Local dissipation limits the dynamics of impacting droplets on smooth and rough substrates

Abstract

A droplet that impacts onto a solid substrate deforms in a complex dynamics. To extract the principal mechanisms that dominate this dynamics we deploy numerical simulations based on the phase field method. Direct comparison with experiments suggests that a dissipation local to the contact line limits the droplet spreading dynamics and its scaled maximum spreading radius β max . By assuming linear response through a drag force at the contact line, our simulations rationalize experimental observations for droplet impact on both smooth and rough substrates, measured through a single contact line friction parameter µ f . Moreover, our analysis shows that at low and intermediate impact speeds dissipation at the contact line limits the dynamics and we describe β max by the scaling law β max ∼ (Reµ l /µ f ) 1/2 that is a function of the droplet viscosity (µ l ) and its Reynolds number (Re).

Universality of Droplet Impingement: Low-to-High Viscosities and Surface Tensions

“…As shown in this paper, our modified model can be universally used to predict the maximum spreading contact area diameter unlike other existing models. In particular, our model shows that constant parameters appearing in some previous models [15,17,33] are not actually constant. The limits of applicability for recent existing models are discussed.…”

“…However, there is no available experimental data [32] to support the solution β m ≈ We 1/2 . In recent numerical simulation [33], the droplet impingement behavior over a wide range of We numbers was investigated using the phase field method, assuming a constant friction factor that depends on the kinds of liquid and solid materials. Finally, the new scaling law β m ≈ (µ l Re/µ f ) 1/2 is proposed.…”

Recent Progress in Preparation and Anti-Icing Applications of Superhydrophobic Coatings

“…The impact of droplets on a solid surface is followed by spreading, recoiling, and bouncing off. It has also been demonstrated that the bouncing dynamics are highly dependent on surface texture and wettability, and also on the properties of the droplet (i.e., impact viscosity, surface tension, density, and radius) [126,127]. Based on these characteristics, many researchers utilized the synergistic actions of surface…”

Numerical Approaches to Complex Fluids

“…Cahn and Hilliard [116] used this approach in the context of phase separation problems deriving an evolution equation for the concentration field. The thermodynamic consistency of the coupled Cahn-Hilliard/Navier-Stokes model [117] and its ability to handle topological changes are the main reasons that justify the increasing use of phase-field methods [118][119][120][121][122]. The fundamental variable of phase-field models is a scalar (x i , t) which represents the relative quantity of one of the two phases, and whose extreme values, = ±1, correspond to the two pure fluids.…”

“…The Navier-Stokes/Cahn-Hilliard model has recently been adopted in several studies of immiscible fluids both in laminar and turbulent conditions, for example, Refs. [122,[125][126][127]. Besides the Cahn-Hilliard formulation, different phase-field methods have been proposed, based on alternative forms of the free energy, see, for example, [128] for compressible flows with phase change for cavitation problems.…”