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Rotational effects are commonly neglected when considering the dynamics of freely rising or settling isotropic particles. Here, we demonstrate that particle rotations play an important role for rising as well as for settling cylinders in situations when mass eccentricity, and thereby a new pendulum timescale, is introduced to the system. We employ two-dimensional simulations to study the motion of a single cylinder in a quiescent unbounded incompressible Newtonian fluid. This allows us to vary the Galileo number, density ratio, relative moment of inertia, and Centre-Of-Mass offset (COM) systematically and beyond what is feasible experimentally. For certain buoyant density ratios, the particle dynamics exhibit a resonance mode, during which the coupling via the Magnus lift force causes a positive feedback between translational and rotational motions. This mode results in vastly different trajectories with significantly larger rotational and translational amplitudes and an increase of the drag coefficient easily exceeding a factor two. We propose a simple model that captures how the occurrence of the COM offset induced resonance regime varies, depending on the other input parameters, specifically the density ratio, the Galileo number, and the relative moment of inertia. Remarkably, depending on the input parameters, resonance can be observed for centre-of-mass offsets as small as a few percent of the particle diameter, showing that the particle dynamics can be highly sensitive to this parameter., Comment: 37 pages, 17 figures

Human respiratory events, such as coughing and sneezing, play an important role in the host-to-host airborne transmission of diseases. Thus, there has been a substantial effort in understanding these processes: various analytical or numerical models have been developed to describe them, but their validity has not been fully assessed due to the difficulty of a direct comparison with real human exhalations. In this study, we report a unique comparison between datasets that have both detailed measurements of a real human cough using spirometer and particle tracking velocimetry, and direct numerical simulation at similar conditions. By examining the experimental data, we find that the injection velocity at the mouth is not uni-directional. Instead, the droplets are injected into various directions, with their trajectories forming a cone shape in space. Furthermore, we find that the period of droplet emissions is much shorter than that of the cough: experimental results indicate that the droplets with an initial diameter $\gtrsim 10\mu$m are emitted within the first 0.05 s, whereas the cough duration is closer to 1 s. These two features (the spread in the direction of injection velocity and the short duration of droplet emission) are incorporated into our direct numerical simulation, leading to an improved agreement with the experimental measurements. Thus, to have accurate representations of human expulsions in respiratory models, it is imperative to include parametrisation of these two features.

Bubble-particle collisions in turbulence are central to a variety of processes such as froth flotation. Despite their importance, details of the collision process have not received much attention yet. This is compounded by the sometimes counter-intuitive behaviour of bubbles and particles in turbulence, as exemplified by the fact that they segregate in space. Although bubble-particle relative behaviour is fundamentally different from that of identical particles, the existing theoretical models are nearly all extensions of theories for particle-particle collisions in turbulence. The adequacy of these theories has yet to be assessed as appropriate data remain scarce to date. In this investigation, we study the geometric collision rate by means of direct numerical simulations of bubble-particle collisions in homogeneous isotropic turbulence using the point-particle approach over a range of the relevant parameters, including the Stokes and Reynolds numbers. We analyse the spatial distribution of bubble and particles, and quantify to what extent their segregation reduces the collision rate. This effect is countered by increased approach velocities for bubble-particle compared to monodisperse pairs, which we relate to the difference in how bubbles and particles respond to fluid accelerations. We found that in the investigated parameter range, these collision statistics are not altered significantly by the inclusion of a lift force or different drag parametrisations, or when assuming infinite particle density. Furthermore, we critically examine existing models and discuss inconsistencies therein that contribute to the discrepancy., Comment: 29 pages, 18 figures to be published in Journal of Fluid Mechanics

We report on the mobility and orientation of finite-size, neutrally buoyant prolate ellipsoids (of aspect ratio $\Lambda=4$) in Taylor-Couette flow, using interface resolved numerical simulations. The setup consists of a particle-laden flow in between a rotating inner and a stationary outer cylinder. We simulate two particle sizes $\ell/d=0.1$ and $\ell/d=0.2$, $\ell$ denoting the particle major axis and $d$ the gap-width between the cylinders. The volume fractions are $0.01\%$ and $0.07\%$, respectively. The particles, which are initially randomly positioned, ultimately display characteristic spatial distributions which can be categorised into four modes. Modes $(i)$ to $(iii)$ are observed in the Taylor vortex flow regime, while mode ($iv$) encompasses both the wavy vortex, and turbulent Taylor vortex flow regimes. Mode $(i)$ corresponds to stable orbits away from the vortex cores. Remarkably, in a narrow $\textit{Ta}$ range, particles get trapped in the Taylor vortex cores (mode ($ii$)). Mode $(iii)$ is the transition when both modes $(i)$ and $(ii)$ are observed. For mode $(iv)$, particles distribute throughout the domain due to flow instabilities. All four modes show characteristic orientational statistics. We find the particle clustering for mode ($ii$) to be size-dependent, with two main observations. Firstly, particle agglomeration at the core is much higher for $\ell/d=0.2$ compared to $\ell/d=0.1$. Secondly, the $\textit{Ta}$ range for which clustering is observed depends on the particle size. For this mode $(ii)$ we observe particles to align strongly with the local cylinder tangent. The most pronounced particle alignment is observed for $\ell/d=0.2$ around $\textit{Ta}=4.2\times10^5$. This observation is found to closely correspond to a minimum of axial vorticity at the Taylor vortex core ($\textit{Ta}=6\times10^5$) and we explain why., Comment: 22 pages, 12 figures

This numerical study presents a simple but extremely effective way to considerably enhance heat transport in turbulent multiphase flows, namely by using oleophilic walls. As a model system, we pick the Rayleigh-B\'enard setup, filled with an oil-water mixture. For oleophilic walls, e.g. using only $10\%$ volume fraction of oil in water, we observe a remarkable heat transport enhancement of more than $100\%$ as compared to the pure water case. In contrast, for oleophobic walls, the enhancement is then only about $20\%$ as compared to pure water. The physical explanation of the highly-efficient heat transport for oleophilic walls is that thermal plumes detach from the oil-rich boundary layer and are transported together with the oil phase. In the bulk, the oil-water interface prevents the plumes to mix with the turbulent water bulk. To confirm this physical picture, we show that the minimum amount of oil to achieve the maximum heat transport is set by the volume fraction of the thermal plumes. Our findings provide guidelines of how to optimize heat transport in thermal turbulence. Moreover, the physical insight of how coherent structures are coupled with one phase of a two-phase system has very general applicability for controlling transport properties in other turbulent multiphase flows., Comment: 11 pages, 4 figues

Many environmental flows arise due to natural convection at a vertical surface, from flows in buildings to dissolving ice faces at marine-terminating glaciers. We use three-dimensional direct numerical simulations of a vertical channel with differentially heated walls to investigate such convective, turbulent boundary layers. Through the implementation of a multiple-resolution technique, we are able to perform simulations at a wide range of Prandtl numbers $Pr$. This allows us to distinguish the parameter dependences of the horizontal heat flux and the boundary layer widths in terms of the Rayleigh number $Ra$ and Prandtl number $Pr$. For the considered parameter range $1\leq Pr \leq 100$, $10^6 \leq Ra \leq 10^9$, we find the flow to be consistent with a 'buoyancy-controlled' regime where the heat flux is independent of the wall separation. For given $Pr$, the heat flux is found to scale linearly with the friction velocity $V_\ast$. Finally, we discuss the implications of our results for the parameterisation of heat and salt fluxes at vertical ice-ocean interfaces., Comment: 18 pages, 7 figures, submitted to J. Fluid Mech

With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation. This novel scheme can significantly reduce the computational cost while retaining the same accuracy as the original procedure. Our phase-field method is built on top of a direct numerical simulation solver, named AFiD (www.afid.eu) and open-sourced by our research group. It relies on a pencil distributed parallel strategy and a FFT-based Poisson solver. To deal with large density ratios between the two phases, a pressure split method [1] has been applied to the Poisson solver. To further reduce computational costs, we implement a multiple-resolution algorithm which decouples the discretizations for the Navier-Stokes equations and the scalar equation: while a stretched wall-resolving grid is used for the Navier-Stokes equations, for the Cahn-Hilliard equation we use a fine uniform mesh. The present method shows excellent computational performance for large-scale computation: on meshes up to 8 billion nodes and 3072 CPU cores, a multiphase flow needs only slightly less than 1.5 times the CPU time of the single-phase flow solver on the same grid. The present method is validated by comparing the results to previous studies for the cases of drop deformation in shear flow, including the convergence test with mesh refinement, and breakup of a rising buoyant bubble with density ratio up to 1000. Finally, we simulate the breakup of a big drop and the coalescence of O(10^3) drops in turbulent Rayleigh-B\'enard convection at a Rayleigh number of $10^8$, observing good agreement with theoretical results., Comment: 32 pages, 14 figures

Indoor ventilation is essential for a healthy and comfortable living environment. A key issue is to discharge anthropogenic air contamination such as CO2 gas or, more seriously, airborne respiratory droplets. Here, by employing direct numerical simulations, we study the mechanical displacement ventilation with the realistic range of air changes per hour (ACH) from 1 to 10. For this ventilation scheme, a cool lower zone is established beneath the warm upper zone with the interface height h depending on ACH. For weak ventilation, we find the scalings relation of the interface height h ~ ACH^{3/5}, as suggested by Hunt & Linden (Build. Environ., vol. 34, 1999, pp. 707-720). Also, the CO2 concentration decreases with ACH within this regime. However, for too strong ventilation, the interface height h becomes insensitive to ACH, and the CO2 concentration remains unchanged. Our results are in contrast to the general belief that stronger flow is more helpful to remove contaminants. We work out the physical mechanism governing the transition between the low ACH and the high ACH regimes. It is determined by the relative strength of the kinetic energy from the inflow, potential energy from the stably-stratified layers, and energy loss due to drag. Our findings provide a physics-based guideline to optimize displacement ventilation., Comment: 10 pages, 5 figures

The ambient conditions surrounding liquid droplets determine their growth or shrinkage. However, the precise fate of a liquid droplet expelled from a respiratory puff as dictated by its surroundings and the puff itself has not yet been fully quantified. From the view of airborne disease transmission, such as SARS-CoV-2, knowledge of such dependencies are critical. Here we employ direct numerical simulations (DNS) of a turbulent respiratory vapour puff and account for the mass and temperature exchange with respiratory droplets and aerosols. In particular, we investigate how droplets respond to different ambient temperatures and relative humidity (RH) by tracking their Lagrangian statistics. We reveal and quantify that in cold and humid environments, as there the respiratory puff is supersaturated, expelled droplets can first experience significant growth, and only later followed by shrinkage, in contrast to the monotonic shrinkage of droplets as expected from the classical view by William F. Wells (1934). Indeed, cold and humid environments diminish the ability of air to hold water vapour, thus causing the respiratory vapour puff to super-saturate. Consequently, the super-saturated vapour field drives the growth of droplets that are caught and transported within the humid puff. To analytically predict the likelihood for droplet growth, we propose a model for the axial RH based on the assumption of a quasi-stationary jet. Our model correctly predicts super-saturated RH conditions and is in good quantitative agreement with our DNS. Our results culminate in a temperature-RH map that can be employed as an indicator for droplet growth or shrinkage., Comment: 7 pages, 6 figures

To quantify the fate of respiratory droplets under different ambient relative humidities, direct numerical simulations of a typical respiratory event are performed. We found that, because small droplets (with initial diameter of 10um) are swept by turbulent eddies in the expelled humid puff, their lifetime gets extended by a factor of more than 30 times as compared to what is suggested by the classical picture by William F. Wells, for 50% relative humidity. With increasing ambient relative humidity the extension of the lifetimes of the small droplets further increases and goes up to around 150 times for 90% relative humidity, implying more than two meters advection range of the respiratory droplets within one second. Employing Lagrangian statistics, we demonstrate that the turbulent humid respiratory puff engulfs the small droplets, leading to many orders of magnitude increase in their lifetimes, implying that they can be transported much further during the respiratory events than the large ones. Our findings provide the starting points for larger parameter studies and may be instructive for developing strategies on optimizing ventilation and indoor humidity control. Such strategies are key in mitigating the COVID-19 pandemic in the present autumn and upcoming winter., Comment: 7 pages, 4 figures, published in Phys. Rev. Lett

It is commonly accepted that the breakup criteria of drops or bubbles in turbulence is governed by surface tension and inertia. However, also {\it{buoyancy}} can play an important role at breakup. In order to better understand this role, here we numerically study Rayleigh-B\'enard convection for two immiscible fluid layers, in order to identify the effects of buoyancy on interface breakup. We explore the parameter space spanned by the Weber number $5\leq We \leq 5000$ (the ratio of inertia to surface tension) and the density ratio between the two fluids $0.001 \leq \Lambda \leq 1$, at fixed Rayleigh number $Ra=10^8$ and Prandtl number $Pr=1$. At low $We$, the interface undulates due to plumes. When $We$ is larger than a critical value, the interface eventually breaks up. Depending on $\Lambda$, two breakup types are observed: The first type occurs at small $\Lambda \ll 1$ (e.g. air-water systems) when local filament thicknesses exceed the Hinze length scale. The second, strikingly different, type occurs at large $\Lambda$ with roughly $0.5 < \Lambda \le 1$ (e.g. oil-water systems): The layers undergo a periodic overturning caused by buoyancy overwhelming surface tension. For both types the breakup criteria can be derived from force balance arguments and show good agreement with the numerical results., Comment: 13 pages, 7 figures

We numerically investigate both single and multiple droplet dissolution with droplets consisting of lighter liquid dissolving in a denser host liquid. The significance of buoyancy is quantified by the Rayleigh number Ra which is the buoyancy force over the viscous damping force. In this study, Ra spans almost four decades from 0.1 to 400. We focus on how the mass flux, characterized by the Sherwood number Sh, and the flow morphologies depend on Ra. For single droplet dissolution, we first show the transition of the Sh(Ra) scaling from a constant value to $Sh\sim Ra^{1/4}$, which confirms the experimental results by Dietrich et al. (J. Fluid Mech., vol. 794, 2016, pp. 45--67). The two distinct regimes, namely the diffusively- and the convectively-dominated regime, exhibit different flow morphologies: when Ra>=10, a buoyant plume is clearly visible which contrasts sharply to the pure diffusion case at low Ra. For multiple droplet dissolution, the well-known shielding effect comes into play at low Ra so that the dissolution rate is slower as compared to the single droplet case. However, at high Ra, convection becomes more and more dominant so that a collective plume enhances the mass flux, and remarkably the multiple droplets dissolve faster than a single droplet. This has also been found in the experiments by Laghezza et al. (Soft Matter, vol. 12, 2016, pp. 5787--5796). We explain this enhancement by the formation of a single, larger plume rather than several individual plumes. Moreover, there is an optimal Ra at which the enhancement is maximized, because the single plume is narrower at larger Ra, which thus hinders the enhancement. Our findings demonstrate a new mechanism in collective droplet dissolution, which is the merging of the plumes, that leads to non-trivial phenomena, contrasting the shielding effect., Comment: 18 pages, 11 figures, submitted to JFM

We present results on the effect of dispersed droplets in vertical natural convection (VC) using direct numerical simulations based on a two-way fully coupled Euler-Lagrange approach with a liquid phase and a dispersed droplets phase. For increasing thermal driving, characterised by the Rayleigh number, $Ra$, of the two analysed droplet volume fractions, $\alpha = 5\times10^{-3}$ and $\alpha = 2\times 10^{-2}$, we find non-monotonic responses to the overall heat fluxes, characterised by the Nusselt number, $Nu$. The $Nu$ number is larger when the droplets are thermally coupled to the liquid. However, $Nu$ retains the effective scaling exponents that are close to the ${1/4}$-laminar VC scaling, suggesting that the heat transport is still modulated by thermal boundary layers. Local analyses reveal the non-monotonic trends of local heat fluxes and wall-shear stresses: Whilst regions of high heat fluxes are correlated to increased wall-shear stresses, the spatio-temporal distribution and magnitude of the increase is non-universal, implying that the overall heat transport is obscured by competing mechanisms. Most crucially, we find that the transport mechanisms inherently depend on the dominance of droplet driving to thermal driving that can quantified by (i) the bubblance parameter $b$, which measures the ratio of energy produced by the dispersed phase and the energy of the background turbulence, and (ii) $Ra_d/Ra$, where $Ra_d$ is the droplet Rayleigh number, which we introduce in this paper. When $b \lesssim O(10^{-1})$ and $Ra_d/Ra \lesssim O(100)$, the $Nu$ scaling is expected to recover to the VC scaling without droplets, and comparison with $b$ and $Ra_d/Ra$ from our data supports this notion., Comment: 23 pages, 11 figures

Previous numerical studies on homogeneous Rayleigh-B\'enard convection, which is Rayleigh-B\'enard convection (RBC) without walls, and therefore without boundary layers, have revealed a scaling regime that is consistent with theoretical predictions of bulk-dominated thermal convection. In this so-called asymptotic regime, previous studies have predicted that the Nusselt number ($Nu$) and the Reynolds number ($Re$) vary with the Rayleigh number ($Ra$) according to $Nu\sim Ra^{1/2}$ and $Re\sim Ra^{1/2}$ at small Prandtl number ($Pr$). In this study, we consider a flow that is similar to RBC but with the direction of temperature gradient perpendicular to gravity instead of parallel; we refer to this configuration as vertical natural convection (VC). Since the direction of the temperature gradient is different in VC, there is no exact relation for the average kinetic dissipation rate, which makes it necessary to explore alternative definitions for $Nu$, $Re$ and $Ra$ and to find physical arguments for closure, rather than making use of the exact relation between $Nu$ and the dissipation rates as in RBC. Once we remove the walls from VC to obtain the homogeneous setup, we find that the aforementioned $1/2$-power-law scaling is present, similar to the case of homogeneous RBC. When focussing on the bulk, we find that the Nusselt and Reynolds numbers in the bulk of VC too exhibit the $1/2$-power-law scaling. These results suggest that the $1/2$-power-law scaling may even be found at lower Rayleigh numbers if the appropriate quantities in the turbulent bulk flow are employed for the definitions of $Ra$, $Re$ and $Nu$. From a stability perspective, at low- to moderate-$Ra$, we find that the time-evolution of the Nusselt number for homogenous vertical natural convection is unsteady, which is consistent with the nature of the elevator modes reported in previous studies on homogeneous RBC.

In thermal convection for very large Rayleigh numbers ($Ra$), the thermal and viscous boundary layers (BL) undergo a transition from a classical state to an ultimate state. In the former state, the BL thicknesses follow a laminar-like Prandtl-Blasius-Polhausen scaling, whereas in the latter, the BLs are turbulent with log-corrections in the sense of Prandtl and von K\'arm\'an. Here, we report evidence of this transition via changes in the BL structure of vertical natural convection (VC), which is a buoyancy driven flow between differentially heated vertical walls. The dataset spans $Ra$-values from $10^5$ to $10^9$ and Prandtl number value of 0.709. For this $Ra$ range, the VC flow exhibits classical state behaviour in a global sense. Yet, with increasing $Ra$, we observe that near-wall higher-shear patches occupy increasingly larger fractions of the wall-areas, which suggest that the BLs are undergoing a transition from the classical state to the ultimate shear-dominated state. The presence of streaky structures-reminiscent of the near-wall streaks in canonical wall-bounded turbulence-further supports the notion of this transition. Within the higher-shear patches, conditionally averaged statistics yield a log-variation in the local mean temperature profiles, in agreement with the log-law of the wall for mean temperature, and a $Ra^{0.37}$ effective power-law scaling of the local Nusselt number, consistent with the logarithmically corrected 1/2-power law scaling predicted for ultimate thermal convection for very large $Ra$. Collectively, the results from this study indicate that turbulent and laminar-like BL coexist in VC at moderate to high $Ra$ and this transition from the classical state to the ultimate state manifests as increasingly larger shear-dominated patches, consistent with the findings reported for Rayleigh-B\'enard convection and Taylor-Couette flows.

Results from direct numerical simulations of vertical natural convection at Rayleigh numbers $1.0\times 10^5$-$1.0\times 10^9$ and Prandtl number $0.709$ support a generalised applicability of the Grossmann-Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh-B{\'e}nard) convection. In accordance with the GL theory, it is shown that the boundary-layer thicknesses of the velocity and temperature fields in vertical natural convection obey laminar-like Prandtl-Blasius-Pohlhausen scaling. Specifically, the normalised mean boundary-layer thicknesses scale with the $-1/2$-power of a wind-based Reynolds number, where the "wind" of the GL theory is interpreted as the maximum mean velocity. Away from the walls, the dissipation of the turbulent fluctuations, which can be interpreted as the "bulk" or "background" dissipation of the GL theory, is found to obey the Kolmogorov-Obukhov-Corrsin scaling for fully developed turbulence. In contrast to Rayleigh-B{\'e}nard convection, the direction of gravity in vertical natural convection is parallel to the mean flow. The orientation of this flow presents an added challenge because there no longer exists an exact relation that links the normalised global dissipations to the Nusselt, Rayleigh and Prandtl numbers. Nevertheless, we show that the unclosed term, namely the global-averaged buoyancy flux that produces the kinetic energy, also exhibits both laminar and turbulent scaling behaviours, consistent with the GL theory. The present results suggest that, similar to Rayleigh-B{\'e}nard convection, a pure power-law relationship between the Nusselt, Rayleigh and Prandtl numbers is not the best description for vertical natural convection and existing empirical relationships should be recalibrated to better reflect the underlying physics.