Topologies of Nanoscale Droplets upon Head-On Collision from Large Molecular Dynamics Simulations

Abstract

The binary collision of nanoscale droplets is studied with molecular dynamics simulation for droplets consisting of up to 2 × 10⁷ molecules interacting via a truncated and shifted form of the Lennard-Jones potential. Considering head-on collisions of droplets with a temperature near the triple point that occur in a saturated vapor of the same fluid, this work explores a range of collision topologies. Four droplet sizes, with a radius ranging from 30 to 120 molecule diameters, are simulated with a varying initial relative collision velocity, covering 36 cases in total. Due to the relatively large size of the droplets, this study aims to resolve the differences in the collision behavior between droplets on the micro- and on the macroscale. By analyzing various metrics of the impact, four distinct collision regimes are found: coalescence, stable collision, holes and shattering. Coalescence, observed at low Weber and Reynolds numbers, is the formation of a stable droplet without significant deformations of the merging objects. Stable collisions, characterized by the formation of one stable droplet with notable deformations during collision, occur within a Weber number range between 10 and 505. The holes regime is only observed for droplet radii greater than 30 molecule diameters and a Weber number between 505 to 750, while collision cases surpassing this Weber number fall into the shattering regime, resulting in the breakup into satellite structures.

Figure 1

Schematic of the initial setup of head-on nanoscale droplet collisions (a) and the cylindrical sampling grid (b) used to sample the relevant volume. Due to rotational symmetry, the simulation data were averaged onto a plane (c).

Figure 2

Surface tension γ at T = 0.7 as a function of droplet radius R₀ based on data from Vrabec et al., considering the planar surface tension at R₀ → ∞.

Figure 3

Topology of the four observed regimes over time: coalescence (far left), stable collision (center left), holes (center right) and shattering (far right). Note that the time origin t = 0 was set to the moment of contact and time proceeds from top to bottom. The shown cases are Coalescence R₀ = 30, v_r = 0.25; Stable collision R₀ = 30, v_r = 1.75; holes R₀ = 60, v_r = 2.0 and shattering R₀ = 90, v_r = 2.5.

Figure 4

Rotationally averaged density profile of the collision case R₀ = 60 and v_r = 1.75. The yellow curve indicates the interface, while the straight lines show the semimajor axis a (orange) and the semiminor axis b (red).

Figure 5

Plots depicting the change in the length of the semimajor axis (top) and the semiminor axis (bottom) for the R₀ = 90 droplets with a varying initial relative velocity v_r.

Figure 6

Weber number over 1 – e, where e is the eccentricity.

Figure 7

Square root of the Weber number over the radius ratio a_max/R₀.

Figure 8

Hydrodynamic velocity profiles of the collision case with R₀ = 60 and v_r = 2.0 over time. The arrows indicate the direction and magnitude of the local hydrodynamic velocity.

Figure 9

Temperature profiles during the collision of droplets with R₀ = 60 for varying initial relative velocity v_r.

Figure 10

Weber number over Reynolds number and estimated regime boundaries based on the present work and literature data by Kalweit and Drikakis as well as Juang et al. For this comparison, the present data were converted to SI units using the potential parameters for argon.