Presentation on theme: "3. Droplet Growth by Condensation"— Presentation transcript:
13. Droplet Growth by Condensation 3.1 Growth of an individual droplet by condensation3.2 Evaporation of droplets3.3 Growth of droplet populations3.4 Factors affecting growth theory
2CCN – once a drop is activated. 3.1 Growth of an individual droplet by condensationCCN – once a drop is activated.Cloud condensation nucleiHow fast does a drop grow?Rate of diffusional growth of water molecules from the vapor onto its surface.Occurs before and after r*.
3Vapor DiffusionDrop is located in a vapor field with the concentration of vapor molecules a distance R from the droplet center, n(R). Drop has radius r.Isotropic conditions assumed, so n(R) or (R) does not depend on direction from the droplet.Concentration of vapor field molecules is assumed to satisfy the diffusion equation.
4Heat DiffusionTemperature is usually not the same as the ambient temperature.Must be determined by considering the heat transfer equation between the droplet and its surroundings.Condensation Latent heat release Drop temperature rises above the ambient value.
83.2 Evaporation of droplets Once a droplet falls from a cloud it enters anunsaturated environment (S<1). The dropletswill begin to evaporate.The evaporation of the droplet is also governedby the same equation as condensation.A small droplet will evaporate very quickly anddisappear, while larger droplets will last longer.
9Rapid increase of distance with the increase of radius Cloud dropsr < 0.1mmDrizzle dropsr is near 0.1mmRaindropsr > 0.1mm (100m)
103.3 Growth of droplet populations Goal of cloud physics:To understand the processes that shape the droplet distribution.FactsA droplet that forms on a small condensation nuclei is seen to grow initially at a rate faster than droplets with large nuclei.Once small nuclei drops reach a comparable radius, the growth rate is about the same.Droplet size distribution is narrowing.
11If environment has an excess of vapor over the equilibrium value……. Growth by condensationIf dry environmental air is mixed with cloudy air……EvaporationSedimentation (gravitational settling)Coagulation (coalescence)Important for growth of larger droplets
12Early DevelopmentCloud drops are too small for sedimentation or coalescence.Condensation is the dominant growth process.Controlled by the ambient saturation ratio.Therefore, we need to know the details of a developing cloud.
17ObservationsDrop distributions within a short distance from the cloud base are narrow (5-10m).Consistent with drop growth by condensation.Higher in cloud, droplet spectra are often broader than predicted by drop growth by condensation.
19Kinetic EffectsRate of heat mass and momentum transfer between drop and its surroundings depends on Knudsen number.Knudsen number = l/rl = Mean free path in airr = radius of dropl 0.06m for normal conditions at sea level.
20l/r << 1 Fields of vapor and temperature are continua. Exchange described by Maxwell continuum approximation.Everything we learned before is valid.
21l/r >> 1Vapor and temperature fields are not considered continua.Exchange described by Molecular Collision theory.Appropriate for particles in the air smaller than 0.06m.Drop has to travel a distance before encountering vapor in the air.
22l/r ~ 1 For small cloud droplets having radius between 0.1 and 1 micron,Neither the free molecular northe Maxwell continuum approximationis valid.
23Kinetic Effects Tends to reduce drop radius for all times. As drop grows, solution tends toward continuum solution.Rate of growth after sufficient time becomes the same.Growth of smaller drops are slowed more than large drops.Broader cloud drop spectrum.
25Ventilation Effects Vapor field is spherically symmetric (isotropic) Good for a drop at rest. What about falling drops?Rate of heat and mass transfer increase and are greatest on upstream side.For large drops, negligible compared to growth by collision or coalescence.Very significant for evaporation of rain drops and other precipitation particles..
26Non-Stationary growth Fields of vapor and temperature about a drop are not exactly steady.Surface of drop is always expanding or contracting.Drops is moving around requiring adjustment of the diffusion field.Temperature and vapor fields adjust very quickly to the presence of a dropmolecular diffusion~10s to reach steady state conditions.Good approximation to neglect this effect..
27Unsteady Updraft Accelerating and decelerating regions of updraft. Capable of broadening the spectrum by continual activation of fresh nuclei.Except for the creation of newly activated droplets in regions of upward acceleration, this effect had little impact on drop evolution.
28Statistical effectsDrops have different historiesExperience different super-saturations.Broadening of the drop spectrum.Currently regarded as a small effect.Drop spectral broadening is still an active area of research.
29Meteorology 342Homework (3)1. Problem 7.22. For radii greater than a few microns, the curvature and solution effectsbecome negligible. Find how long it would take to grow a droplet from5 to 50 microns for the following conditions, a saturation ratio of ,a temperature of 273K, and a pressure of 1000 hPa.3. Consider the diffusional growth stage which will dominate the growthprocess until the drop grows to sufficient size so that collisionsbecome important. Briefly discuss each physical process that mustbe considered if you were to accurately model the growth of an initialpopulation of cloud droplets by diffusional processes.