Arrested Dynamics of Droplet Spreading on Ice

Energetic analysis of spreading of impacting drops on cold surfaces

“…Current works on freezing-impeded spreading of droplets debate on if CLP mechanism occur within the local vicinity of contact line (Schiaffino, & Sonin et al, 1997;Tavakoli et al, 2015;de Ruiter et al, 2017, Koldeweij et al, 2021 or within the bulk due to basal solidification (Gielen et al, 2019;Thiévenaz et al, 2020;. At increased impact velocities, aligned with previous experiments (Gielen et al, 2019;Shirota et al, 2022;Lolla et al, 2022;Nakagawa et al, 2023) we show that contact line appears to continue advancing even after being locally hindered by solidification front. Therefore, together with the fact that spreading ratio continuously deviates from isothermal spreading, it appears that a frictional dissipative force localizes that contact line when lamella overflows the solidified volumes at contact line, simultaneously with observed locally increased dynamic contact angle.…”

“…1, freezinginduced dissipation may occur within bulk in boundary layer (Thiévenaz et al, 2020) and at triple contact line as lamella overflows the solidified volumes or contact line de-pins, experimentally evidenced by both 1/6 spreading dynamics (Lolla et al, 2022) or direct observations of freezing front (Gielen et al, 2019;Shirota et al, 2022;Nakagawa et al, 2023) Additional dissipation due to solidification effect is modeled in effective viscosity. As growth of viscous boundary layer and freezing layer follow the same √𝑑𝑑 and thermal diffusivity and kinematic viscosity are of same order of magnitude for hexadecane and range of substrate Ste, thickness of viscous boundary layer and solidification are comparable (Thiévenaz et al, 2020), so that the mixed boundary layer thickness can be added as Ruiter et al, 2017;Herbaut et al, 2019;Gielen et al, 2019;Koldeweij et al, 2021;Lolla et al, 2022),…”

“…After CL being caught up by freezing front, a radial dissipation force opposite to direction of CL motion is in place, as the lamella spreads over the locally solidified part in proximity of CL, shown either by spreading dynamics (Tavakoli et al, 2014;de Ruiter et al, 2017;Lolla et al, 2022) or directly observed dynamics of solidification front (Gielen et al, 2019;Shirota et al, 2022;Nakagawa et al, 2023). Similar to roughness/ microstructure-induced or general kinetic friction at contact line (Roisman et al, 2002;Wang et al, 2017;Gao et al, 2023;Li et al, 2023), we characterize an effective friction factor 𝑓𝑓 𝑠𝑠,𝑅𝑅𝑒𝑒𝑒𝑒 in force per unit length, invariant during advancement of lamella when caught by freezing front, regardless of solidified geometry at contact line, dynamic contact angle, or contact line velocity.…”

“…ρ, σ, L, c p,i , and T m denote for liquid density, surface tension, latent heat, solid specific heat capacity, and melting temperature. To minimize effects of losses in kinetic energy associated with complicated deformation modes in elastic regime at We < 30 (Wildeman et al, 2016) and splashing-induced volume losses due to ejected secondary satellite droplets (Lolla et al, 2022), we limit We in our experiments; thus, all spreading are inelastic as drops deform into "pizza" shape (Wildeman et al, 2016) and no apparent instability nor splashing events are observed.…”

Freezing of water and melting of ice: theoretical modeling at the nanoscale

“…For example, Ahmadi investigated the arrested spreading of room-temperature droplets impacting flat ice and indicated that in the absence of an appreciable nucleation energy barrier, the dynamics of droplet impact and spreading are profoundly disrupted by disparate freezing phenomena. 15 Moreover, his review article highlighted recent developments in the nucleation, growth, and departure behaviors of droplets by using static (passive) and dynamic (active) approaches, which provided a strong guidance and research foundation for future research. 5 Manka et al 16 demonstrated that the freezing temperature ( T f ) occurs in the “no man's land”, and adopted the pressure trace measurements, small angle X-ray scattering (SAXS), and Fourier-transform infrared (FTIR) techniques to determine ice nucleation rates when the nanodroplet radius is between 3.2 and 5.8 nm.…”