Grantee Research Project Results
2000 Progress Report: Modeling Collision Efficiencies for Coalescence of Small Drops and Particles
EPA Grant Number: R827115Title: Modeling Collision Efficiencies for Coalescence of Small Drops and Particles
Investigators: Koch, Donald L.
Institution: Cornell University
EPA Project Officer: Hahn, Intaek
Project Period: October 1, 1998 through September 30, 2001
Project Period Covered by this Report: October 1, 1999 through September 30, 2000
Project Amount: $305,155
RFA: Exploratory Research - Physics (1998) RFA Text | Recipients Lists
Research Category: Air Quality and Air Toxics , Land and Waste Management , Air , Safer Chemicals
Objective:
The objective of the project is to determine the rate of coagulation of small particles and drops driven by Brownian motion, turbulence, and differential sedimentation. Particular attention will be given to the influence of non-continuum gas flow between colliding particles on the collision efficiency.Progress Summary:
An important component needed for modeling collision efficiencies in aerosol systems is the resistance produced by the non-continuum gas to the relative motion of the aerosol particles. In previous work, we predicted the resistance for the case of two rigid spheres when the mean free path is either much greater than or much less than the sphere dimension. In each case, the drag force acting on the spheres was derived and the criterion for contact to occur due to non-continuum effects was obtained.When droplets collide, the interfaces deform due to the pressure induced by the flow of the gas in the intervening gap. The drops may coalesce or bounce depending on whether the gas is forced out of the gap between the drops before the kinetic energy of their relative motion is transformed into energy of surface deformation. We have formulated a general theory that not only models the flow inside the drop but also takes into account evolution of the gap between the drops. The drop deformation in the near-contact inner region is determined by solving the lubrication equations and matching to an outer solution. The resulting equations are solved numerically using a direct, semi-implicit, matrix inversion technique. By simultaneously including both strong retarding viscous forces and surface deformation, our work provides a rational basis to understanding and predicting collision outcomes. The general program we have developed during the course of our investigation allows us to simulate the collision of two deformable spheres or the collision of a deformable sphere with a deformable interface in a non-continuum isothermal gas.
To obtain a better understanding of the role played by surface deformation, we have considered the continuum limit wherein all collisions result in rebound. A physical application where this condition is realized is in pressurized gas turbines. Our numerical results present the following picture of the rebound process. For collisions characterized by small droplet inertia, the collisional dynamics resemble those of rigid spheres and the colliding drops come to rest without any significant rebound. As inertia becomes more important, the drop surfaces deform noticeably and a dimple forms when the pressure in the gap balances the capillary pressure due to the curvature of the interface. The dimple is characterized by a large radius of curvature, i.e., it is almost flat. The radial extent of the dimple increases, reaches a maximum, and then decreases to zero. The centroids of the two drops come to rest momentarily and then the drops rebound, executing oscillatory motions before finally coming to rest. For large values of the inertia parameter, more energy is stored as deformation energy and the maximum radial extent of the dimple increases accordingly. The temporal evolution of the minimum gap thickness exhibits two minima. A detailed analysis of the interface shapes, pressure profiles, and the force acting on the drops allows us to obtain a complete picture of the collision and rebound process. In addition to the numerical solutions to the complete set of equations, we also obtained complete analytical expressions for the bounce time and the maximum dimple extent formed using a simplified model valid when the viscous dissipation in the gas is negligible. According to this simple model, the only effect of the gas is to supply a constant disjoining pressure to keep the drop interfaces from touching. We find that the analytical expressions for the rebound times match extremely well with the numerical solutions of our model, existing simulations, and available experimental data.
To complement this theoretical analysis, we have developed an experimental apparatus to observe droplet collisions with a gas-liquid surface. Drops are fired from a piezo-electric drop generator toward the interface and the impact velocity is controlled by varying the distance from the generator to the interface. A pressure chamber encloses the apparatus allowing variation in gas pressure and composition. The droplet trajectories are observed using a high-speed video camera and a long-range microscope. The trajectories are fit with a solution for the drop motion based on a balance of drop inertia, gravity, and nonlinear drag to determine the drop radius and the impact and rebound velocity.
The coefficient of restitution (or ratio of the rebound to impact velocity) for drop interface collisions is observed to pass through a maximum as the drop impact velocity is increased. At small impact velocities, the gas film between the drop and interface becomes very thin before a sufficient pressure is built up to result in a bounce and, as a result, viscous dissipation consumes much of the impact energy. At large impact velocities, much of the energy is lost due to surface deformation and the generation of capillary waves. We also observe a critical velocity for transition from coalescence to bouncing, which depends on the surface tension, drop radius, the liquid density, gas viscosity and the mean-free path in the gas. Increasing the pressure in the gas and thereby decreasing the mean-free path allows a bounce to occur at smaller impact velocities. The smaller mean-free path allows the gas film to become thinner before non-continuum effects lead to a breakdown of lubrication forces.
Future Activities:
We currently are using the numerical simulation to investigate two important factors that could influence the collision process and lead to coalescence instead of a rebound? non-continuum effects and London-van der Waals interparticle attractive forces. The main aim of this study is to obtain accurate predictions of the bounce-coalescence transition. The simulation also will be extended to predict the behavior of drop-interface collisions facilitating a direct comparison of our experimental measurements with theory. In the experimental work, we are conducting a parametric study of the effects of gas viscosity and pressure, surface tension, and drop radius on the critical velocity for the coalescence-bounce transition and on the coefficient of restitution.Journal Articles on this Report : 1 Displayed | Download in RIS Format
Other project views: | All 7 publications | 4 publications in selected types | All 4 journal articles |
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Type | Citation | ||
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Gopinath A, Koch DL. Collision and rebound of small droplets in an incompressible continuum gas. Journal of Fluid Mechanics 2002;454:145-201. |
R827115 (2000) R827115 (Final) |
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Supplemental Keywords:
air, atmosphere, precipitation, particulates, physics, mathematics., RFA, Scientific Discipline, Air, Waste, particulate matter, Physics, Environmental Chemistry, Atmospheric Sciences, Ecology and Ecosystems, Incineration/Combustion, Engineering, Chemistry, & Physics, collision efficiency models, pollution control technologies, air pollution modeling system, air pollution, Brownian motion, pollutant transport, differential sedimentation, emission controls, atmospheric transport, coalescence, particle surface interactions, incineration, pollution dispersion models, particle collision models, atmospheric models, particle collision, particle transportRelevant Websites:
http://www.cheme.cornell.edu/peopleevents/faculty/kochProgress and Final Reports:
Original AbstractThe perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Conclusions drawn by the principal investigators have not been reviewed by the Agency.