Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2503.13659

Scaling Laws Governing Droplet Spreading and Merging Dynamics on Solid Surfaces: A Molecular Simulation Study

Ertiza Hossain Shopnil·Jahid Emon·Md Nadeem Azad·AKM Monjur Morshed
View original source ↗Read source document ↗Export metadata ↓

Abstract

This study employs molecular dynamics simulations to investigate droplet dynamics when a stationary droplet on a solid surface is struck by another droplet of similar size from above. The focus is on the jumping behavior of the merged droplet and the associated energy conversion. The process is primarily governed by the amount of energy converted into kinetic energy after dissipation. At high impact velocities, the energy conversion efficiency becomes constant, with only about 1% lost due to surface adhesion, an effect that diminishes with increasing velocity. Factors such as impact velocity, droplet size, surface texture, and wettability significantly influence the jumping velocity. Scaling laws are developed for the maximum spreading time, spreading factor, and restitution coefficient based on the Weber (We) and Reynolds (Re) numbers, which differ from those for single droplet impacts. On superhydrophobic surfaces, the spreading time is approximated as three times droplet radius to impact velocity, and its dimensionless form scales linearly with We 0.31. The general scaling laws for the spreading factor for velocity dependent and velocity independent spreading regimes are developed.

Explore related subjects

physics.flu-dyn

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ertiza Hossain Shopnil, Jahid Emon, Md Nadeem Azad, AKM Monjur Morshed. 2026-03-23. Scaling Laws Governing Droplet Spreading and Merging Dynamics on Solid Surfaces: A Molecular Simulation Study. https://arxiv.org/abs/2503.13659

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Kolmogorov scale in turbulence of surface gravity waves

In this paper, we study the analogue of the Kolmogorov scale in surface gravity wave turbulence, characterized by the cutoff wavenumber $k_c$ at which the power-law inertial range transitions into the dissipation range. We perform numerical simulations of the primitive dynamical equations with a broad-scale dissipation of magnitude $γ_0 k^2$ in spectral space to establish the relation between $k_c$ and $γ_0$. Our results show a scaling $k_c\simγ_0^β$, where $β$ depends on the slope $α$ of the power-law spectrum. We find that $β(α)$ agrees more closely with the prediction obtained by balancing the nonlinear and dissipation terms in the dynamical equations than with that based on the kinetic equation. This observation reveals that non-resonant triad interactions play a more significant role than resonant quartet interactions in the formation of $k_c$.

physics.flu-dyn↗
arXiv2026

Structural identifiability and stress reconstruction from incomplete optical maps with velocimetry

Reconstructing the stress field of a planar viscoelastic flow from optical measurements loses its direct evidence wherever optical coverage is interrupted, and no improvement in optical precision restores an observation that was never made. We characterize what a second, velocity channel adds, and what neither channel can supply. Two calibrated optical components determine the local deviatoric stress pointwise, while velocity constrains spatial stress variation through momentum balance, so the two channels are complementary rather than redundant. The isotropic part of the stress is unobservable to both: the divergence of an isotropic field is a pure gradient, which the Leray projection annihilates, so every representable isotropic mode lies in the joint null space. That accounts for the null space exactly when the optical field is complete, and bounds it from below otherwise, since finite incomplete sampling and aperture zeros can remove further directions. We verify the count directly on three discretizations. In paired synthetic tests with finite measurement apertures, spatially correlated noise and optical stripe dropout, adding velocity reduces the mean whole-domain deviatoric error from 50.40% to 27.82% at 3% reference noise, and the improvement survives shared gaps, inverse-grid refinement at fixed physical sampling, and a constitutively generated stress field. The improvement does not rest on how the regularization parameter is chosen: it holds under both the expected-norm discrepancy rule and generalized cross-validation, and we report each selection with its position in the search interval, which is where the two rules differ.

physics.flu-dyn↗
arXiv2026

A unified multirate lattice Boltzmann framework for thermosolutal dendritic solidification

Thermosolutal dendritic solidification involves interface evolution, solute diffusion, heat transfer, and melt flow over markedly different time scales. In lattice Boltzmann simulations, a single numerical time interval may place different transport processes in unfavorable relaxation ranges, while asynchronous updates require consistent transfer of phase-change contributions. To address these issues, a unified multirate multiple-relaxation-time lattice Boltzmann method is developed for thermal, solutal, and thermosolutal dendritic solidification. The coupled fields share a common moment-space framework but evolve at different update rates. The concentration and temperature source terms are separated into transport-related and phase-change contributions, and each resolved phase increment is used to immediately transfer the corresponding solutal and latent-heat contributions. The method reproduces characteristic dendritic morphologies and tip-velocity trends under pure diffusion and forced convection, with weak sensitivity to the tested update factors. Directional solidification over Lewis numbers \(Le=1\)--\(1000\) captures the transition from nearly planar to cellular and strongly branched growth, including vertically aligned dendrites and solute-rich interdendritic channels for saline water, in qualitative agreement with experiments. Source-coupling ablation shows that delayed coarse-step transfer produces increasingly strong local source pulses and eventual loss of numerical stability as time-scale separation increases, whereas phase-step instantaneous transfer remains stable over the tested conditions. These results demonstrate the applicability of the proposed framework to dendritic solidification with strongly separated transport time scales. The source code is publicly available in the \emph{DendriteLBM} repository.

physics.flu-dyn↗