Effect of surfactant-laden droplets on turbulent flow topology

In this work, we investigate flow topology modifications produced by a swarm of large surfactant-laden droplets released in a turbulent channel flow. Droplets have same density and viscosity of the carrier fluid, so that only surface tension effects are considered. We run one single-phase flow simulation at $Re_\tau=\rho u_\tau h / \mu = 300$, and ten droplet-laden simulations at the same $Re_\tau$ with a constant volume fraction equal to $\Phi \simeq5.4\%$. For each simulation, we vary the Weber number ($We$, ratio between inertial and surface tension forces) and the elasticity number ($\beta_s$, parameter that quantifies the surface tension reduction). We use direct numerical simulations of turbulence coupled with a phase field method to investigate the role of capillary forces (normal to the interface) and Marangoni forces (tangential to the interface) on turbulence (inside and outside the droplets). As expected, due to the low volume fraction of droplets, we observe minor modifications in the macroscopic flow statistics. However, we observe major modifications of the vorticity at the interface and important changes in the local flow topology. We highlight the role of Marangoni forces in promoting an elongational type of flow in the dispersed phase and at the interface. We provide detailed statistical quantification of these local changes as a function of the Weber number and elasticity number, which may be useful for simplified models

Mass-conservation-improved phase field methods for turbulent multiphase flow simulation

The phase field method has emerged as a powerful tool for the simulation of multiphase flow. The method has great potential for further developments and applications: it has a sound physical basis, and when associated with a highly refined grid, physics is accurately rendered. However, in many cases, especially when dealing with turbulent flows, the available computational resources do not allow for a complete resolution of the interfacial phenomena and some undesired effects such as shrinkage, coarsening and misrepresentation of surface tension forces and thermo-physical properties can affect the accuracy of the simulations. In this paper, we present two improved phase field method formulations (profile-corrected and flux-corrected), specifically developed to overcome the previously mentioned drawbacks, and we benchmark their performance versus the classic one. The formulations are first tested considering the rise of a bubble in a quiescent fluid and the interaction of two droplets in laminar shear flow; then, their performances are compared in the simulation of a droplet-laden turbulent flow. The aim of this work is to review and benchmark the different phase field method formulations, with the final goal of laying down useful guidelines for the accurate simulation of turbulent multiphase flow with the phase field method

Heat transfer in drop-laden turbulence

Heat transfer by large deformable drops in a turbulent flow is a complex and rich in physics system, in which drops deformation, breakage and coalescence influence the transport of heat. We study this problem coupling direct numerical simulations (DNS) of turbulence, with a phase-field method for the interface description. Simulations are run at fixed shear Reynolds and Weber numbers. To evaluate the influence of microscopic flow properties, like momentum/thermal diffusivity, on macroscopic flow properties, like mean temperature or heat transfer rates, we consider four different values of the Prandtl number, which is the momentum to thermal diffusivity ratio: Pr=1, Pr=2, Pr=4 and Pr=8. The drops volume fraction is Phi=5.4% for all cases. Drops are initially warmer than the turbulent carrier fluid, and release heat at different rates, depending on the value of Pr, but also on their size and on their own dynamics (topology, breakage, drop-drop interaction). Computing the time behavior of the drops and carrier fluid average temperatures, we clearly show that an increase of Pr slows down the heat transfer process. We explain our results by a simplified phenomenological model: we show that the time behavior of the drops average temperature is self similar, and a universal behavior can be found upon rescaling by t/Pr^2/3

Turbulent Flows With Drops and Bubbles: What Numerical Simulations Can Tell Us—Freeman Scholar Lecture

Turbulent flows laden withlarge, deformable drops or bubbles are ubiquitous in nature and a number of industrial processes. These flows are characterized by physics acting at many different scales: from the macroscopic length scale of the problem down to the microscopic molecular scale of the interface. Naturally, the numerical resolution of all the scales of the problem, which span about eight to nine orders of magnitude, is not possible, with the consequence that numerical simulations of turbulent multiphase flows impose challenges and require methods able to capture the multiscale nature of the flow. In this review, we start by describing the numerical methods commonly employed and by discussing their advantages and limitations, and then we focus on the issues arising from the limited range of scales that can be possibly solved. Ultimately, the droplet size distribution, a key result of interest for turbulent multiphase flows, is used as a benchmark to compare the capabilities of the different methods and to discuss the main insights that can be drawn from these simulations. Based on this, we define a series of guidelines and best practices that we believe to be important in the analysis of the simulations and the development of new numerical methods

Modelling the direct virus exposure risk associated with respiratory events

The outbreak of the COVID-19 pandemic highlighted the importance of accurately modelling the pathogen transmission via droplets and aerosols emitted while speaking, coughing and sneezing. In this work, we present an effective model for assessing the direct contagion risk associated with these pathogen-laden droplets. In particular, using the most recent studies on multi-phase flow physics, we develop an effective yet simple framework capable of predicting the infection risk associated with different respiratory activities in different ambient conditions. We start by describing the math- ematical framework and benchmarking the model predictions against well-assessed literature results. Then, we provide a systematic assessment of the effects of physical distancing and face coverings on the direct infection risk. The present results indicate that the risk of infection is vastly impacted by the ambient conditions and the type of respiratory activity, suggesting the non-existence of a universal safe distance. Meanwhile, wearing face masks provides excellent protection, effectively limiting the transmission of pathogens even at short physical distances, i.e. 1 m

Short-range exposure to airborne virus transmission and current guidelines

After the Spanish flu pandemic, it was apparent that airborne transmission was crucial to spreading virus contagion, and research responded by producing several fundamental works like the experiments of Duguid [J. P. Duguid, J. Hyg. 44, 6 (1946)] and the model of Wells [W. F. Wells, Am. J. Hyg. 20, 611–618 (1934)]. These seminal works have been pillars of past and current guidelines published by health organizations. However, in about one century, understanding of turbulent aerosol transport by jets and plumes has enormously progressed, and it is now time to use this body of developed knowledge. In this work, we use detailed experiments and accurate computationally intensive numerical simulations of droplet-laden turbulent puffs emitted during sneezes in a wide range of environmental conditions. We consider the same emission—number of drops, drop size distribution, and initial velocity—and we change environmental parameters such as temperature and humidity, and we observe strong variation in droplets’ evaporation or condensation in accordance with their local temperature and humidity microenvironment. We assume that 3% of the initial droplet volume is made of nonvolatile matter. Our systematic analysis confirms that droplets’ lifetime is always about one order of magnitude larger compared to previous predictions, in some cases up to 200 times. Finally, we have been able to produce original virus exposure maps, which can be a useful instrument for health scientists and practitioners to calibrate new guidelines to prevent short-range airborne disease transmission

Direct numerical simulation of turbulence-interface interactions

In this thesis, the interactions between a deformable interface and turbu- lence have been investigated using Direct Numerical Simulations (DNS). The interface and the surfactant concentration are tracked using a Phase Field Method (PFM). The turbulence-interface interactions have been anal- ysed in two different flow configurations, a dispersed and a stratified flow. First, a dispersed flow is considered, a swarm of large deformable drops is re- leased in a turbulent channel flow. The coalescence and breakup rates have been characterised for different values of the surface tension and viscosity ratios. Results show that the drop size, determined by the equilibrium be- tween coalescence and breakup, is influenced either by the surface tension, either by the internal viscosity. In particular, for small values of the surface tension values, the internal viscosity enhances the stability of the interface and prevent drop breakup. Second, a viscosity stratified configuration is considered. This setup mimics a core annular flow; a low viscosity fluid is interposed between the core and the walls to decrease the pressure drop. Results show that the interface is able to damp the near-wall turbulence, an increase of the core flow rate is observed. For the range of viscosity ratios analysed, the turbulence-interface interactions play a key role for obtaining Drag Reduction (DR). The DR performance is slighty affected by the viscosity ratio.In this thesis, the interactions between a deformable interface and turbu- lence have been investigated using Direct Numerical Simulations (DNS). The interface and the surfactant concentration are tracked using a Phase Field Method (PFM). The turbulence-interface interactions have been anal- ysed in two different flow configurations, a dispersed and a stratified flow. First, a dispersed flow is considered, a swarm of large deformable drops is re- leased in a turbulent channel flow. The coalescence and breakup rates have been characterised for different values of the surface tension and viscosity ratios. Results show that the drop size, determined by the equilibrium be- tween coalescence and breakup, is influenced either by the surface tension, either by the internal viscosity. In particular, for small values of the surface tension values, the internal viscosity enhances the stability of the interface and prevent drop breakup. Second, a viscosity stratified configuration is considered. This setup mimics a core annular flow; a low viscosity fluid is interposed between the core and the walls to decrease the pressure drop. Results show that the interface is able to damp the near-wall turbulence, an increase of the core flow rate is observed. For the range of viscosity ratios analysed, the turbulence-interface interactions play a key role for obtaining Drag Reduction (DR). The DR performance is slighty affected by the viscosity ratio

Deformation of clean and surfactant-laden droplets in shear flow

In this work we study the deformation of clean and surfactant-laden droplets in laminar shear-flow. The simulations are based on Direct Numerical Simulation of the Navier–Stokes equations coupled with a Phase Field Method to describe interface topology and surfactant concentration. Simulations are performed considering both 2D (circular droplet) and 3D (spherical droplet) domains. First, we focus on clean droplets and we characterize the droplet shape and deformation. This enables us to define the range of parameters in which theoretical models well predict the results obtained from 2D and 3D simulations. Then, surfactant-laden droplets are considered; the main factors leading to larger droplet deformation are carefully described and quantified. Results obtained indicate that the average surface tension reduction and the accumulation of surfactant at the tips of the deformed droplet have a dominant role, while tangential stresses at the interface (Marangoni stresses) have a limited effect on the overall droplet deformation. Finally, the distribution of surfactant over the droplet surface is examined in relation to surface deformation and shear stress distribution.FSE EUSAIR-EUSAL

Coalescence of surfactant-laden drops by Phase Field Method

In this work, we propose and test the validity of a modified Phase Field Method (PFM), which was specifically developed for large scale simulations of turbulent flows with large and deformable surfactant-laden droplets. The time evolution of the phase field, {\phi}, and of the surfactant concentration field, {\psi}, are obtained from two Cahn-Hilliard-like equations together with a two-order-parameter Time-Dependent Ginzburg-Landau (TDGL) free energy functional. The modifications introduced circumvent existing limitations of current approaches based on PFM and improve the well-posedness of the model. The effect of surfactant on surface tension is modeled via an Equation Of State (EOS), further improving the flexibility of the approach. This method can efficiently handle topological changes, i.e. breakup and coalescence, and describe adsorption/desorption of surfactant. The capabilities of the proposed approach are tested in this paper against previous experimental results on the effects of surfactant on the deformation of a single droplet and on the interactions between two droplets. Finally, to appreciate the performances of the model on a large scale complex simulation, a qualitative analysis of the behavior of surfactant-laden droplets in a turbulent channel flow is presented and discussed