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  • Low, T. B., , and R. List, 1982b: Collision, coalescence and breakup of raindrops. Part II: Parameterization of fragment distributions. J. Atmos. Sci., 39 , 16071619.

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  • View in gallery

    Schematic diagram of overall setup.

  • View in gallery

    Drop production and accelerator units: A—drop propulsion unit; B—acceleration tube for large drop; C—small drop source (dropper); D—small drop deflecting electrode.

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    Accelerator tubes: A—vacuum chamber; B—accelerator tubes (inside diameter 1.6–2.2 cm); C—drop accelerators.

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    Timer and merger section: A—photo cell array for velocity measurement and coincident data collection; B—deflector unit for small drop; C—tube shielding large drops from crossflow; D—feed from ring blower.

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    Overview of vacuum chamber: A—air–drop separation region; B—electronic timing section; C—deflector for small drop (total height of unit 14 cm); D—photography section; E—synchronized camera.

  • View in gallery

    Overview of main system: A—EG&G flash unit; B—electronic auxiliary systems; C—system vacuum pump; D—timer and deflector chamber; E—air calming and photography section; F—ring pump for drop deflection.

  • View in gallery

    Collision products for 50 kPa, for different drop pairs. (a) Filament breakup of (0.46; 0.10); ΔT = 2.5 ms; note tiny fragment trail after breakup. (b) Filament breakup (0.18; 0.10); ΔT = 3.0 ms. (c) Sheet breakup (0.46; 0.10); ΔT = 2.5 ms. (d) Sheet breakup (0.18; 0.10); 3.0 ms; note sheet collapse into filament configuration. (e) Disk breakup (0.46; 0.10); Δt = 2.5 ms, with waves around perimeter; only 2 fragments. (f) Disk breakup (0.18; 0.10); ΔT = 3.0 ms; note elongation in vertical after disk formation. (g) Coalescence (0.18; 0.10); ΔT = 3.0 ms; collision resulted first in oscillating disk. (h) Coalescence (0.45; 0.04); ΔT = 2.5 ms; only slight oscillation after collision.

  • View in gallery

    Fragment distribution of (0.46; 0.10), with parameterization for 50 kPa by Fung (1984); one coalescence.

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    Fragment distribution of (0.261; 0.117), with parameterization for 50 kPa by Fung (1984); three coalescences.

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    Fragment distributions of (0.18; 0.1), with parameterization by Fung (1984); (a) filament breakup, (b) sheet breakup, (c) disk breakup, (d) total collisions 142 and 12 coalescences.

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    Fragment distribution of (0.44; 0.04), filament breakup only; with parameterization by Fung (1984); 69 coalescences.

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    Fragment distribution of (0.18; 0.04); filament breakup only; 57 coalescences.

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    Fragment distributions of (0.18; 0.04) for pure water with σ = 0.0728 N m−1 (solid line) and treated water with a surface tension of σ = 0.054 N m−1 (dashed–dotted line).

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Effects of Pressure on Collision, Coalescence, and Breakup of Raindrops. Part I: Experiments at 50 kPa

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  • 1 Department of Physics, University of Toronto, Toronto, Ontario, Canada
  • | 2 Environmental Protection Department, Hong Kong, China
  • | 3 Environment Canada, Vancouver, British Columbia, Canada
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Abstract

Previous breakup experiments have been carried out at laboratory pressures (∼100 kPa). However, raindrop interactions mainly take place higher up in the atmosphere, even in the supercooled part of a cloud where drops can be initiated by shedding from hailstones. Thus, 50 kPa, corresponding to a height of ∼5.5 km in the atmosphere at a temperature of ∼−20°C, was selected to bracket the region of interest for rain. Six drop pairs were studied at 50 kPa and laboratory temperature (∼20°C), one of them with reduced surface tension.

The apparatus consists of drop-producing nozzles, acceleration systems, deflectors, a timing and selection control, a pressure regulator, and a photographic unit, mostly set up in a low-pressure chamber. After acceleration to terminal speed, a smaller drop is blown into the path of the larger one while an electronic timing system selects suitable drop pairs that may collide, thereby triggering eight subsequent flashes with a frequency of up to 100 kHz. The results are displayed in terms of a normalized fragment probability per size bin, ready for parameterization in the Part II of this paper.

Five drop pairs were studied in 772 individual events. Overall, 51% resulted in filament breakup, 22% in sheet breakup, 7% in disk breakup, and 20% ended in coalescence. No bag breakups were observed. When compared to the 100-kPa results, the fragment numbers increased at large collision kinetic energies (CKEs) by factors of between 2.64 and 4.37 with pressure decreasing from 100 to 50 kPa, and they remained unchanged at low CKE. Detailed diagrams and tables show the results for the different drop pairs and collision categories. Increasing the sensitivity of the optical measurements from 0.05 to 0.01 cm increased the number of recognized fragments by factors up to 4.4, but only for the two higher-CKE cases. The higher resolution did not increase the fragment numbers detected in the lower-CKE range.

Corresponding author address: Prof. Roland List, Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada. Email: list@atmosp.physics.utoronto.ca

Abstract

Previous breakup experiments have been carried out at laboratory pressures (∼100 kPa). However, raindrop interactions mainly take place higher up in the atmosphere, even in the supercooled part of a cloud where drops can be initiated by shedding from hailstones. Thus, 50 kPa, corresponding to a height of ∼5.5 km in the atmosphere at a temperature of ∼−20°C, was selected to bracket the region of interest for rain. Six drop pairs were studied at 50 kPa and laboratory temperature (∼20°C), one of them with reduced surface tension.

The apparatus consists of drop-producing nozzles, acceleration systems, deflectors, a timing and selection control, a pressure regulator, and a photographic unit, mostly set up in a low-pressure chamber. After acceleration to terminal speed, a smaller drop is blown into the path of the larger one while an electronic timing system selects suitable drop pairs that may collide, thereby triggering eight subsequent flashes with a frequency of up to 100 kHz. The results are displayed in terms of a normalized fragment probability per size bin, ready for parameterization in the Part II of this paper.

Five drop pairs were studied in 772 individual events. Overall, 51% resulted in filament breakup, 22% in sheet breakup, 7% in disk breakup, and 20% ended in coalescence. No bag breakups were observed. When compared to the 100-kPa results, the fragment numbers increased at large collision kinetic energies (CKEs) by factors of between 2.64 and 4.37 with pressure decreasing from 100 to 50 kPa, and they remained unchanged at low CKE. Detailed diagrams and tables show the results for the different drop pairs and collision categories. Increasing the sensitivity of the optical measurements from 0.05 to 0.01 cm increased the number of recognized fragments by factors up to 4.4, but only for the two higher-CKE cases. The higher resolution did not increase the fragment numbers detected in the lower-CKE range.

Corresponding author address: Prof. Roland List, Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada. Email: list@atmosp.physics.utoronto.ca

1. Introduction

Langmuir’s idea that raindrops would become aerodynamically unstable when reaching a diameter of 0.5 cm, known as the “Langmuir chain process” (Langmuir 1948), has misled many scientists and continues to do so. It was Magarvey and Taylor (1956) who first challenged this idea, proposing that it was collisions with other droplets that led to a de facto limitation in size. They also experimentally provided evidence to support this idea. Magono and Nakamura (1959) supported these findings. There have been observations of large drops with spherical equivalent diameters of 0.9 cm in Hawaii that clearly contradict Langmuir’s chain reaction process, as do the large raindrops often observed at the beginning of thunderstorms. Similar observations could be made in the wide-orifice wind tunnel at the State University of New York in Albany (Spengler and Gokhale 1972). The senior author (RL) has floated and frozen drops with actual diameters of 1.7 cm and a thickness of ∼0.2–0.3 cm in a Blanchard-type wind tunnel (Blanchard 1957). They wobbled like flying omelets. This then encouraged the Toronto group to start a series of experiments on drop interactions. The secret of the success was the design of a linear (vertical) accelerator by McTaggart-Cowan (1973). Such accelerators can speed up falling drops to terminal velocity (equivalent to free-fall speed). For the large drops, three accelerators, mounted in series, were required. The exit vertical speeds and horizontal oscillations were as observed in nature. To create collisions, the smaller drop of the parallel accelerator systems is gently blown into the path of the larger drop for probable collision. The collision rate was only 2%–7%, which further supported the observation that the collisions were random. The McTaggart-Cowan and List (1975a,b, hereafter MLa and MLb) experiments produced collision photographs for processing under a projection microscope. At best, particles with diameters of 500 μm could be resolved. The results of these experiments were then used in a parameterization scheme by Gillespie and List (1978). List (1988) expanded the ideas produced by the drop evolution model and concluded that “equilibrium drop size distributions” had to exist. Recognizing the importance of these studies led Low (1977) to embark on rebuilding MLa’s apparatus while at the same time increasing the sensitivity of the system to recognize, in special cases, droplets as small as 100 μm. Ten drop size pairs were then selected to provide the frame of a measurement series. In agreement with MLa, the experiments confirmed three different major types of breakups: filaments, sheets, and disks. In several hundreds of experiments, only three spectacular “bag breakups” were seen. Bag breakups are very rare in collisions at terminal speeds. They are irrelevant for rain evolution. The results have been published in Low and List (1982a,b, hereafter LLa and LLb) and also contain a parameterization scheme. This covers every possible combination of raindrop sizes and represents a surface in four-parameter space (a colliding pair of drops produces one fragment distribution, the variation of the size of the smaller drop leads to a surface in 3-space, and the additional variation of the larger drop leads to a surface in 4-space).The parameterization consists of ∼70 equations that cannot be automatically processed and need constant attention. It was first used to calculate spectral evolution by Valdez and Young (1985), who used a Markov chain process. Another approach has been chosen by List et al. (1987). Brown (1988) suggested a third solution; however, this promising approach was not pursued. McFarquhar (2004) drew attention to the importance of the choice of the shape of the fragment distributions in parameterizations. Topological considerations (List and McFarquhar 1990) also add to a better understanding about spectral evolution. Reisin et al. (1996), among others, applied the LLb parameterization in two-dimensional numerical cloud models.

The Low and List experiments were carried out at laboratory pressure (∼100 kPa). However, in the atmosphere raindrops interact with each other not only near the ground, but even in the cold part of convective clouds. There, growing hailstones shed water drops under heat transfer conditions in which not all the accreted water is frozen or is built into a hailstone’s ice framework (List 1959); hence, water being shed. Shed water drops have typical diameters of ∼0.12 cm (Joe et al. 1980; Lesins et al. 1980; Lesins and List 1986). This is a very effective, direct conversion of cloud water into rain drops! In such situations, parallel but interacting particle evolutions are developing between the growing/shedding hailstones, the warm rain process with its evolving rain drop spectra, and the freezing of the drops into ice pellets, which can grow into hailstones. This led to the present study of raindrop–raindrop and raindrop–cloud droplet interactions at a pressure of 50 kPa (equivalent to a height of ∼5500 m in the atmosphere).

To run experiments at lower pressures required rebuilding the LLa apparatus to be airtight for work at 50 kPa. Part I of this manuscript, which heavily relies on the work by Fung (1984), describes the depressurized drop colliding system at 50 kPa and the results of six experimental drop interaction series. Although preliminary parameterizations are shown by Fung (1984), the finalized study of spectra evolution at 50 kPa and the comparisons with the 100-kPa data will follow Nissen (1996), who readjusted Fung’s (1984) parameterization to achieve computational stability. Thereby little differences were introduced in the region of the investigated drops. No attempt is being made to interpolate for pressures between 100 and 50 kPa.

2. The collision apparatus

The apparatus to observe drop collisions and their outcomes is based on the one described by MLa for experiments at 100 kPa. It is adapted and modified to work at 50 kPa. Its components and functions are divided into 1) drop production, 2) drop acceleration, 3) drop deflection, 4) drop timing and selection, 5) pressure control, 6) photographic recording, and 7) a low pressure chamber (Fig. 1).

  1. Uniform-sized drops are produced by two droppers that work on the principle of breaking up the jet coming out of the nozzle with a fixed frequency vibration induced by a speaker-type induction device. Pressure is equalized between the induction device and the rest of the system, and dissolved air is eliminated to minimize interference from bubbles. White Ecoline watercolor paint was added to make the drops more visible without affecting the surface tension. The water flow is controlled by flowmeters and high-precision needle valves. Most of the small drops are produced at rates that are much too high. Thus, after being charged, most drops are deflected by an electric field. At regular intervals, however, a drop will not be charged and will be let through the electrically neutral free-fall region, as controlled by a timing device.
  2. The need to simulate breakup requires drops to fall at terminal speed. They are accelerated first by gravity and then by downward-pointed accelerators. The large drops, after being produced by the droppers, reach about half their terminal fall speed in a free-fall of 1 m. Then they fall into an accelerator into which air is added, rectified, and pushed downward into a conical propulsion unit into which the drops fall (Fig. 2). Their shape becomes flattened, a deformation that is less pronounced at 50 kPa. The tube diameter may decrease in steps, depending on drop size and the need for multistage accelerators. In the final phase, the air is stripped off and the drops enter a low-pressure chamber. The large and small accelerators have a length of approximately 4 and 2 m, respectively (Fig. 3). They are secured on a rigid Dexion frame, as close to each other as possible (9 cm between center lines). The flow inside the accelerators is controlled by the pressure in the vacuum chamber and by the valve and flowmeters at the inlet of the propulsion units. To allow visual control, most parts of the propulsion units were made of Plexiglas.
  3. The deflection of the small drops into the path of the large drop is done below the accelerator systems within a “deflector box” while the large drop passes through the center of the box along its height, shielded in a vertical tube (Fig. 4). The horizontal airflow was produced by a 7.4-kW nonpulsating, oil-free liquid ring blower. It imparted enough horizontal momentum to eventually push (below the box) the small drop into the path of the large one. This air was then returned to the deflector box by the pump in a continuous operation and with minimum interference with the rest of the system.
  4. The timing modules (Fig. 4) determine the speed of the drops and further select the drop pairs that have a good chance of colliding for photographic recording. Drops are timed by light and photo diode devices mounted 10 cm apart to determine the free-fall velocity. Another drop detector is positioned at a predetermined location in each of the drop paths. The time coincidence detectors (TCDs) serve to indicate a high chance of a collision to open a “drop selection shutter” that allows a drop to pass into the collision region. This selective gating serves to keep the turbulence in the collision area at a minimum.
  5. The photographic module (Fig. 5) consists of a self-winding high–film capacity 35-mm Nikon camera system, placed outside the vacuum chamber, while the drops pass through an aluminum box with black velvet lining on one inner surface (the backdrop for the pictures) and a flash tube powered by a high-intensity EG&G strobe in a corner. The strobe light is concentrated on the drop path by a concave mirror. The experiment is carried out in the dark and the camera shutter is always open. When the TCD senses coincidence, a series of eight flashes is produced by a high-intensity EG&G strobe at frequencies up to 100 kHz, chosen appropriately for the terminal velocities of the drops. Then the camera advances the film and is ready for the next potential collision. The chances of catching an interaction event are 2%–7%.
  6. The ∼2-m-tall vacuum chamber (Fig. 5) is made from 2.5-cm-thick Plexiglas plates. The upper half houses the structure to strip air from the accelerators, the drop detectors, and the drop deflector. The lower part houses the photographic unit. The low pressure in this chamber is monitored by a pressure gauge and maintained by suction through the top by a 740-W vacuum pump. The air and suction for the drop deflector come from two sides through flanges (ring pump). A view of the apparatus with auxiliary equipment is presented in Fig. 6.
  7. Additional comments on the apparatus: All appropriate parts of the system are vacuum/pressure sealed. A few mechanical parts in the chamber, such as the drop detectors or the drop deflector need aligning (i.e., they have to be remotely adjusted while maintaining low pressure). A drainage system operating at low pressure prevents excessive water buildup during an experiment.

3. Collisions and breakup classification

a. Nomenclature

The following convention is introduced: “Drops” will always refer to the particles before collision. After collision, “fragment(s)” will be used. Fragments will be called large, small, or tiny. The large fragment will always be the remnant of the large drop. The second-largest or small fragment will always be the remnant of the small drop. Note that small fragments are only produced in filament breakup. Tiny always refers to the rest of the fragments. The breakup types will be listed as f for filament, s for sheet, and d for disk. The total of the three will be denoted by t.

In the display of fragment distributions, the bin width for low-energy collisions [collision kinetic energy (CKE) <9 × 10−7 J] is 0.005 cm for sizes between 0.01 to 0.10 cm, 0.01 cm between 0.10 and 0.20 cm, and 0.02 cm from 0.20 to 0.50 cm. For higher-energy collisions, a bin width of 0.01 cm is used from 0.05 to 0.10 cm, 0.02 cm from 0.10 to 0.20 cm, 0.025 cm from 0.20 to 0.40 cm, and 0.05 cm from 0.40 to 0.50 cm. The width was chosen to create relatively smooth normalized probability density functions P(Di) with statistically significant fragment numbers in each bin.

Here P(Di) is defined as
i1520-0469-66-8-2190-e1

The size of the largest fragment in all collisions is the most difficult to measure because of the large distortion during collision and the duration of the oscillations. The small fragments usually assumed equilibrium shape with a few milliseconds. The procedure to assess the large fragment size was adopted from LLb. Mass conservation could be applied for every single collision. That would make any conservation for whole datasets superfluous. However, this would leave out an estimate of the masses of tiny fragments that are below the detection limit—if they could be separated from the measurement errors. Thus, the data in this paper reflect the data of the experiments, without any massaging.

b. Drop properties

To provide consistency with MLa and LLa, the drop free-fall velocities, VT, were calculated as a function of diameter D and altitude z, according to the formula given by Best (1950):
i1520-0469-66-8-2190-e2
with A = 9.32 m s−1, n = 1.147, a = 0.177, and b = 0.0405 km−1 for an International Commission for Air Navigation (ICAN) standard atmosphere. (Note that there is also standard tropical atmosphere, which would show an air temperature close to the freezing point at 50 kPa.)

The properties of the drops produced in the drop accelerator system are summarized as follows: The free-fall velocities are within ±1% of the calculated value, and the mean oblate/prolate ratio of the oscillation is 0.83/1.02 compared to values of natural rain drops (at the ground) of 0.84/1.18. The drop oscillation frequency is 55 Hz as compared to 65 Hz in nature. Note that the drop diameters are always given in equivalent spherical diameters. Electrical charges on the drops were not measured because of the confined experiment space. However, charges are expected to be small and similar to LLb’s drops [−8.2 × 10−14 C for small drops (D = 0.0395 cm) and 1.7 × 10−12 C for large drops (D = 0.4 cm)], which were produced similarly to the present experiments. The surface tension is 7.28 × 10−2 N m−1 for de-ionized water at 20°C and 7.24 × 10−2 N m−1 with the addition of Ecoline white ink in a concentration of 1:300. The range of natural rainwater is (7.1–7.4) × 10−2 N m−1. The conductivity is 7.80 × 102 μMho m−1 after de-ionizing and dying. This compares to (7–474) × 102 μMho m−1 for rainwater (Egner and Eriksson 1955).

It was observed that the shapes of the drops at 50 kPa were more spherical than those at 100 kPa. Interplay among the 37% decrease in Reynolds number, an increase of free-fall speed by 28%, and different hydrostatic pressures within the drops might hold the explanation. The only drop shape measurements for lower air pressures were carried out by Beard (1976) for diameters <0.1 cm. The lack of experimental data for drop shapes with diameters >0.1 cm is deplorable and is one of the weaknesses of Best’s Eq. (1). Using Reynolds numbers also implies similar shapes.

c. Drop collision patterns and breakup types

A collision between two drops is defined as an event in which water is interchanged. However, this cannot always be ascertained when there is no visible distortion of shape, but only a change in drop trajectory after passing each other. This could be a result of bouncing, but to be in line with LLa, this type of trajectory has been accepted as a collision.

Each breakup type is characterized as a filament, sheet, or disk, according to the shape of each conglomerate in the first or second frame after collision. This is similar to the procedure used by MLa and LLb. It is based on the film images of collisions and their outcomes, as analyzed on a projection microscope. Images belonging to each collision are isolated by trajectory analysis when images from different times overlap.

1) Filament breakup

When a small drop hits a large one near or at its equator, the small drop may move around the large one, but it soon will be carried away and separated by its own momentum from the large drop while temporarily connected to it by a filament of fluid. This filament will be stretched, becoming thinner and eventually unstable, and soon disintegrates into a string of tiny fragments, much smaller then the small drop.

The momentum transfer between the two largest fragments, remnants of the original drops, and their distortions are the smallest of the three breakup types. The speed of the largest fragment remains almost unchanged whereas that of the second-largest fragment can increase by up to 15% over that of the original small drop. This momentum transfer also produces a change in direction of the second-largest fragment. The breakup of the filament usually starts within 1 ms of contact and is usually over in <5 ms. (Figs. 7a,b).

2) Sheet breakup

If the small drop hits closer to the center, then it rips a whole sheet out of the large drop (Figs. 7c,d). Time does not allow a complete contraction into a filament; instability will disintegrate the sheet much faster. This sheet is roughly at an angle of 45° from the vertical. The small drop loses its identity into the fragments of the sheet. There is no distinct fragment that reflects the size of the small drop. The velocities of the fragments gradually approach their terminal speed. The breakup is normally complete before 8 ms have elapsed, but severe oscillation of the large fragment can persist beyond 15 ms.

Any overall energy consideration must include 1) the momentum transferred from the small drop to the conglomerate, 2) all surface energies, and 3) the work done by aerodynamic drag.

3) Disc breakup

When the small drop hits the large one in or close to the center, the resulting conglomerate forms a horizontal disk. If the radial expansion of the disk is not stopped, disintegration will occur (Fig. 7e). If the expansion is halted, then the disk may pull together and expand in the vertical. This oblate–prolate oscillation can also lead to fragment production in the prolate stage (Fig. 7f). Both these stages are seen for the high-energy drop pairs (0.46; 0.10), while for low-energy pairs, e.g., (0.18; 0.10), waves around the disk are usually absent, and only the prolate stage produces fragments. (Throughout this paper drops are measured in centimeters and discussed in pairs as shown above.) Major fragments can still break off 12 ms after initial impact.

From the energy point of view, the disk breakup is the most inelastic of the three. Once the disk is formed, it has the biggest aerodynamic drag because of its shape, far bigger than that of the original large drop. In many cases decelerations >10 g were measured. Aerodynamic (Bernoulli) forces acting on a disk help to spread the mass further, enhancing breakup into fragments.

In a disk breakup, fragments break away from the main conglomerate at the periphery where the local outward inertial force exceeds the surface tension. In the case of a disk collision, the kinetic energy is more evenly distributed because of the greater axial symmetry. This explains why the disk mode, although more violent then the sheet or filament collisions, is the first one to result in coalescence when CKE is low.

However, CKE cannot be the sole explanation of the breakup phenomenon because waves in the conglomerate play a strong role in determining the number and size of the fragments.

The reduction of pressure does not affect the breakup types and their classification, as established by MLa and LLa. However, differences exist. At 100 kPa, the small drop re-emerged relatively intact to form the second-largest fragment in a filament breakup, distinct from the tiny fragments. At 50 kPa, this is less distinguishable when DLDS, resulting in a filament looking more like a rod than like an inverted pendulum.

4) Bag breakup

A bag results when a disk is inflated by air and forms a bag, which then disintegrates into many, many fragments (>100). MLb reported three bag breakups out of 130 collisions for the (0.46; 0.10 cm) pair. For the same pair combination, of the present 134 experiments with 30% higher relative velocities, a 69% higher CKE, and a Reynolds number smaller by 37% than their ground-level counterpart, none of the collisions produced a bag breakup. This pair also produced significantly less fragments at 50 kPa than at 100 kPa. This statement is not necessarily characteristic of all 50-kPa experiments. It points to a significant change in the contribution of aerodynamics to the breakup energy between the two pressure levels.

5) Coalescence

Out of 772 collisions, 156 or 20% resulted in coalescence (Figs. 7g,h). They occurred mostly in the lower-CKE cases.

4. Results of drop collisions

Five sets of collision experiments were performed at 50 kPa with drop pairs (0.261; 0.117), (0.46; 0.10), (0.18; 0.10), (0.44; 0.04), and (0.18; 0.04). The first pair was used to test the capabilities of the system, whereas the next four were used for comparison with LLb at 100 kPa. A sixth series was used to probe the effect of lowering the surface tension by 36%. There were 772 collisions in total (Table 1). Each set comprises at least 104 collisions. Overall, 51% resulted in filament breakup, 22% in sheet breakup, and 7% in disk breakup, whereas 20% led to coalescence. The breakdown for the individual drop pairs is displayed in Table 2.

For the two cases of the largest CKE, the number of tiny fragments is up to 4.4 times larger at 50 kPa than at 100 kPa, whereas the numbers are slightly smaller or similar for the remaining lower-CKE cases. The exception is for sheets of the (0.261; 0.117) pair breakup. There is no pressure response for the lowest-CKE cases, whereas for (0.18; 0.10) the effect is even reversed; that is, the fragment number concentration decreases with decreasing pressure.

Table 3 displays all the data of Table 2 in terms of ratios. The resolution factor gives the increase in fragment numbers when the resolution is increased by a factor of 5 from 0.05 cm to 0.01 cm. The pressure factor gives the increase (decrease) in fragment numbers when the pressure is decreased from 100 to 50 kPa. The pressure factors for high resolution are based on extra measurements carried out by Fung (1984) at 100 kPa. The low-resolution data at 50 kPa were also provided by Fung (1984).

Figure 8 depicts the (0.46; 0.10) pair with the most pronounced fragment number increases (by factors of 2.6 to 4.4) due to pressure drop. At the same time, increasing the resolution by a factor of 5 increases the fragment numbers from 1.8 to 2.8. The increase in fragment numbers is evident in the fragment distributions for the different breakup types. The fragment distributions show that the tiny fragment peak was clearly established for all types of breakup, which is not the case for any breakup cases of the same drop pair at 100kPa (LLa).

At intermediate CKE (Fig. 9), the increase in fragment numbers occurs only for filament and disk breakup but not for sheets. In this case the effect of an increase in resolution is quite reduced to values between 1.1 and 2.2. There is not an equivalent case for 100 kPa.

Cases 3 to 5 depict low-CKE cases showing no increases in fragment numbers due to pressure changes (Figs. 10 –12). However, there is evidence in case 3 that the effect is opposite to all other cases, showing a decrease no matter what the resolution is.

Comparisons of the different breakup types show that the violence of the breakup (CKE) is responsible for the creation of the small fragments. Their number concentration is drastically reduced at lower CKE (see spectra in Figs. 10 –12) and is unaffected by pressure.

The pairs (0.44; 0.04) and (0.18; 0.04) (cases 4 and 5; Figs. 11 and 12) only experienced filament breakup or coalescence because the small drop does not have enough mass and momentum to initiate breakup into sheets and disks. This assessment also holds for these types at 100 kPa. The experiments show that all breakup types will only occur when the small drop diameters are close to or larger than 0.10 cm. In those cases coalescences will be reduced from 39% and 56%, respectively, to <14%. At 100 kPa there is no coalescence for the high-CKE case (0.46; 0.10), whereas the coalescence efficiency for the three low-CKE cases was measured to be between 21% and 65%.

All tiny particle peaks for all breakup types are clearly defined in the high-resolution cases at 50 kPa. For 100 kPa this is only the case for filaments of the (0.44; 0.04) and (0.18; 0.04) pairs and the (0.18; 0.10) sheets. All disk breakups at 100 kPa require high resolution.

The limited experimental data available do not allow a full-fledged comparison of the effects of pressure and extended range. Thus, the comparison is deferred to Part II of this paper (List et al. 2009, hereafter Part II) and will be based on the parameterization.

It might be assumed that surface tension is an important factor in the breakup. Figure 13 shows that this is not correct considering that lowering the surface tension by 26% had no significant effect on fragment size distribution. This result is in agreement with Whelpdale and List (1971) and may discourage operators from trying to employ surfactants to modify the precipitation process. There is another related point: simulating conditions at 50 kPa at a temperature of ∼20°C does not take account of the drops supercooling to ∼−20°C at that pressure level in the atmosphere. This would require an additional lowering of the surface tension to values not listed in handbooks. Even if that could be artificially achieved, the viscosity of the water would also have to be changed to uncharted values. Its increase could not be reproduced by supercooling in a laboratory environment. It would be possible only if a surrogate fluid could be found with properties of water at ∼−20°C. That aspect was not pursued because the low-pressure experiments themselves were challenging enough.

The detailed datasets can be found in the Ph.D. theses of McTaggart-Cowan (1973), Low (1977), and Fung (1984).

5. Summary and comments

An apparatus is described that is used to study collisions between water drops ranging in size from 0.04 to 0.46 cm at terminal free-fall speeds and at low pressure. Experiments at 50 kPa show that the collision types are not different from those in experiments at 100 kPa, as reported by MLb and LLb. Thus, the breakup forms are again classified as filament, sheet, and disk. Another outcome is coalescence. No bag breakups were observed.

The data are displayed in histograms. Parameterizations by Fung (1984) are also displayed. They are somewhat different from those by LLb in the region beyond the range of the presently treated drop pairs. The full parameterization for 50 kPa has been worked out by Nissen (1996) and will be described and displayed in Part II, together with details of the pressure effects and their time evolution from specific initial distributions. The advantage of the new parameterization is its greater computational stability. Part II will also describe the pressure dependence of the different collision products.

The conclusions are as follows:

  1. There is no need for higher resolution in measurements of fragment sizes than 0.01 cm. All peaks are clearly established.
  2. It is found that the small drop has to be close to or larger than 0.1 cm to trigger breakups in the form of sheets and disks.
  3. Lowering the pressure from 100 to 50 kPa increases fragment numbers, but only for high and intermediate collision kinetic energies. At low CKE the pressure effect is negligible or even reversed.
  4. Higher measurement resolution can reveal a stronger pressure effect.
  5. For high-CKE experiments, in which collisions are more violent than at low CKE, the fragment number is higher when measured at the higher sensitivity. At low CKE the fragment numbers found with sizes between 0.05 and 0.1 mm are small and negligible.

The original purpose of the measurements was to establish products of raindrop–raindrop and raindrop–cloud droplet interactions over a range of atmospheric pressures. With the impressive theoretical calculation of drop interaction products by solving the Navier–Stokes equations for collisions by Beheng et al. (2006), it is now also possible to study these phenomena numerically. Indeed, the agreement for 100 kPa is astounding. Once numerical calculations for 50 kPa agree with the new experimental data, a shift of studies to computation is indicated (also because of lack of laboratory facilities). Numerical exploration of the physics of the collision/breakup process may be easier than to deal with the excessive complexity of such experiments.

Acknowledgments

These studies have been supported by the former Atmospheric Environment Service (now Environment Canada), whereas publication was sponsored by the Roland List Foundation. The authors TL and RN appreciated the fellowships received from the Atmospheric Environment Service and the Natural Sciences and Engineering Research Council of Canada.

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Fig. 1.
Fig. 1.

Schematic diagram of overall setup.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 2.
Fig. 2.

Drop production and accelerator units: A—drop propulsion unit; B—acceleration tube for large drop; C—small drop source (dropper); D—small drop deflecting electrode.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 3.
Fig. 3.

Accelerator tubes: A—vacuum chamber; B—accelerator tubes (inside diameter 1.6–2.2 cm); C—drop accelerators.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 4.
Fig. 4.

Timer and merger section: A—photo cell array for velocity measurement and coincident data collection; B—deflector unit for small drop; C—tube shielding large drops from crossflow; D—feed from ring blower.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 5.
Fig. 5.

Overview of vacuum chamber: A—air–drop separation region; B—electronic timing section; C—deflector for small drop (total height of unit 14 cm); D—photography section; E—synchronized camera.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 6.
Fig. 6.

Overview of main system: A—EG&G flash unit; B—electronic auxiliary systems; C—system vacuum pump; D—timer and deflector chamber; E—air calming and photography section; F—ring pump for drop deflection.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 7.
Fig. 7.

Collision products for 50 kPa, for different drop pairs. (a) Filament breakup of (0.46; 0.10); ΔT = 2.5 ms; note tiny fragment trail after breakup. (b) Filament breakup (0.18; 0.10); ΔT = 3.0 ms. (c) Sheet breakup (0.46; 0.10); ΔT = 2.5 ms. (d) Sheet breakup (0.18; 0.10); 3.0 ms; note sheet collapse into filament configuration. (e) Disk breakup (0.46; 0.10); Δt = 2.5 ms, with waves around perimeter; only 2 fragments. (f) Disk breakup (0.18; 0.10); ΔT = 3.0 ms; note elongation in vertical after disk formation. (g) Coalescence (0.18; 0.10); ΔT = 3.0 ms; collision resulted first in oscillating disk. (h) Coalescence (0.45; 0.04); ΔT = 2.5 ms; only slight oscillation after collision.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 8.
Fig. 8.

Fragment distribution of (0.46; 0.10), with parameterization for 50 kPa by Fung (1984); one coalescence.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 9.
Fig. 9.

Fragment distribution of (0.261; 0.117), with parameterization for 50 kPa by Fung (1984); three coalescences.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 10.
Fig. 10.

Fragment distributions of (0.18; 0.1), with parameterization by Fung (1984); (a) filament breakup, (b) sheet breakup, (c) disk breakup, (d) total collisions 142 and 12 coalescences.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 11.
Fig. 11.

Fragment distribution of (0.44; 0.04), filament breakup only; with parameterization by Fung (1984); 69 coalescences.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 12.
Fig. 12.

Fragment distribution of (0.18; 0.04); filament breakup only; 57 coalescences.

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Fig. 13.
Fig. 13.

Fragment distributions of (0.18; 0.04) for pure water with σ = 0.0728 N m−1 (solid line) and treated water with a surface tension of σ = 0.054 N m−1 (dashed–dotted line).

Citation: Journal of the Atmospheric Sciences 66, 8; 10.1175/2009JAS2863.1

Table 1.

Number (#) and percentage (%) of drop interaction products classified as filaments, sheets, and disks, with number of coalescences; ordered in descending values of CKE. Experiment 6 (0.18; 0.10) is for a surface tension reduced by 26% from that of water.

Table 1.
Table 2.

Comparison of fragment numbers for different breakup products of five different drop pairs at 50 and 100 kPa, for resolutions of 0.01 (Fung 1984; Low 1977) and 0.05 cm (Fung 1984; McTaggart-Cowan 1973). The data for the experiment (0.261; 0.117) at 100 kPa are according to the LLb parameterization.

Table 2.
Table 3.

Ratio response to pressure and resolution for the three breakup modes, with the sensitivity factor indicating the fragment increase with 0.01- or 0.05-cm resolution, whereas pressure ratios characterize the increase in fragment numbers by lowering air pressure from 100 to 50 kPa. LR indicates low resolution (≥0.05 cm); HR, high resolution (≥0.01 cm). RF indicates resolution factor, and PF indicates pressure factor.

Table 3.
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