Theoretical deformation modeling and drop size prediction in the multimode breakup regime

We present direct numerical simulations of the splashing process between two cylindrical liquid rims. This belongs to a class of impact and collision problems with a wide range of applications in science and engineering, and motivated here by splashing of breaking ocean waves. Interfacial perturbations with a truncated white noise frequency profile are introduced to the rims before their collision, whose subsequent morphological development is simulated by solving the two-phase incompressible Navier–Stokes equation with the adaptive mesh refinement technique, within the Basilisk software environment. We first derive analytical solutions predicting the unsteady interfacial and velocity profiles of the expanding sheet forming between the two rims, and develop scaling laws for the evolution of the lamella rim under capillary deceleration. We then analyse the formation and growth of transverse ligaments ejected from the lamella rims, which we find to originate from the initial corrugated geometry of the perturbed rim surface. Novel scaling models are proposed for predicting the decay of the ligament number density due to the ongoing ligament merging phenomenon, and found to agree well with the numerical results presented here. The role of the mechanism in breaking waves is discussed further and necessary next steps in the problem are identified.

Section: Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fragmentation of colliding liquid rims

Tang,

Adcock,

Mostert

2024

“…2019; Rimbert et al. 2020; Obenauf & Sojka 2021). In addition, from the perspective of droplet external airflow, the formation and shedding of vortices outside the droplet are found to significantly affect the droplet breakup at high Weber numbers (Liu et al.…”

Section: Introductionmentioning

confidence: 99%

“…the droplet deformation and breakup model) are proposed to describe the droplet deformation and breakup. Different variations and improvements have been developed based on this perspective, but mostly for low Weber numbers (Wang et al 2015;Stefanitsis et al 2019;Rimbert et al 2020;Obenauf & Sojka 2021). In addition, from the perspective of droplet external airflow, the formation and shedding of vortices outside the droplet are found to significantly affect the droplet breakup at high Weber numbers (Liu et al 2018;Dorschner et al 2020;Wang et al 2020).…”

Section: Introductionmentioning

confidence: 99%

Breakup of particle-laden droplets in airflow

Xu,

Wang,

Che

2023

The atomisation of a suspension containing liquid and dispersed particles is prevalent in many applications. Previous studies of droplet breakup mainly focused on homogeneous fluids, and the heterogeneous effect of particles on the breakup progress is unclear. In this study, the breakup of particle-laden droplets in airflow is investigated experimentally. Combining synchronised high-speed images from the side view and the 45 $^\circ$ view, we compare the morphology of particle-laden droplets with that of homogeneous fluids in different breakup modes. The results show that the higher effective viscosity of particle-laden droplets affects the initial deformation, and the heterogeneous effect of particles appears in the later breakup stage. To evaluate the heterogeneous effect of particles quantitatively, we eliminate the effect of the higher effective viscosity of particle-laden droplets by comparing cases corresponding to the same inviscid Weber number. The quantitative comparison reveals that the heterogeneous effect of particles accelerates the fragmentation of the liquid film and promotes localised rapid piercing. A correlation length that depends on the particle diameter and the volume fraction is proposed to characterise the length scale of the concentration fluctuation under the combined effect of the initial flattening and later stretching during the droplet breakup process. Based on this correlation length, the fragment size distributions are analysed, and the scaling results agree well with the experimental data.

“…However, instability theories have difficulty in accounting for the viscous effects (Jalaal & Mehravaran 2014), flow dynamics prior to drop flattening and finite thickness and peripheral boundary of the flattened disc (Jackiw & Ashgriz 2021). Alternatively, some works highlight the influence of the internal flow within the droplets on the deformation process (Guildenbecher et al 2009;Villermaux & Bossa 2009;Jackiw & Ashgriz 2021;Obenauf & Sojka 2021;Ling & Mahmood 2023). The internal flow model compensates for the drawback of the RT instability model in predicting early-time drop deformation; however, this approach is somewhat simplified and cannot account for the complex interaction between wake vortices and drop surface (Marcotte & Zaleski 2019).…”

Section: Introductionmentioning

confidence: 99%

Bag film breakup of droplets in uniform airflows

Tang,

Adcock,

Mostert

2023

We present novel numerical simulations investigating the bag breakup of liquid droplets. We first examine the viscous effect on the early-time drop deformation, comparing with theory and experiment. Next, a bag film forms at late time and is susceptible to spurious mesh-induced breakup in numerical simulations, which has prevented previous studies from reaching grid convergence of fragment statistics. We therefore adopt the manifold death (MD) algorithm which artificially perforates thin films once they reach a prescribed critical thickness independent of the grid size, controlled by a numerical parameter $L_{sig}$ . We show grid convergence of fragment statistics when utilising the MD algorithm, and analyse the fragment behaviour and bag film disintegration mechanisms including ligament breakup, node detachment and rim destabilisation. Our choice of the critical thickness parameter $L_{sig}$ is limited by numerical constraints and thus has not been matched to experiment or theory; consequently, the current simulations yield critical bag film perforation thicknesses larger than experimentally observed. The influence of the MD algorithm configuration on the bag breakup phenomena and statistics will be investigated in future work. We also study the effects of moderate liquid Ohnesorge number ( $0.005 \leqslant Oh \leqslant 0.05$ ) on the bag breakup process and fragment statistics, where a non-monotonic dependency of the average diameter of bag film fragments on $Oh$ is found. These results highlight the utility of the MD algorithm in multiphase simulations involving topological changes, and pave the way for physics-based numerical investigations into spume generation at the air–sea interface.