Order to Disorder Transition in a Coarsening Two-Dimensional Foam

Characterizing Aqueous Foams by In Situ Viscosity Measurement in a Foam Column

Foam characterization is essential in many applications of foams, such as cleaning, food processing, cosmetics, and oil production, due to these applications' diversified requirements. The standard characterization method, the foam column test, cannot provide sufficient information for in-depth studies. Hence, there have been many studies that incorporated different characterization methods into a standard test. It should be enlightening and feasible to measure the foam viscosity, which is both of practical and fundamental interest during the foam column test, but it has never been done before. Here, we demonstrate a method to characterize aqueous foams and their aging behaviors with the simultaneous measurement of foam viscosity and foam height. Using a vibration viscometer, we integrate foam column experiments with in situ foam viscosity measurements. We studied the correlation among the foam structure, foam height, and foam viscosity during the foam decay process. We found a drastic decrease in foam viscosity in the early foam decay, while the foam height remained unchanged, which is explained by coarsening. This method is much more sensitive and time-efficient than conventional foam-height-based methods by comparing the half-life. This method successfully characterizes the stability of foams made of various combinations of surfactants and gases.

Simply solvable model capturing the approach to statistical self-similarity for the diffusive coarsening of bubbles, droplets, and grains

Aqueous foams and a wide range of related systems are believed to coarsen by diffusion between neighboring domains into a statistically self-similar scaling state, after the decay of initial transients, such that dimensionless domain size and shape distributions become time independent and the average grows as a power law. Partial integrodifferential equations for the time evolution of the size distribution for such phase separating systems can be formulated for arbitrary initial conditions, but these are cumbersome for analyzing data on nonscaling state preparations. Here we show that essential features of the approach to the scaling state are captured by an exactly-solvable ordinary differential equation for the evolution of the average bubble size. The key ingredient is to characterize the bubble size distribution approximately, using the average size of all bubbles and the average size of the critical bubbles, which instantaneously neither grow nor shrink. The difference between these two averages serves as a proxy for the width of the size distribution. Solution of our model shows that behavior is controlled by a signed length δ that is proportional to the width of the initial distribution relative to that in the scaling state. In particular, δ is negative if the initial preparation is too monodisperse, and is positive if it is too polydisperse. To test our approach, we compare with data for quasi-two dimensional dry foams created with three different initial amounts of polydispersity. This allows us to readily identify the critical radius from the average area of six-sided bubbles, whose growth rate is zero by the von Neumann law. The growth of the average and critical radii agree quite well with exact solution, though the most monodisperse sample crosses over to the scaling state faster than expected. A simpler approximate solution of our model performs equally well. Our approach is applicable to 3d foams, which we demonstrate by re-analyzing prior data, as well as to froths of dilute droplets and to phase separation kinetics for more general systems such as emulsions, binary mixtures, and alloys.

Unraveling hidden rules behind the wet-to-dry transition of bubble array by glass-box physics rule learner

A liquid–gas foam, here called bubble array, is a ubiquitous phenomenon widely observed in daily lives, food, pharmaceutical and cosmetic products, and even bio- and nano-technologies. This intriguing phenomenon has been often studied in a well-controlled environment in laboratories, computations, or analytical models. Still, real-world bubble undergoes complex nonlinear transitions from wet to dry conditions, which are hard to describe by unified rules as a whole. Here, we show that a few early-phase snapshots of bubble array can be learned by a glass-box physics rule learner (GPRL) leading to prediction rules of future bubble array. Unlike the black-box machine learning approach, the glass-box approach seeks to unravel expressive rules of the phenomenon that can evolve. Without known principles, GPRL identifies plausible rules of bubble prediction with an elongated bubble array data that transitions from wet to dry states. Then, the best-so-far GPRL-identified rule is applied to an independent circular bubble array, demonstrating the potential generality of the rule. We explain how GPRL uses the spatio-temporal convolved information of early bubbles to mimic the scientist’s perception of bubble sides, shapes, and inter-bubble influences. This research will help combine foam physics and machine learning to better understand and control bubbles.

Intermittent dynamics of bubble dissolution due to interfacial growth of fat crystals

Foams are inherently unstable objects, that age and disappear over time. The main cause of foam aging is Ostwald ripening: smaller air bubbles within the foam empty their gas content into larger ones. One strategy to counter Ostwald ripening consists in creating armored bubbles, where solid particles adsorbed at the air/liquid interface prevent bubbles from shrinking below a given size. Here, we study the efficiency of coating air bubbles with fat crystals to prevent bubble dissolution. A monoglyceride, monostearin, is directly crystallized at the air/oil interface. Experiments on single bubbles in a microfluidic device show that the presence of monostearin fat crystals slows down dissolution, with an efficiency that depends on the crystal size. Bubble ripening in the presence of crystals exhibits intermittent dissolution dynamics, with phases of arrest, when crystals jam at the interface, followed by phases of dissolution, when monostearin crystals are ejected from the interface. In the end, crystals do not confer enough mechanical strength to the bubbles to prevent them from fully dissolving.

Dynamics and mechanism of liquid film collapse in a foam

Foams have unique properties that distinguish them from ordinary liquids and gases, and are ubiquitously observed in nature, both in biological systems and industrial products. Foams are known to eventually collapse over time; given their wide-range industrial application, understanding how bubbles in a foam collapse is an important aspect for product longevity and tailoring physical properties. Previously, it was shown that droplets are emitted during the collective bubble collapse, however the mechanism of the droplet emission in a foam is not yet clearly understood. It is directly related to the stability of the foam, thus we quantitatively investigate collapse dynamics in liquid films in a foam, and identify some unique features. When one film breaks, we see that the oscillation of the vertical Plateau border to which it is connected induces anomalous liquid transport from the edge of the border to the center. Once a crack appears near the border and a collapse front is formed, we find that the curvature of the front reverses as it migrates, followed by the emergence and emission of droplets. We elucidate the origins of this behavior and discuss the stability of foams, establishing how the characteristic time scales of the process relate to each other.