Literature reviews

1.3.1 Droplet growth

Hu, et al. [1998], propose the stochastic growth of cloud droplet distributions due to collection processes is studied using a detailed microphysical parcel model. The evolution of rainwater content (L-R) and the radar reflectivity factor (Z) are plotted in order to trace the progress of transfer of cloud water into rainwater and determine the importance of droplet collection in different size ranges. The results indicate that the van der Waals forces are effective in enhancing droplet collision when the droplets are small and the distributions are narrow.

1.3.2 Droplet-droplet collision

Ashgriz and Poo [1990] carried out collision experiments with water drops in the micrometer to millimeter size range. Two drop streams collided with relative velocities of 1–20 m/s, and single collisions were followed with high-speed video recording. Two different types of separating collisions were identified, reflexive and stretching separating, and they determined the boundaries between these processes

and coalescence. Reflexive separation was found for near head-on collisions with high velocity while stretching separation occurred for large impact parameter.

Panand Law [2004], presented a dynamics of head-on collision between two identical droplets was experimentally and computationally investigated, with particular emphasis on the transitions from merging to bouncing to merging again as the collision Weber number increased.

Later, Pan and Law [2005] extend the research to a head-on collision of a droplet onto a liquid layer of the same material, sitting on a solid surface. Both experimental and computational methods were applied to illuminate the transition from bouncing of the droplet to its absorption by the film for given droplet Weber number, We, and the film thickness scaled by the droplet radius, Hf.

1.3.3 Simulation methods for droplet collision dynamics

The simulation methods for droplet collision dynamic can be classified into two major groups, depending on the size scale of simulation system. as the

continuum-scale and atomic-scale methods.

1.3.3.1 Continuum-scale simulation methods 1.3.3.1.1 Navier-Stokes equation method

Harlow and Shannon [1967] were the first to simulate droplet impact on the solid surface. They used a “marker-and-cell” (MAC) finite-difference method to solve the fluid mass and momentum conservation equations. Tsurutani et al. [1990] enhanced

the MAC model to include surface tension and viscosity effects, and also considered heat transfer from a hot surface to a cold liquid droplet as it spread on the surface.

Trapaga and Szekely [1991] used the “volume of fluid” (VOF) method, to study impact of molten particles in a thermal spray process. Liu et al. employed another VOF based code, to simulate molten metal droplet impact. Zhao et al. [1996]

formulated a finite-element model of droplets deposited on solid surfaces.

Adaptive-grid finite element methods were used first by Fukai et al. [1995] to simulate water droplet impact, and later by e.g., [Bertagnolli et al., 1997], [Waldvogel and Poulikakos, 1997] to study thermal spraying of molten ceramic particles.

Bussmann et al. [1999] publish a description of a three-dimensional, fine-difference, fixed-grid Eulerian model the developed, to simulate water droplets falling with low velocity (~1m/s), onto either an inclined plane or the edge of a step.

Pasandideh-Fard et al. [2002] extended the 3-dimensional model of Bussmann’s model to include heat transfer and solidification. In addition, they also accommodate

the presence of an irregular moving solidification front within the computational grid.

1.3.3.1.2 Lattice Boltzmann methods

Lattice Boltzmann method [Succi, 2001] excels in modeling flow problems involving multiphase materials and complicated geometry. It is highly suitable to model the droplet collision dynamics. For example, Inamuro, et al. [2004] presented a

applied the method to the simulations of binary droplet collisions for various Weber numbers and impact parameters. They simulated the there exist other types of binary droplet collisions under certain conditions, bouncing collision for low Weber numbers and shattering collision (Disruption or fragmentation) for high Weber numbers and

discussed the mixing processes in different conditions.

1.3.3.2 Atomic-scale simulation methods 1.3.3.2.1 Molecular dynamics under vacuum

Greenspan and Heath [1991] studied the collision dynamics of nanometer-sized particles. They carried out classical trajectory calculations of collisions between water clusters with a size of 2051 monomers. The individual molecules were modeled as single mass particles and the molecule–molecule interaction was described by a Lennard–Jones potential. Different modes that the colliding system could obtain were identified and compared with observations made for colliding large drops.

Gay and Berne [1986]studied head-on collisions between clusters where the atom–atom interaction was described by a L-J pair potential. They varied the cluster size ~19–135 atoms/cluster in the same temperature, and relative velocity and found that the collisions were accompanied by internal heating and that the clusters coalesced.

Svanberg et al. [1997] performed MD calculations of collision between Ar1000

clusters to investigate the effects of relative velocities (100-1000 m/s ) and impact

parameter (0-4 nm) on energy transfer and dynamical behavior.

Later, Svanberg et al. [1998] increased the complexity of the system and studied the droplet collision dynamics of liquid-like water clusters with an internal temperature of 300K. Collisions between (H2O)n (n=125, 1000), and investigated the effects of cluster velocity and impact parameter on the outcome of the collisions.

Blaisten–Barojas and Zachariah [1992] studied Si15–Si15 collisions at a temperature of about 2000K using molecular dynamics. Chen et al. [1993] carried out molecular dynamics simulations of Au55-Au55 collisions using an embedded atom method potential. Collisions with clusters initially at 0 or 300K were studied, and all collisions resulted in cluster aggregation with significant inelastic deformation of the

original clusters.

1.3.3.2.2 Molecular dynamics with ambient gas

Murad and Law [1999] presented a molecular dynamic simulation with L-J potential for droplet–droplet collision with ambient gas. Bouncing between droplets was only found within a narrow band of state conditions collision, which is mainly attributed to the existence of background gas. However, not much parametric study has been conducted to further understand the effects of the ambient pressure..

Based on the reviews in the above, only preliminary studies have been done in the simulation of nanoscale droplet-droplet collision. Understanding of the droplet

technology. Thus, MD simulation will be used to study the physics of the droplet-droplet collision dynamics in the nanocale regime.