Contact time of a droplet impacting hydrophobic surfaces

Abstract

A droplet impacting hydrophobic surfaces is explored via lattice Boltzmann method simulations. Dynamics of the spreading and retraction processes of the impacting droplet with different surface wettability ( θ = 106°–145°) at various Weber numbers ( We = 15–35) and Reynolds numbers ( Re = 235–359) are investigated. It indicates that the spreading time, the time interval from a droplet just touching the surface to reaching the maximum spreading diameter, is a fixed value that is not related to the above factors. The retraction time, the time interval from a droplet reaching the maximum spreading diameter to rebounding the surface, is just closely dependent on the surface wettability. Therefore, the contact time, the sum of the spreading time and the retraction time, is mainly related to the retraction process and dependent on the surface wettability. The time is commonly normalized as the non-dimensional time, τ =  t/( ρR03/ σ)1/2, where R0 is the initial droplet radius and σ is the surface tension. The emphasis of this work is placed on establishing a relationship of the contact time with the surface wettability. Based on simulation research and theoretical modeling, the surface wettability is incorporated into the scaling law of contact time, and a modified scaling law, tc  ∼  ( R0/ V0) We1/2(1  − cos θ)−1/2, where V0 denotes the initial impact velocity, is established for a droplet impacting hydrophobic surfaces of θ = 106°–145°and We = 15–35. It is demonstrated that the scale relationship can be well applied to calculate the contact time of a droplet impacting hydrophobic surfaces for moderate Weber numbers.