An energy balance approach of the dynamics of drop impact on a solid surface

Abstract

The description of physical mechanisms involved in the impact of a drop upon a dry, partially wettable substrate is still a matter of debate. One way to analyze the balance of these mechanisms is the development of an analytical one-dimensional ͑1D͒ model based upon the energy equation. The assimilation of the drop to a cylinder allows a reduction of the energy equation to a second-order differential equation. This paper proposes a semi-empirical description of viscous dissipation taking into account the rolling motion near the contact line. The dissipation due to the rolling motion is added to the calculated dissipation in the core of the droplet. We compare our model to previous ones using a large set of literature data covering a wide range of viscosity, velocity impact, and equilibrium contact angle values. The new dissipation description proposed is shown to supersede those described in previous 1D models. Our model closely predicts the maximum spread factor and the time at which it is obtained on the whole range of Ohnesorge and Weber numbers considered. It also distinguishes between deposition with a steady variation in the wetted area from deposition with advancing and receding phases. The main limitations of the model lie in its inability to reproduce the spread factor at the very beginning of the impact and the rebounding observed after a receding phase for very high values of the equilibrium contact angle.

Sensible Heat Transfer during Droplet Cooling: Experimental and Numerical Analysis

“…Particularly, a dip in the heat flux was noticed close to the droplet rim when the film becomes thinner and thus unable to remove as much heat as the other regions of the spreading droplet. In fact, despite being recognized by many authors that the lamella has an irregular shape, e.g., [32], such shape, including the flow within the rim are sparsely considered, e.g., in [33]. The authors in [30], also emphasised that the heat removed during the spreading of the droplet is not negligible, despite the short characteristic time intervals addressed (maximum of tens of milliseconds).…”

The impact of raindrops on sand

“…The deceleration of the drop scales as the impact velocity over a typical time scale, i.e., a = U . This scaling was found to be consistent with experiments for low-viscous drops of We > 30 [33,39,[43][44][45]. A combination of this scaling with the viscous one, similar to the energy conservation model discussed above, can be used to capture the transition from this capillary regime into the viscous one and has shown to collapse with experimental data [39].…”

“…Our data fit the first mentioned way better (figure 3.7a which is the same as figure 3.2). Furthermore, the We 1/4 scaling has been reported in various impact experiments [39,45,94] and has been realized for We > 30 using a more detailed energy balance model [44]. In conclusion, we find that the power …”

Simulation of the spreading of a gas-propelled micro-droplet upon impact on a dry surface using a lattice-Boltzmann approach

“…Numerous analytic models have been proposed to determine the maximum spreading diameter for the moderate to high impact We and Re numbers [29][30][31][32][33]. There are however few dynamic models to compute the instantaneous droplet diameter [34][35][36]. Several of these models are presented in Table III and are compared against the experimental data of Briones et al [18], Figure 5 presents the error in predicting the maximum spreading diameter, ξ max , using these models.…”