella q′′ Heat flux (W/m2) R Radius (mm) r Non-dimensional radius T Temperature (°C) t Time (s) U Velocity (m/s) Uo Initial velocity (m/s) u Non-dimensional velocity Re Reynolds number We Weber number Greek letters 𝛼 Volume fraction μ Dynamic viscosity (Ns/m2) ρ Density (kg/m3) σ Surface tension (N/m) τ Non-dimensional time 𝜅 Mean curvature of the interface θ Contact angle η Constant non-dimensional parameter Subscripts l Lamella r Rim s Surface
1 Introduction The phenomenon of dro
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