Emulsions are paramount in various interdisciplinary topical areas, yet a satisfactory understanding of their behavior in buoyancy-driven thermal flows has not been established. In the present work, we unravel the dynamical regimes of thermal convection in emulsions by leveraging a large set of mesoscale numerical simulations. Emulsions are prepared with a given volume fraction of the initially dispersed phase, φ, ranging from dilute (low values of φ) to jammed emulsions (high values of φ), resulting in different rheological responses of the emulsion, i.e., from Newtonian to non-Newtonian yield-stress behaviors, respectively. We then characterize the dynamics of the emulsions in the paradigmatic setup of the Rayleigh-Bénard convection, i.e., when confined between two parallel walls at different temperatures under the effect of buoyancy forces, the latter encoded in the dimensionless Rayleigh number Ra. We thoroughly investigated the dynamics of the emulsion in the changing of φ and Ra. For a given φ, at increasing Ra, we observe that the emulsion exhibits convection states, where structural changes may appear (i.e., droplet breakup, coalescence, or phase inversion), which inevitably impact the emulsion rheology. For sufficiently high values of Ra, two states of convection are observed: for low/moderate values of φ (Newtonian emulsions), we observe breakup-dominated dynamics, whereas for high values of φ (non-Newtonian emulsions), we observe phase-inverted states. For both scenarios, the droplet size distribution depends on Ra, and scaling laws for the average droplet size are analyzed and quantified. Our results offer insights into the rich dynamics of emulsions under thermal convection, offering a detailed characterization of the various dynamical regimes to be expected and their relation with structural changes occurring in such complex fluids.

Most vaccines require multiple doses, the first to induce recognition and antibody production and subsequent doses to boost the primary response and achieve optimal protection. We show that properly prioritizing the administration of first and second doses can shift the epidemic threshold, separating the disease-free from the endemic state and potentially preventing widespread outbreaks. Assuming homogeneous mixing, we prove that at a low vaccination rate, the best strategy is to give absolute priority to first doses. In contrast, for high vaccination rates, we propose a scheduling that outperforms a first-come first-served approach. We identify the threshold that separates these two scenarios and derive the optimal prioritization scheme and interdose interval. Agent-based simulations on real and synthetic contact networks validate our findings. We provide specific guidelines for effective resource allocation, showing that adjusting the timing between the primer and booster significantly impacts epidemic outcomes and can determine whether the disease persists or disappears.

In this note, we show how the exploitation of the lattice momentum balance condition allows us to envisage an analytical procedure to define the lattice pressure tensor (LPT) for the multi-phase Shan–Chen (SC) lattice Boltzmann method (LBM) with single-range potential. This con- struction ensures that the LPT normal component to a flat interface is constant to machine precision on each lattice node, i.e., it exactly implements the mechanical equilibrium condition on the lattice. We demonstrate the robustness of the approach by providing analytical expressions for the coexistence curves for different choices of the pseudo-potential and forcing schemes in the SC-LBM. This paper offers a novel and rigorous perspective for controlling the LPT in the SC-LBM, paving the way for its application in more general settings.

Based on mesoscale lattice Boltzmann numerical simulations, we characterize the Rayleigh-Bénard (RB) convective dynamics of dispersions of liquid droplets in another liquid phase. Our numerical methodology allows us to modify the droplets’ interfacial properties to mimic the presence of an emulsifier (e.g., a surfactant), resulting in a positive disjoining pressure which stabilizes the droplets against coalescence. To appreciate the effects of this interfacial stabilization on the RB convective dynamics, we carry out a comparative study between a proper emulsion, i.e., a system where the stabilization mech- anism is present (stabilized liquid-liquid dispersion), and a system where the stabilization mechanism is absent (nonstabilized liquid-liquid dispersion). The study is conducted by systematically changing both the volume fraction φ and the Rayleigh number Ra. We find that the morphology of the two systems is dramatically different due to the different inter- facial properties. However, the two systems exhibit similar global heat transfer properties, expressed via the Nusselt number Nu. Significant differences in heat transfer emerge at smaller scales, which we analyze via the Nusselt number defined at mesoscales Numes. In particular, stabilized systems exhibit more intense mesoscale heat flux fluctuations due to the persistence of fluid velocity fluctuations down to small scales, which are instead dissipated in the interfacial dynamics of nonstabilized dispersions. For fixed Ra, the difference in mesoscale heat-flux fluctuations depends nontrivially on φ, featuring a maximum in the range 0.1 < φ < 0.2. Taken all together, our results highlight the role of interfacial physics in mesoscale convective heat transfer of complex fluids.

We develop a mesoscale computational model to describe the interaction of a droplet with a solid. The model is based on the hybrid combination of the immersed boundary and the lattice Boltzmann computational schemes: The former is used to model the nonideal sharp interface of the droplet coupled with the inner and outer fluids, simulated with the lattice Boltzmann scheme. We further introduce an interaction force to model the wetting interactions of the droplet with the solid at mesoscale: This interaction force is designed with the key computational advantage of providing a regularization of the interface profile close to the contact line, avoiding abrupt curvature changes that could otherwise cause numerical instabilities. The proposed model substantially improves earlier immersed boundary-lattice Boltzmann models for wetting in that it allows a description of an ample variety of wetting interactions, ranging from hydrophobic to hydrophilic cases, without the need for any precalibration study on model parameters to be used. Model validations against analytical results for droplet shape at equilibrium and scaling laws for droplet spreading dynamics are addressed.

The flow of emulsions in confined microfluidic channels is affected by surface roughness. Directional roughness effects have recently been reported in channels with asymmetric boundary conditions featuring a flat wall, and a wall textured with directional roughness, the latter promoting a change in the velocity profiles when the flow direction of emulsions is inverted [D. Filippi et al., Adv. Mater. Technol., 2023, 8, 2201748]. An operative protocol is needed to reconstruct the stress profile inside the channel from velocity data to shed light on the trigger of the directional response. To this aim, we performed lattice Boltzmann numerical simulations of the flow of model emulsions with a minimalist model of directional roughness in two dimensions: a confined microfluidic channel with one flat wall and the other patterned by right-angle triangular-shaped posts. Simulations are essential to develop a protocol based on mechanical arguments to reconstruct stress profiles. Hence, one can analyze data to relate directional effects in velocity profiles to different rheological responses close to the rough walls associated with opposite flow directions. We finally show the universality of this protocol by applying it to other realizations of directional roughness by considering experimental data on emulsions in a microfluidic channel featuring a flat wall and a wall textured by herringbone-shaped roughness.

The steady-state behavior of a single drop under shear flow has been extensively investigated in the limit of small deformation and negligible inertia effects. In this work, we combine the calculations proposed by Flumerfelt [R. W. Flumerfelt, J. Colloid Interface Sci. 76, 330 (1980)0021-979710.1016/0021-9797(80)90377-X] for unconfined drops with interface viscosity, with those by Shapira and Haber [M. Shapira and S. Haber, Int. J. Multiphase Flow 16, 305 (1990)0301-932210.1016/0301-9322(90)90061-M] for confined drops without interface viscosity. By merging these two approaches, we provide comprehensive analytical predictions for steady-state drop deformation and inclination angle across a wide range of physical conditions, from confined to unconfined droplets, including or excluding the effect of interface viscosity. The proposed analytical predictions are also robust concerning variations in the viscosity ratio, making our model general enough to include any of the above conditions.

We study the process of thermal convection in jammed emulsions with a yield-stress rheology. We find that heat transfer occurs via an intermittent mechanism, whereby intense short-lived convective “heat bursts” are spaced out by long-lasting conductive periods. This behavior is the result of a sequence of fluidization-rigidity transitions, rooted in a nontrivial interplay between emulsion yield-stress rheology and plastic activity, which we characterize via a statistical analysis of the dynamics at the droplet scale. We also show that droplets’ coalescence induced during heat bursts leads to a spatially heterogeneous phase inversion of the emulsion which eventually supports a sustained convective state.

Employing numerical simulations, we provide an accurate insight into the heat transfer mechanism in the Rayleigh-Bénard convection of concentrated emulsions with finite-size droplets. We focus on the unsteady dynamics characterizing the thermal convection of these complex fluids close to the transition from conductive to convective states, where the heat transfer phenomenon, expressed in terms of the Nusselt number Nu, is characterized by pronounced fluctuations triggered by collective droplet motion [F. Pelusi et al., Soft Matter, 2021, 17(13), 3709-3721]. By systematically increasing the droplet concentration, we show how these fluctuations emerge along with the segregation of “extreme events” in the boundary layers, causing intermittent bursts in the heat flux fluctuations. Furthermore, we quantify the extension S and the duration of the coherent droplet motion accompanying these extreme events via a suitable statistical analysis involving the droplet displacements. We show how the increase in droplet concentration results in a power-law behaviour of the probability distribution function of S and and how this outcome is robust at changing the analysis protocol. Our work offers a comprehensive picture, linking macroscopic heat transfer fluctuations with the statistics of droplets at the mesoscale.

Membrane viscosity is known to play a central role in the transient dynamics of isolated viscoelastic capsules by decreasing their deformation, inducing shape oscillations and reducing the loading time, that is, the time required to reach the steady-state deformation. However, for dense suspensions of capsules, our understanding of the influence of the membrane viscosity is minimal. In this work, we perform a systematic numerical investigation based on coupled immersed boundary-lattice Boltzmann (IB-LB) simulations of viscoelastic spherical capsule suspensions in the non-inertial regime. We show the effect of the membrane viscosity on the transient dynamics as a function of volume fraction and capillary number. Our results indicate that the influence of membrane viscosity on both deformation and loading time strongly depends on the volume fraction in a non-trivial manner: dense suspensions with large surface viscosity are more resistant to deformation but attain loading times that are characteristic of capsules with no surface viscosity, thus opening the possibility to obtain richer combinations of mechanical features.

The wetting dynamics of liquid particles, from coated droplets to soft capsules, holds significant technological interest. Motivated by the need to simulate liquid metal droplets with an oxidized surface layer, in this work, we introduce a computational scheme that allows us to simulate droplet dynamics with general surface properties and model different levels of interface stiffness, also describing cases that are intermediate between pure droplets and capsules. Our approach is based on a combination of the immersed boundary and the lattice Boltzmann methods. Here, we validate our approach against the theoretical predictions in the context of shear flow and static wetting properties, and we show its effectiveness in accessing the wetting dynamics, exploring the ability of the scheme to address a broad phenomenology.

In this paper, we present TLBfind, a GPU code for simulating the hydrodynamics of droplets along with a dynamic temperature field. TLBfind hinges on a two-dimensional multi-component lattice Boltzmann (LB) model simulating a concentrated emulsion with finite-size droplets evolving in a thermal convective state, just above the transition from conduction to convection. The droplet concentration of the emulsion system is tunable and at the core of the code lies the possibility to measure a large number of physical observables characterising the flow and droplets. Furthermore, TLBfind includes a parallel implementation on GPU of the Delaunay triangulation useful for the detection of droplets' plastic rearrangements, and several types of boundary conditions, supporting simulations of channels with structured rough walls. Program summary: Program Title: TLBfind CPC Library link to program files: https://doi.org/10.17632/hbk45696nf.1 Developer's repository link: https://github.com/FrancescaPelusi/TLBfind Licensing provisions: MIT Programming language: CUDA-C Nature of problem: Hydrodynamics of concentrated emulsions with finite-size droplets in a thermal convective state. Solution method: Single relaxation time Lattice Boltzmann method to solve Navier-Stokes equations for fluids, coupled with the temperature field dynamics. The output describes the dynamics of finite-size droplets of concentrated emulsions in presence of a temperature field. The temperature field obeys the advection-diffusion equation. Additional comments including restrictions and unusual features: Plastic rearrangements of droplets are detected via the parallel implementation of the Delaunay triangulation, and boundary conditions are tunable.

Under the condition of partial surface wettability, thin liquid films can be destabilized by small perturbations and rupture into droplets. As successfully predicted by the thin film equation (TFE), the rupture dynamics are dictated by the liquid-solid interaction. The theory describes the latter using the disjoining pressure or, equivalently, the contact angle. The introduction of a secondary fluid can lead to a richer phenomenology, thanks to the presence of different fluid/surface interaction energies but has so far not been investigated. In this work, we study the rupture of liquid films with different heights immersed in a secondary fluid using a multi-component lattice Boltzmann (LB) approach. We investigate a wide range of surface interaction energies, equilibrium contact angles, and film thicknesses. We found that the rupture time can differ by about one order of magnitude for identical equilibrium contact angles but different surface free energies. Interestingly, the TFE describes the observed breakup dynamics qualitatively well, up to equilibrium contact angles as large as 130°. A small film thickness is a much stricter requirement for the validity of the TFE, and agreement with LB results is found only for ratios ε = h / L of the film height h and lateral system size L, such as ε≲ × 10 - 3.

We present mesoscale numerical simulations of Rayleigh-Bénard (RB) convection in a two-dimensional model emulsion. The systems under study are constituted of finite-size droplets, whose concentration is systematically varied from small (Newtonian emulsions) to large values (non-Newtonian emulsions). We focus on the characterisation of the heat transfer properties close to the transition from conductive to convective states, where it is well known that a homogeneous Newtonian system exhibits a steady flow and a time-independent heat flux. In marked contrast, emulsions exhibit non-steady dynamics with fluctuations in the heat flux. In this paper, we aim at the characterisation of such non-steady dynamics via detailed studies on the time-averaged heat flux and its fluctuations. To quantitatively understand the time-averaged heat flux, we propose a side-by-side comparison between the emulsion system and a single-phase (SP) system, whose viscosity is suitably constructed from the shear rheology of the emulsion. We show that such local closure works well only when a suitable degree of coarse-graining (at the droplet scale) is introduced in the local viscosity. To delve deeper into the fluctuations in the heat flux, we furthermore propose a side-by-side comparison between a Newtonian emulsion (i.e., with a small droplet concentration) and a non-Newtonian emulsion (i.e., with a large droplet concentration), at fixed time-averaged heat flux. This comparison elucidates that finite-size droplets and the non-Newtonian rheology cooperate to trigger enhanced heat-flux fluctuations at the droplet scales. These enhanced fluctuations are rooted in the emergence of space correlations among distant droplets, which we highlight via direct measurements of the droplets displacement and the characterisation of the associated correlation function. The observed findings offer insights on heat transfer properties for confined systems possessing finite-size constituents.

We study the coarsening dynamics of a two-dimensional system via numerical simulations. The system under consideration is a biphasic system consisting of domains of a dispersed phase closely packed together in a continuous phase and separated by thin interfaces. Such a system is elastic and typically out of equilibrium. The equilibrium state is attained via the coarsening dynamics, wherein the dispersed phase slowly diffuses through the interfaces, causing the domains to change in size and eventually rearrange abruptly. The effect of rearrangements is propagated throughout the system via the intrinsic elastic interactions and may cause rearrangements elsewhere, resulting in intermittent bursts of activity and avalanche behaviour. Here we aim at quantitatively characterizing the corresponding avalanche statistics (i.e. size, duration, and inter-avalanche time). Despite the coarsening dynamics is triggered by an internal driving mechanism, we find quantitative indications that such avalanche statistics displays scaling-laws very similar to those observed in the response of disordered materials to external loads.