Representation of cloud microphysics is a key aspect of simulating clouds. From the early days of cloud modeling, numerical models have relied on an Eulerian approach for all cloud and thermodynamic and microphysics variables. Over time the sophistication of microphysics schemes has steadily increased, from simple representations of bulk masses of cloud and rain in each grid cell, to including different ice particle types and bulk hydrometeor concentrations, to complex schemes referred to as bin or spectral schemes that explicitly evolve the hydrometeor size distributions within each model grid cell. As computational resources grow, there is a clear trend toward wider use of bin schemes, including their use as benchmarks to develop and test simplified bulk schemes. We argue that continuing on this path brings fundamental challenges difficult to overcome. The Lagrangian particle-based probabilistic approach is a practical alternative in which the myriad of cloud and precipitation particles present in a natural cloud is represented by a judiciously selected ensemble of point particles called superdroplets or superparticles. The advantages of the Lagrangian particle-based approach when compared to the Eulerian bin methodology are explained, and the prospects of applying the method to more comprehensive cloud simulations—for instance, targeting deep convection or frontal cloud systems—are discussed.

First-order virial expansion of short-time diffusion and sedimentation coefficients of permeable particles suspensions Phys. Fluids 23, 083303 (2011); 10.1063/1.3626196 Rotational and translational self-diffusion in concentrated suspensions of permeable particles We present a comprehensive computational study of the short-time transport properties of bidisperse hard-sphere colloidal suspensions and the corresponding porous media. Our study covers bidisperse particle size ratios up to 4 and total volume fractions up to and beyond the monodisperse hard-sphere close packing limit. The many-body hydrodynamic interactions are computed using conventional Stokesian Dynamics (SD) via a Monte-Carlo approach. We address suspension properties including the short-time translational and rotational self-diffusivities, the instantaneous sedimentation velocity, the wavenumber-dependent partial hydrodynamic functions, and the high-frequency shear and bulk viscosities and porous media properties including the permeability and the translational and rotational hindered diffusivities. We carefully compare the SD computations with existing theoretical and numerical results. For suspensions, we also explore the range of validity of various approximation schemes, notably the pairwise additive approximations with the Percus-Yevick structural input. We critically assess the strengths and weaknesses of the SD algorithm for various transport properties. For very dense systems, we discuss in detail the interplay between the hydrodynamic interactions and the structures due to the presence of a second species of a different size. C 2015 AIP Publishing LLC. [http://dx.

This paper investigates spectral broadening of droplet size distributions through a mechanism referred to as the eddy hopping. The key idea, suggested a quarter century ago, is that droplets arriving at a given location within a turbulent cloud follow different trajectories and thus experience different growth histories and that this leads to a significant spectral broadening. In this study, the adiabatic parcel model with superdroplets is used to contrast droplet growth with and without turbulence. Turbulence inside the parcel is described by two parameters: (i) the dissipation rate of the turbulent kinetic energy ε and (ii) the linear extent of the parcel L. As expected, an adiabatic parcel without turbulence produces extremely narrow droplet spectra. In the turbulent parcel, a stochastic scheme is used to account for vertical velocity fluctuations that lead to local supersaturation fluctuations for each superdroplet. These fluctuations mimic the impact of droplets hopping turbulent eddies in a natural cloud. For L smaller than a few meters, noticeable spectral broadening is possible only for strong turbulence—say, ε > 100 cm2 s−3. For L typical for grid lengths of large-eddy simulation (LES) models (say, L between 10 and 100 m), the impact is significant even with relatively modest turbulence intensities. The impact increases with both L and ε. The representation of eddy hopping developed in this paper can be included in a straightforward way in the subgrid-scale scheme of a Lagrangian LES cloud model and may lead to a significant acceleration of simulated rain development through collision–coalescence.

This paper discusses the effects of cloud turbulence, turbulent entrainment, and entrained cloud condensation nuclei (CCN) activation on the evolution of the cloud droplet size spectrum. We simulate an ensemble of idealized turbulent cloud parcels that are subject to entrainment events modeled as a random process. Entrainment events, subsequent turbulent mixing inside the parcel, supersaturation fluctuations, and the resulting stochastic droplet activation and growth by condensation are simulated using a Monte Carlo scheme. Quantities characterizing the turbulence intensity, entrainment rate, CCN concentration, and the mean fraction of environmental air entrained in an event are all specified as independent external parameters. Cloud microphysics is described by applying Lagrangian particles, the so-called superdroplets. These are either unactivated CCN or cloud droplets that grow from activated CCN. The model accounts for the addition of environmental CCN into the cloud by entraining eddies at the cloud edge. Turbulent mixing of the entrained dry air with cloudy air is described using the classical linear relaxation to the mean model. We show that turbulence plays an important role in aiding entrained CCN to activate, and thus broadening the droplet size distribution. These findings are consistent with previous large-eddy simulations (LESs) that consider the impact of variable droplet growth histories on the droplet size spectra in small cumuli. The scheme developed in this work is ready to be used as a stochastic subgrid-scale scheme in LESs of natural clouds.

Short-time dynamic properties of concentrated suspensions of colloidal core-shell particles are studied using a precise force multipole method which accounts for many-particle hydrodynamic interactions. A core-shell particle is composed of a rigid, spherical dry core of radius a surrounded by a uniformly permeable shell of outer radius b and hydrodynamic penetration depth κ(-1). The solvent flow inside the permeable shell is described by the Brinkman-Debye-Bueche equation, and outside the particles by the Stokes equation. The particles are assumed to interact non-hydrodynamically by a hard-sphere no-overlap potential of radius b. Numerical results are presented for the high-frequency shear viscosity, η(∞), sedimentation coefficient, K, and the short-time translational and rotational self-diffusion coefficients, D(t) and D(r). The simulation results cover the full three-parametric fluid-phase space of the composite particle model, with the volume fraction extending up to 0.45, and the whole range of values for κb, and a/b. Many-particle hydrodynamic interaction effects on the transport properties are explored, and the hydrodynamic influence of the core in concentrated systems is discussed. Our simulation results show that for thin or hardly permeable shells, the core-shell systems can be approximated neither by no-shell nor by no-core models. However, one of our findings is that for κ(b - a) ≳ 5, the core is practically not sensed any more by the weakly penetrating fluid. This result is explained using an asymptotic analysis of the scattering coefficients entering into the multipole method of solving the Stokes equations. We show that in most cases, the influence of the core grows only weakly with increasing concentration.

We determine the high-frequency limiting shear viscosity, η ∞ , in colloidal suspensions of rigid, uniformly porous spheres of radius a as a function of volume fraction φ and (inverse) porosity parameter x. Our study covers the complete fluid-state regime. The flow inside the spheres is modeled by the Debye-Bueche-Brinkman equation using the boundary condition that fluid velocity and stress change continuously across the sphere surfaces. The many-sphere hydrodynamic interactions in concentrated systems are fully accounted for by a precise hydrodynamic multipole method encoded in our hydromultipole program extended to porous particles. A truncated virial expansion is used to derive an accurate and easy-to-use generalized Saitô formula for η ∞ .The simulation data are used to test the performance of two simplifying effective particle models.The first model describes the effective particle as a non-porous sphere characterized by a single effective radius a eff (x) < a. In the more refined second model, the porous spheres are modeled as spherical annulus particles with an inner hydrodynamic radius a eff (x) defining the non-porous dry core and characterizing hydrodynamic interactions, and an outer excluded volume radius a characterizing the unchanged direct interactions. Only the second model is in a satisfactory agreement with the simulation data.

We calculate short-time diffusion properties of suspensions of porous colloidal particles as a function of their permeability, for the full fluid-phase concentration range. The particles are modeled as spheres of uniform permeability with excluded volume interactions. Using a precise multipole method encoded in the HYDROMULTIPOLE program, results are presented for the hydrodynamic function, H(q), sedimentation coefficient, and self-diffusion coefficient with a full account of manybody hydrodynamic interactions. While self-diffusion and sedimentation are strongly permeability dependent, the wavenumber dependence of the hydrodynamic function can be reduced, by appropriate shifting and scaling, to a single master curve, independent of permeability. Generic features of the permeable sphere model are discussed.Suspensions of solvent-permeable colloidal particles can be found in a great variety of synthesized materials. Examples are fuzzy-sphere systems consisting of highly porous, cross-linked microgel spheres exhibiting large volume changes as a function of temperature [1,2]. Another experimentally well-studied class of permeable colloids are core-shell-like particles consisting of an impermeable rigid core and a permeable stabilizing layer of some soft material [3,4], such as grafted polymers [5,6]. Despite the importance of permeable particles both from a fundamental viewpoint and in terms of applications, little is known theoretically about transport properties in non-dilute systems, such as self-and collective diffusion coefficients. The calculation of transport properties is a challenging problem since one has to cope with manybody hydrodynamic interactions (HIs) by accounting for the fluid flow inside the porous particles relative to their skeletons. A better control on diffusion and viscoelastic properties for industrial processing of concentrated colloids requires a deeper understanding of the influence of the HIs.Theoretical and simulation work on diffusion and sedimentation of porous particles was primarily concerned so far with dilute systems. Chen and Cai [7] calculated the sedimentation velocity in a suspension of uniformly porous spheres to first order in the volume fraction φ, demonstrating that sedimentation is quite sensitive to direct interactions and permeability. Mo and Sangani [8] used a multipole expansion method for hydrodynamically interacting porous spheres to obtain numerical results for the average drag force per particle in random and in bcc fixed-bed arrays.Clearly, there is a strong demand on exploring generic HIs effects in concentrated porous particle systems where pairwise additivity approximations are bound to fail. In this letter, we describe a comprehensive simulation study of short-time diffusion properties for systems of permeable non-overlapping spheres. Our study covers the whole fluid-phase regime including concentrated systems with strong many-body HIs. The considered permeability range from fully impermeable to strongly permeable particles. Numerical results are presented f...

We study the dynamics of a probe particle driven by a constant force through a colloidal glass of hard spheres. This nonequilibrium and anisotropic problem is investigated using a new implementation of the mode-coupling approximation with multiple relaxation channels and Langevin dynamics simulations. A force threshold is found, below which the probe remains localized, while above it the probe acquires a finite velocity. We focus on the localized regime, comparing theory and simulations concerning the dynamics in the length scale of the cage and the properties of the transition to the delocalized regime, such as the critical power-law decay of the probe correlation function. Probe van Hove functions predicted by the theory show exponential tails reminiscent of an intermittent dynamics of the probe. This scenario is microscopically supported by simulations.