Water drops moving on surfaces are not only an everyday phenomenon seen on windows but also form an essential part of many industrial processes. Previous understanding is that drop motion is dictated by viscous dissipation and activated dynamics at the contact line. Here we demonstrate that these two effects cannot fully explain the complex paths of sliding or impacting drops. To accurately determine the forces experienced by moving drops, we imaged their trajectory when sliding down a tilted surface, and applied the relevant equations of motion. We found that drop motion on low-permittivity substrates is substantially influenced by electrostatic forces. Our findings confirm that electrostatics must be taken into consideration for the description of the motion of water, aqueous electrolytes and ethylene glycol on hydrophobic surfaces. Our results are relevant for improving the control of drop motion in many applications, including printing, microfluidics, water management and triboelectric nanogenerators.

Liquid drops sliding on tilted surfaces is an everyday phenomenon and is important for many industrial applications. Still, it is impossible to predict the drop’s sliding velocity. To make a step forward in quantitative understanding, we measured the velocity $$(U)$$ ( U ) , contact width $$(w)$$ ( w ) , contact length $$(L)$$ ( L ) , advancing $$({\theta }_{{{{{{\rm{a}}}}}}})$$ ( θ a ) , and receding contact angle $$({\theta }_{{{{{{\rm{r}}}}}}})$$ ( θ r ) of liquid drops sliding down inclined flat surfaces made of different materials. We find the friction force acting on sliding drops of polar and non-polar liquids with viscosities ($${\eta }$$ η ) ranging from 10−3 to 1 $${{{{{\rm{Pa}}}}}}\cdot {{{{{\rm{s}}}}}}$$ Pa ⋅ s can empirically be described by $${F}_{{{{{{\rm{f}}}}}}}(U)={F}_{0}+\beta w\eta U$$ F f ( U ) = F 0 + β w η U for a velocity range up to 0.7 ms−1. The dimensionless friction coefficient $$(\beta )$$ ( β ) defined here varies from 20 to 200. It is a material parameter, specific for a liquid/surface combination. While static wetting is fully described by $${\theta }_{{{{{{\rm{a}}}}}}}$$ θ a and $${\theta }_{{{{{{\rm{r}}}}}}}$$ θ r , for dynamic wetting the friction coefficient is additionally necessary.

Droplets wetting and moving on fibres are omnipresent in both nature and industry. However, little is known on the local stresses the fibre substrates experiences and, in turn, the local forces acting on those droplets while moving on vertical fibre strands. This work is concerned with disclosing the influence of droplet volume, viscosity and chemical substrate heterogeneity on droplet motion. For this purpose, we pursue a computational simulation campaign by means of direct numerical simulations resolving all relevant spatial and temporal scales. On the basis of local simulation data, we evaluate and analyse effective viscous dissipation rates as well as viscous and capillary forces. We also assess the validity of an assumption which is frequently used in correlations for droplets moving on single fibre strands - neglecting the capillary force. Our computational analysis allows to falsify/verify this assumption for different scenarios and reveals that such correlations have to be applied with care, particularly when it comes to chemical heterogeneity of the fibre substrates.

In the version of this article initially published, in the "Sample preparation" section of Methods, the solvent used for 1wt% Teflon AF1600 solution was incorrectly specified as FC-43 (Sigma-Aldrich) rather than perfluoro-2-butyltetrahydrofuran (FC-75, 97%, Fisher Scientific). The error has been corrected in the HTML and PDF versions of the article.

The motion of droplets on inclined surfaces is a ubiquitous phenomenon, yet the underlying dissipative mechanisms remain poorly understood. Employing direct numerical simulations, we investigate water and water-glycerol (85% wt.) droplets (∼25 μL) moving on smooth surfaces, with contact angles of around 90º, at varying inclinations. Our focus is on elucidating the role of wedge and bulk viscous dissipation in the droplets. We observe that, for fast-moving droplets, both mechanisms contribute comparably, while the wedge dissipation dominates in slow-moving cases. Comparisons with existing estimates reveal the inadequacy of previous predictions in capturing the contributions of wedge and bulk dissipation forces in fast-moving droplets. Furthermore, we demonstrate that droplets with identical sliding velocities can exhibit disparate viscous dissipation forces due to variations in internal fluid dynamics.