Swirling Fluid Reduces the Bounce of Partially Filled Containers

Certain spatial distributions of water inside partially filled containers can significantly reduce the bounce of the container. In experiments with containers filled to a volume fraction ϕ, we show that rotation offers control and high efficiency in setting such distributions and, consequently, in altering bounce markedly. High-speed imaging evidences the physics of the phenomenon and reveals a rich sequence of fluid-dynamics processes, which we translate into a model that captures our overall experimental findings.

Mutation and SARS-CoV-2 strain competition under vaccination in a modified SIR model

The crisis caused by the COVID-19 outbreak around the globe raised an increasing concern about the ongoing emergence of variants of the virus that may evade the immune response provided by vaccines. New variants appear due to mutation, and as the cases accumulate, the probability of the emergence of a variant of concern increases. In this article, we propose a modified susceptible, infected, and recovered (SIR) model with waning immunity that captures the competition of two strain classes of an infectious disease under the effect of vaccination with a highly contagious and deadlier strain class emerging from a prior strain due to mutation. When these strains compete for a limited supply of susceptible individuals, changes in the efficiency of vaccines may affect the behaviour of the disease in a non-trivial way, resulting in complex outcomes. We characterise the parameter space including intrinsic parameters of the disease, and using the vaccine efficiencies as control variables. We find different types of transcritical bifurcations between endemic fixed points and a disease-free equilibrium and identify a region of strain competition where the two strain classes coexist during a transient period. We show that a strain can be extinguished either due to strain competition or vaccination, and we obtain the critical values of the efficiency of vaccines to eradicate the disease. Numerical studies using parameters estimated from publicly reported data agree with our theoretical results. Our mathematical model could be a tool to assess quantitatively the vaccination policies of competing and emerging strains using the dynamics in epidemics of infectious diseases.

Universal Wrinkling of Supported Elastic Rings

An exactly solvable family of models describing the wrinkling of substrate-supported inextensible elastic rings under compression is identified. The resulting wrinkle profiles are shown to be related to the buckled states of an unsupported ring and are therefore universal. Closed analytical expressions for the resulting universal shapes are provided, including the one-to-one relations between the pressure and tension at which these emerge. The analytical predictions agree with numerical continuation results to within numerical accuracy, for a large range of parameter values, up to the point of self-contact.

Agar Biopolymer Films for Biodegradable Packaging: A Reference Dataset for Exploring the Limits of Mechanical Performance

This article focuses on agar biopolymer films that offer promise for developing biodegradable packaging, an important solution for reducing plastics pollution. At present there is a lack of data on the mechanical performance of agar biopolymer films using a simple plasticizer. This study takes a Design of Experiments approach to analyze how agar-glycerin biopolymer films perform across a range of ingredients concentrations in terms of their strength, elasticity, and ductility. Our results demonstrate that by systematically varying the quantity of agar and glycerin, tensile properties can be achieved that are comparable to agar-based materials with more complex formulations. Not only does our study significantly broaden the amount of data available on the range of mechanical performance that can be achieved with simple agar biopolymer films, but the data can also be used to guide further optimization efforts that start with a basic formulation that performs well on certain property dimensions. We also find that select formulations have similar tensile properties to thermoplastic starch (TPS), acrylonitrile butadiene styrene (ABS), and polypropylene (PP), indicating potential suitability for select packaging applications. We use our experimental dataset to train a neural network regression model that predicts the Young's modulus, ultimate tensile strength, and elongation at break of agar biopolymer films given their composition. Our findings support the development of further data-driven design and fabrication workflows.

Stress distribution and surface shock wave of drop impact

Drop impact causes severe surface erosion, dictating many important natural, environmental and engineering processes and calling for substantial prevention and preservation efforts. Nevertheless, despite extensive studies on the kinematic features of impacting drops over the last two decades, the dynamic process that leads to the drop-impact erosion is still far from clear. Here, we develop a method of high-speed stress microscopy, which measures the key dynamic properties of drop impact responsible for erosion, i.e., the shear stress and pressure distributions of impacting drops, with unprecedented spatiotemporal resolutions. Our experiments reveal the fast propagation of self-similar noncentral stress maxima underneath impacting drops and quantify the shear force on impacted substrates. Moreover, we examine the deformation of elastic substrates under impact and uncover impact-induced surface shock waves. Our study opens the door for quantitative measurements of the impact stress of liquid drops and sheds light on the origin of low-speed drop-impact erosion.

The dynamic process behind the low-speed drop-impact erosion remains challenging to understand. Cheng et al. develop a method of high-speed microscopy, revealing the fast propagation of self-similar stress maxima underneath impacting drops and the formation of surface waves on impacted substrates.

Faraday-Wave Contact-Line Shear Gradient Induces Streaming and Tracer Self-Organization: From Vortical to Hedgehoglike Patterns

In this Letter, we experimentally demonstrate self-organization of small tracers under the action of longitudinal Faraday waves in a narrow container. We observe a steady current formation dividing the interface in small cells given by Faraday-wave symmetries. These streaming currents rotate in each cell, and their circulation increases with wave amplitude. This streaming flow drives the tracers to form patterns, whose shapes depend on the Faraday-wave amplitude: From low to high amplitudes, we find tracers dispersed on vortices, narrow rotating rings, and a hedgehoglike pattern. We first describe the main pattern features and characterize the wave and tracers' motion. We then show experimentally that the main source of the streaming flow is the spatiotemporal-dependent shear at the wall contact line created by the Faraday wave itself. We end by presenting a 2D compressible advection model that considers the minimal ingredients present in the Faraday experiment, namely, the stationary circulation, the stretching component due to the oscillatory wave, and a steady converging field, which combined produce the observed self-organized patterns.

Shape of a recoiling liquid filament

We study the capillary retraction of a Newtonian semi-infinite liquid filament through analytical methods. We derive a long-time asymptotic-state expansion for the filament profile using a one-dimensional free-surface slender cylindrical flow model based on the three-dimensional axisymmetric Navier-Stokes equations. The analysis identifies three distinct length and time scale regions in the retraction domain: a steady filament section, a growing spherical blob, and an intermediate matching zone. We show that liquid filaments naturally develop travelling capillary waves along their surface and a neck behind the blob. We analytically prove that the wavelength of the capillary waves is approximately 3.63 times the filament’s radius at the inviscid limit. Additionally, the waves’ asymptotic wavelength, decay length, and the minimum neck size are analysed in terms of the Ohnesorge number. Finally, our findings are compared with previous results from the literature and numerical simulations in Basilisk obtaining a good agreement. This analysis provides a full picture of the recoiling process going beyond the classic result of the velocity of retraction found by Taylor and Culick.

Fluid-supported elastic sheet under compression: Multifold solutions

The properties of a hinged floating elastic sheet of finite length under compression are considered. Numerical continuation is used to compute spatially localized buckled states with many spatially localized folds. Both symmetric and antisymmetric states are computed and the corresponding bifurcation diagrams determined. Weakly nonlinear analysis is used to analyze the transition from periodic wrinkles to singlefold and multifold states and to compute their energy. States with the same number of folds have energies that barely differ from each other and the energy gap decreases exponentially as localization increases. The stability of the different competing states is studied and the multifold solutions are all found to be unstable. However, the decay time into solutions with fewer folds can be so slow that multifolds may appear to be stable.

Localized Faraday patterns under heterogeneous parametric excitation

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schrödinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength.

Dynamic self-assembly of charged colloidal strings and walls in simple fluid flows

Colloidal particles can self-assemble into various ordered structures in fluid flows that have potential applications in biomedicine, materials synthesis and encryption. These dynamic processes are also of fundamental interest for probing the general principles of self-assembly under non-equilibrium conditions. Here, we report a simple microfluidic experiment, where charged colloidal particles self-assemble into flow-aligned 1D strings with regular particle spacing near a solid boundary. Using high-speed confocal microscopy, we systematically investigate the influence of flow rates, electrostatics and particle polydispersity on the observed string structures. By studying the detailed dynamics of stable flow-driven particle pairs, we quantitatively characterize interparticle interactions. Based on the results, we construct a simple model that explains the intriguing non-equilibrium self-assembly process. Our study shows that the colloidal strings arise from a delicate balance between attractive hydrodynamic coupling and repulsive electrostatic interaction between particles. Finally, we demonstrate that, with the assistance of transverse electric fields, a similar mechanism also leads to the formation of 2D colloidal walls.

Experiments on generation of surface waves by an underwater moving bottom

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

Dissipation-driven behavior of nonpropagating hydrodynamic solitons under confinement

We have identified a physical mechanism that rules the confinement of nonpropagating hydrodynamic solitons. We show that thin boundary layers arising on walls are responsible for a jump in the local damping. The outcome is a weak dissipation-driven repulsion that determines decisively the solitons' long-time behavior. Numerical simulations of our model are consistent with experiments. Our results uncover how confinement can generate a localized distribution of dissipation in out-of-equilibrium systems. Moreover, they show the preponderance of such a subtle effect in the behavior of localized structures. The reported results should explain the dynamic behavior of other confined dissipative systems.

Impact dynamics of granular jets with noncircular cross sections

Using high-speed photography, we investigate two distinct regimes of the impact dynamics of granular jets with noncircular cross sections. In the steady-state regime, we observe the formation of thin granular sheets with anisotropic shapes and show that the degree of anisotropy increases with the aspect ratio of the jet's cross section. Our results illustrate the liquidlike behavior of granular materials during impact and demonstrate that a collective hydrodynamic flow emerges from strongly interacting discrete particles. We discuss the analogy between our experiments and those from the Relativistic Heavy Ion Collider, where similar anisotropic ejecta from a quark-gluon plasma have been observed in heavy-ion impact.

Coalescence cascade of dissipative solitons in parametrically driven systems

Parametrically driven spatially extended systems exhibit uniform oscillations which are modulationally unstable. The resulting periodic state evolves to the creation of a gas of dissipative solitons. Driven by the interaction of dissipative solitons, the multisoliton state undergoes a cascade of coalescence processes, where the average soliton separation distance obeys a temporal self-similar law. Starting from the soliton pair interaction law, we have derived analytically and characterized the law of this multisoliton coarsening process. A comparison of numerical results obtained with different models such as the parametrically driven damped nonlinear Schrödinger equation, a vertically driven chain of pendula, and a parametrically forced magnetic wire, shows remarkable agreement. Both phenomena, the pair interaction law and the coarsening process, are also observed experimentally in a quasi-one-dimensional layer of Newtonian fluid which is oscillated vertically.