Wörner, Martin

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An energy balance model for the maximum spread diame-ter upon droplet impact on surfaces of arbitrary wettabilityMartin Wörner1,∗1Karlsruhe Institute of Technology (KIT), Institute of Catalysis Research and Technology (IKFT),Engesserstr. 20, 76131 Karlsruhe, GermanyAbstract. Understanding the impact of liquid droplets on dry solid surfaces isrelevant for many applications in natural, agricultural and industrial processes.In the absence of splashing, the droplet (initial diameter d0) spreads on the sur-face until the wetting diameter reaches a maximum (dm). Thereafter the dropletrecoils and finally comes to rest. For technical applications, the maximumdroplet spreading as characterized by the spreading factor βm = dm/d0 is ofspecial interest. Physically, βm depends in a complex manner on Weber number(We), Reynolds number (Re) and surface wettability expressed by the contactangle θ. In literature, two approaches are common to derive relations of theform βm = βm(We,Re, θ). By rescaling of the cross-over between the capillaryand the viscous regimes, several universal fitting models have been proposed de-pending on an impact parameter P = P(We,Re) [1, 2]. For the second approach,which uses a mechanical energy balance, mechanistic models have been derivedfor certain regimes and conditions only while a universal mechanistic model forβm(We,Re, θ) is still missing. The energy balance approach requires modelingof the gas-liquid interfacial area (S m) and of the dissipation (Wm) at maximumspreading. In this contribution, significant progress on the development of auniversal mechanistic energy balance model for the maximum spreading factoris reported. It is shown that the two commonly used models for S m have sig-nificant shortcomings for hydrophobic surfaces. Therefore, an improved modelfor S m is developed, which is derived from a spherical-cap approximation. Assecond novelty, a new concept for modeling dissipation at maximum spreadingis proposed. In contrast to existing models, the new model does not relate dis-sipation at maximum spreading to polynomials in βm. Instead, the new modeluses Wm = wmWtot, where Wtot denotes the overall energy available for dissipa-tion, while wm = wm(P) with P = We/Re0.4 is a function fulfilling 0 ≤ wm ≤ 1.Thereby, the proposed model respects for the first time the overall energy con-servation principle of the entire spreading and recoil process. The new modelyields an explicit relation βm = βm(We,Re, θ) that is developed and tested usingexperimental data [2, 3] covering wide ranges of We, Re and θ.References[1] N. Laan, K.G. de Bruin, D. Bartolo et al., Phys. Rev. Appl. 2 044018 (2014)[2] J.B. Lee, N. Laan, K.G. de Bruin, G. Skantzaris et al., J. Fluid Mech. 786 R4 (2016)[3] Y.T. Aksoy, P. Eneren, E. Koos, M.R. Vetrano, Phys. Fluids 34 042106 (2022)∗e-mail: martin.woerner@kit.edu

An energy balance model for the maximum spread diameter upon droplet impact on surfaces of arbitrary wettability

https://publikationen.bibliothek.kit.edu/1000153952/149856508

An energy balance model for the maximum spread diameter upon droplet impact on surfaces of arbitrary wettability

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