Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the non-equilibrium properties of the system. We derive a general dynamical density functional theory (DDFT) which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing DDFTs and a Navier-Stokes-like equation with additional non-local terms.Comment: 5 pages, 4 figures, 4 supplementary movie files, I supplementary pd

Unification of dynamic density functional theory for colloidal fluids to include inertia and hydrodynamic interactions: derivation and numerical experiments.

Starting from the Kramers equation for the phase-space dynamics of the N-body probability distribution, we derive a dynamical density functional theory (DDFT) for colloidal fluids including the effects of inertia and hydrodynamic interactions (HI). We compare the resulting theory to extensive Langevin dynamics simulations for both hard rod systems and three-dimensional hard sphere systems with radially symmetric external potentials. As well as demonstrating the accuracy of the new DDFT, by comparing with previous DDFTs which neglect inertia, HI, or both, we also scrutinize the significance of including these effects. Close to local equilibrium we derive a continuum equation from the microscopic dynamics which is a generalized Navier–Stokes-like equation with additional non-local terms governing the effects of HI. For the overdamped limit we recover analogues of existing configuration-space DDFTs but with a novel diffusion tensor

Coagulation and fragmentation dynamics of inertial particles

Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process in time-periodic incompressible flows. We find that this process approaches an asymptotic, dynamical steady state where the average number of particles of each size is roughly constant. We compare the steady-state size distributions corresponding to two fragmentation mechanisms and for different flows and find that the steady state is mostly independent of the coagulation process. While collision rates determine the transient behavior, fragmentation determines the steady state. For example, for fragmentation due to shear, flows that have very different local particle concentrations can result in similar particle size distributions if the temporal or spatial variation of shear forces is similar.Comment: 8 pages, 7 figure

A Thermal Analysis of a Hot-Wire Probe for Icing Applications

This paper presents a steady-state thermal model of a hot-wire instrument applicable to atmospheric measurement of water content in clouds. In this application, the power required to maintain the wire at a given temperature is used to deduce the water content of the cloud. The model considers electrical resistive heating, axial conduction, convection to the flow, radiation to the surroundings, as well as energy loss due to the heating, melting, and evaporation of impinging liquid and or ice. All of these parameters can be varied axially along the wire. The model further introduces a parameter called the evaporation potential which locally gauges the maximum fraction of incoming water that evaporates. The primary outputs of the model are the steady-state power required to maintain a spatially-average constant temperature as well as the variation of that temperature and other parameters along the wire. The model is used to understand the sensitivity of the hot-wire performance to various flow and boundary conditions including a detailed comparison of dry air and wet (i.e. cloud-on) conditions. The steady-state power values are compared to experimental results from a Science Engineering Associates (SEA) Multi-Element probe, a commonly used water-content measurement instrument. The model results show good agreement with experiment for both dry and cloud-on conditions with liquid water content. For ice, the experimental measurements under read the actual water content due to incomplete evaporation and splashing. Model results, which account for incomplete evaporation, are still higher than experimental results where the discrepancy is attributed to splashing mass-loss which is not accounted in the model

Particle tracking for polydisperse sedimenting droplets in phase separation

When a binary fluid demixes under a slow temperature ramp, nucleation, coarsening and sedimentation of droplets lead to an oscillatory evolution of the phase separating system. The advection of the sedimenting droplets is found to be chaotic. The flow is driven by density differences between the two phases. Here, we show how image processing can be combined with particle tracking to resolve droplet size and velocity simultaneously. Droplets are used as tracer particles, and the sedimentation velocity is determined. Taking these effects into account, droplets with radii in the range of 4 -- 40 micrometers are detected and tracked. Based on this data we resolve the oscillations in the droplet size distribution which are coupled to the convective flow.Comment: 13 pages; 16 figures including 3 photographs and 3 false-color plot

Ice structures, patterns, and processes: A view across the ice-fields

We look ahead from the frontiers of research on ice dynamics in its broadest sense; on the structures of ice, the patterns or morphologies it may assume, and the physical and chemical processes in which it is involved. We highlight open questions in the various fields of ice research in nature; ranging from terrestrial and oceanic ice on Earth, to ice in the atmosphere, to ice on other solar system bodies and in interstellar space

The study of atmospheric ice-nucleating particles via microfluidically generated droplets

Ice-nucleating particles (INPs) play a significant role in the climate and hydrological cycle by triggering ice formation in supercooled clouds, thereby causing precipitation and affecting cloud lifetimes and their radiative properties. However, despite their importance, INP often comprise only 1 in 10³–10⁶ ambient particles, making it difficult to ascertain and predict their type, source, and concentration. The typical techniques for quantifying INP concentrations tend to be highly labour-intensive, suffer from poor time resolution, or are limited in sensitivity to low concentrations. Here, we present the application of microfluidic devices to the study of atmospheric INPs via the simple and rapid production of monodisperse droplets and their subsequent freezing on a cold stage. This device offers the potential for the testing of INP concentrations in aqueous samples with high sensitivity and high counting statistics. Various INPs were tested for validation of the platform, including mineral dust and biological species, with results compared to literature values. We also describe a methodology for sampling atmospheric aerosol in a manner that minimises sampling biases and which is compatible with the microfluidic device. We present results for INP concentrations in air sampled during two field campaigns: (1) from a rural location in the UK and (2) during the UK’s annual Bonfire Night festival. These initial results will provide a route for deployment of the microfluidic platform for the study and quantification of INPs in upcoming field campaigns around the globe, while providing a benchmark for future lab-on-a-chip-based INP studies