Numerical Investigation of Drop Size Distributions Generated from Randomly Corrugated Liquid Ligaments

Khái niệm cốt lõi

The study demonstrates a precisely controllable and reproducible numerical framework to investigate the mechanisms responsible for the polydispersity of drop sizes found in complex fluid fragmentation scenarios.

Tóm tắt

The content presents a numerical investigation of the statistics of drop sizes generated from the capillary-driven breakup of randomly corrugated liquid ligaments. The key highlights are:

The authors perform direct numerical simulations of air-water systems consisting of slender ligaments with random surface corrugations. This allows them to precisely control and reproduce the initial conditions of the ligaments, in contrast to physical experiments.

The simulations reveal a two-stage breakup process. In the first stage (S1), the ligament disintegrates into primary, satellite and secondary drops, along with some elongated structures. In the second stage (S2), the elongated structures further break down into smaller fragments.

The probability density functions of the drop sizes show three stable peaks corresponding to the satellite (D/W ≃0.6), primary (D/W ≃1.9) and secondary (D/W ≃2.3) drops.

The tail of the drop size distribution at the end of the first stage (S1) is well described by a volume-weighted Poisson distribution, based on an exponential distribution of pinch-off locations along the ligament.

For the large drops formed during the second stage (S2), the Log-Normal and Gamma distributions provide the best fit, with the Log-Normal distribution better capturing the primary peak and the tail of the distribution.

The study demonstrates a reproducible numerical framework to investigate the mechanisms underlying the polydispersity of drop sizes in complex fluid fragmentation scenarios.

Thống kê

The diameter of the primary drops is approximately 1.9 times the mean width of the ligament.
The diameter of the satellite drops is approximately 0.6 times the mean width of the ligament.
The diameter of the secondary drops is approximately 2.3 times the mean width of the ligament.
The critical aspect ratio (Λcr) below which the elongated structures are stable against Rayleigh-Plateau instability is around 11.5.

Trích dẫn

"The size of drops resulting from the breakup of ligaments governs physical mechanisms underlying a broad range of natural processes and industrial applications."
"The inherent non-linearity of the equations governing the ligament destabilization leads to significant differences in the resulting drop sizes, owing to small fluctuations in the myriad initial conditions."
"Our present numerical framework allows us to obtain reproducible drop size distributions, which are purely outcomes of the mathematical model (Navier Stokes with surface tension), subject to a chosen set of parameters, initial and boundary conditions."

Thông tin chi tiết chính được chắt lọc từ

Statistics of drops generated from ensembles of randomly corrugated ligaments

by Saga... lúc arxiv.org 10-02-2024

https://arxiv.org/pdf/2106.16192.pdf

Yêu cầu sâu hơn

How would the drop size distributions change if the ligaments were subjected to a stretching flow or turbulent fluctuations in the surrounding gas phase?

The introduction of a stretching flow or turbulent fluctuations in the surrounding gas phase would significantly alter the dynamics of ligament breakup and, consequently, the resulting drop size distributions. In a stretching flow, the ligaments would experience additional tensile forces that could enhance the rate of breakup by promoting the elongation of the ligaments. This elongation could lead to a more pronounced Rayleigh-Plateau instability, resulting in a wider range of drop sizes due to increased fragmentation. The stretching flow may also favor the formation of larger primary drops, as the increased tension could stabilize larger structures momentarily before they break apart.
On the other hand, turbulent fluctuations in the surrounding gas phase would introduce chaotic and random perturbations to the ligament surfaces. This turbulence could enhance the initial conditions for breakup by providing a broader spectrum of perturbation wavelengths, leading to a more complex and varied drop size distribution. The turbulence could also facilitate the coalescence of smaller droplets, potentially skewing the distribution towards larger sizes over time. Overall, both stretching flows and turbulent fluctuations would likely result in a more polydisperse drop size distribution, characterized by a shift in the peaks of the distribution and an increase in the tail of larger drops.

What are the potential limitations of the Log-Normal and Gamma distributions in capturing the full complexity of drop size distributions in more realistic fragmentation scenarios?

While the Log-Normal and Gamma distributions have been shown to fit certain aspects of drop size distributions effectively, they have inherent limitations when applied to more complex fragmentation scenarios. The Log-Normal distribution, which assumes a multiplicative process leading to drop formation, may not adequately capture the effects of coalescence and breakup dynamics that are influenced by external factors such as turbulence or stretching flows. In scenarios where these factors play a significant role, the resulting drop size distribution may exhibit behaviors that deviate from the Log-Normal model, particularly in the tail region where larger drops are formed.
Similarly, the Gamma distribution, which is often used to model the time until an event occurs (such as drop formation), may not fully account for the intricate interactions between fragmentation and coalescence processes. In realistic scenarios, the interplay between these processes can lead to non-exponential behaviors that are not well-represented by the Gamma distribution. Additionally, both distributions may struggle to capture the effects of initial conditions and the chaotic nature of fluid dynamics, leading to discrepancies between predicted and observed drop size distributions. Therefore, while these distributions provide useful frameworks, they may require modifications or the incorporation of additional parameters to accurately reflect the complexities of real-world fragmentation phenomena.

How can the insights from this study on the mechanisms of ligament breakup be extended to understand the formation of droplets in other complex multiphase flows, such as atomizing jets or bursting bubbles?

The insights gained from the study of ligament breakup mechanisms can be instrumental in understanding droplet formation in other complex multiphase flows, such as atomizing jets or bursting bubbles. The deterministic nature of ligament breakup, characterized by the influence of initial geometrical shapes and perturbations, can be applied to analyze how similar factors affect droplet formation in these other contexts. For instance, in atomizing jets, the initial conditions of the jet, including its velocity and surface tension, play a crucial role in determining the size and distribution of the resulting droplets. By applying the principles of ligament breakup, researchers can develop predictive models that account for the effects of initial perturbations and flow dynamics on droplet size distributions.
Furthermore, the study's findings regarding the two distinct stages of breakup (S1 and S2) can be relevant for understanding the dynamics of bursting bubbles, where the initial formation of droplets occurs during the rapid expansion and subsequent collapse of the bubble. The mechanisms of capillary-driven instabilities observed in ligaments can similarly be expected to influence the breakup of liquid films formed during bubble collapse, leading to the generation of droplets. By integrating the knowledge of ligament dynamics with the specific characteristics of atomizing jets and bursting bubbles, researchers can create a more comprehensive framework for predicting droplet formation across various multiphase flow scenarios, ultimately enhancing our understanding of processes such as spray formation, aerosol generation, and liquid dispersion in turbulent environments.