Freezing-induced contact line friction and universal scaling for maximum spreading of impacting drops on cold solid substrates

The mechanisms by which freezing limits the spreading of impacting droplets on cold substrates remain under debate—particularly whether the dominant dissipation arises near the advancing contact line or within the shear layer. We present a predictive scaling model for the maximum spreading diameter that incorporates both forms of freezing-induced dissipation contributing to contact line pinning. Using hexadecane and pentadecane drops, we conduct experiments over a range of impact Weber numbers (We = 5–450) on substrates cooled below the freezing points of liquids. Beyond the effective boundary layer that couples viscous and phase-change effects (Sarlin et al., 2024), we identify an additional frictional resistance at the contact line as the lamella advances over solidified regions (Gielen et al., 2020; Lolla et al., 2022; Yan et al., 2025). This contact line friction—analogous to roughness-induced one—is velocity-dependent and is modeled based on local thickness of solidifying layer. Such friction is added into the scaling for universal spreading in terms of dynamic wetting. Theoretically predicted maximum solidification-limited spreading agrees well with experiments. We further introduce a dimensionless number, Di, to quantify the competing influences of basal and lateral dissipation, suggesting a non-negligible role of freezing-induced dissipation at contact line at intermediate We. These findings have practical implications for controlling footprint of deposited droplet in processes such as spray coating and additive manufacturing.