[Paper Review] Dynamics of capillary coalescence and breakup: quasi-two-dimensional nematic and isotropic droplets

P. V. Dolganov, А. С. Зверев+2 more|arXiv (Cornell University)|Nov 18, 2020

Fluid Dynamics and Heat Transfer40 references17 citations

TL;DR

This study reveals a previously unobserved coalescence dynamics in quasi-two-dimensional nematic and isotropic droplets within a Hele-Shaw cell, where both an outer bridge (connecting outer fluid regions) and a droplet bridge (connecting coalescing droplets) coexist during early coalescence. The outer bridge becomes unstable, leading to pinch-off, formation of pointed end domains, and eventual satellite droplet generation—linking coalescence and breakup phenomena in a single process for the first time, with a measured 1/4 power-law scaling of bridge width over time.

ABSTRACT

For the first time we observed formation of small satellite droplets from the bridge at droplet coalescence. Investigations were made using a Hele-Shaw cell in the two-phase region at nematic-isotropic phase transition. In previous works on coalescence it was considered that before start of coalescence there exists a bridge between the outer fluid connecting regions on the two sides of the droplets (outer bridge). After start of coalescence a bridge connecting the two droplets appears (droplet bridge) and the outer bridge is broken. For the first time we have shown that there are coalescence processes when after start of coalescence both the droplet bridge and the outer bridge can exist. This cardinally changes the coalescence process. During the first coalescence stage the size of the outer bridge decreases, the size of the droplet bridge increases. During the second stage the outer bridge becomes unstable with pinch-off, formation of pointed end domains, secondary instability, splitting of pointed end domains and formation of satellite droplets. Our work connects two areas of fluid dynamics: coalescence and breakup with formation of satellite droplets.

Motivation & Objective

• To investigate the dynamics of droplet coalescence in a two-phase region at the nematic-isotropic transition using a Hele-Shaw cell.
• To examine how the presence of orientational order in nematic droplets affects coalescence and bridge evolution.
• To identify and characterize previously unobserved coalescence stages involving dual bridges (outer and droplet) and their instability.
• To explore the formation of satellite droplets during coalescence, a phenomenon typically associated with jet breakup, not coalescence.
• To establish a scaling law for coalescence dynamics and correlate characteristic times across stages.

Proposed method

• Experiments were conducted using a liquid crystal E7 in a Hele-Shaw cell with controlled thickness (5–50 μm) and temperature to access the two-phase region (56.6–58.8 °C).
• Droplet coalescence was observed via optical microscopy with crossed polarizers at frame rates from 400 to 50 fps, enabling real-time tracking of shape and internal structure.
• The temporal evolution of bridge width (W(t)) was measured to analyze coalescence regimes, revealing a power-law dependence W(t) ∝ t^{1/4} during the intermediate stage.
• The system was cooled slowly (≤0.1 °C/min) to allow nematic droplets to form and coalesce, or heated to induce isotropic droplet nucleation.
• Analysis of bridge instability and satellite droplet formation was based on high-resolution time-lapse imaging and comparison with Rayleigh-Plateau instability theory.
• Internal droplet structures, including line, elongated, and circular domains, were tracked to infer phase behavior and interfacial energy effects.

Experimental results

Research questions

• RQ1 Can both an outer bridge and a droplet bridge coexist during the coalescence of quasi-two-dimensional droplets?
• RQ2 What causes the instability of the outer bridge, and how does it lead to satellite droplet formation?
• RQ3 How does the dynamics of bridge width during coalescence scale with time, and what does this imply about the underlying physics?
• RQ4 To what extent does the internal structure of nematic droplets influence the coalescence process and bridge evolution?
• RQ5 Can the observed coalescence dynamics be linked to classical breakup phenomena such as Rayleigh-Plateau instability?

Key findings

• For the first time, both an outer bridge and a droplet bridge were observed to coexist during the early stage of droplet coalescence, contradicting the conventional model where only one bridge exists at a time.
• The outer bridge gradually shrinks while the droplet bridge grows, indicating a transition from outer-fluid connectivity to direct droplet merging.
• When the outer bridge becomes sufficiently thin, it undergoes a nonlinear instability leading to pinch-off and formation of pointed end domains.
• Secondary instability results in the splitting of pointed end domains and the generation of small satellite droplets, a phenomenon previously unobserved in coalescence.
• A power-law scaling of bridge width with time was measured as W(t) ∝ t^{1/4} during the intermediate coalescence stage, consistent with viscous-capillary balance.
• The observed breakup process shares characteristics with Rayleigh-Plateau instability, but occurs on a bridge formed *during* coalescence rather than on a pre-existing filament or jet.