Fundamental Phenomena and Principles 193
3.2.0DROPLET DEFORMATION ON A SURFACE
Droplet deformation during impact onto a surface is an interesting subject in many scientific and engineering fields. The icing and erosion/ablation of aircraft surfaces may be caused by the impact of droplets in clouds and/or rains on the surfaces during flight.[44][45] The erosion of turbine blades[46] operating in wet steam, the erosion of terrestrial surfaces during rain, and the erosion-corrosion of inhibitors in wet, CO2-containing environment present in gas production and transportation facilities[333] are all related to droplet impact. The phenomena of droplet impinging and spreading on a solid surface are encountered in a wide range of processes and applications. These include, for example, spray combustion, spray cooling (quenching) of surfaces,[17] dispersed two-phase flow in once-through boilers, post-critical heat flux cooling, ink-jet printing,[47] metal welding/soldering, spray painting, lubrication, oil recovery from porous rocks,[48] and production of fine metal powders via impact atomization.[49] The spreading phenomenon is typically accompanied by simultaneous heat transfer and solidification of droplets on deposition surfaces in picoliter solder droplet dispensing for mounting of microelectronic components,[50] spray forming for near-net shape materials synthesis,[3] and thermal spray deposition for surface
coating.[18][51][52]
Droplet impact on a surface is often accompanied by breakup of larger droplets into smaller ones due to droplet deformation, splashing and/or solidification on a cold surface, and/or vapor formation at liquid-solid interface on a hot surface. This phenomenon is typically observed in spray cooling of hot surfaces,[334] and in spray combustion where fuel droplets impinge on the hot wall of combustion chamber.[335] Impinging liquid droplets at a suitable impinging rate has been considered as a potential means for cooling integrated microelectronic equipment due to the high heat transfer rate, and reduced consumption of coolant as compared to liquid jet cooling.[336] In these applications, droplets may impact a dry or wet surface (a deep or shallow liquid pool). Bouncing of liquid may take place during impingement of droplets. Phase change such as solidification of liquid
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metals or evaporation of normal liquids may occur during spreading of droplets on a cold or heated surface. In most situations of practical interest, multiple droplets impact a surface, a physical phenomenon distinctly different from that in single droplet impact process.
The observations of deformation of a single droplet impinging on a surface started in 1876, as described extensively by Worthington.[337] Detailed studies of the deformation process were not possible until the development of high-speed photographic techniques and computer systems. To date, numerous theoretical, modeling, and experimental studies have been conducted to investigate the phenomena related to droplet deformation on a surface, such as spreading,[48][338]-[354] splashing/ejection and breakup,[355-360] wetting and contact angle,[361]-[366] mass trans-
fer,[376][377] solidification,[144][157][367][378]-[382] and shock wave for-
mation[383] of droplets of normal liquids, melts, and polymer[384] on flat and non-flat surfaces, ceramic porous surface,[385] and liquid surface.[386] Extensive reviews of the previous studies have been made by Rein,[387] Liu et al.,[388][389] Dykhuizen,[390] and Dussan.[391]
3.2.1Deformation of a Single Droplet on Flat and Non-Flat Surfaces
The deformation processes of a single droplet on flat and non-flat surfaces are shown in Fig. 3.13 and Fig. 3.14, respectively. In these figures, the impact Reynolds and Weber numbers are defined as Re = ρ L u0 D0 /µL and We = u20 ρ L D0 /σ , respectively, where u0 and D0 are the initial droplet velocity and diameter at impact, respectively. D/D0 and H/D0 are the dimensionless diameter and height of flattening droplet, respectively, and t/(D0 / u0) is the dimensionless time. The roughness or unevenness of a non-flat surface may be described by two parameters, i.e., roughness height and roughness spacing. Dimensionless roughness height and dimensionless roughness spacing may be conveniently defined as ε /D0 and λ /D0, respectively, where ε and λ are the amplitude and wavelength of the sinusoidal wave function for the surface shape,[389] respectively.
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During impingement on a flat surface (Fig. 3.13), a single droplet spreads uniformly in the radial direction from the impingement point as a thin liquid film, maintaining spherical shape at its top end. It eventually forms a thin, flat splat. The liquid that makes up the portion of the droplet that first impacts the surface ends up at the periphery of the splat. The spreading is fast initially, and the radial spreading velocity of the liquid may be as high as two to three times the impact velocity. The spreading rates decrease monotonically
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During impingement onto a non-flat, waved surface (Fig. 3.14), a single droplet spreads along the surface and eventually forms a thin, non-flat splat. Unlike the spreading behavior on a flat surface, the spreading rates on a non-flat surface do not decrease monotonically with time, but instead, exhibit a periodic repetition of a de- crease-increase pattern (Fig. 3.15). The spreading of a droplet is fast when the liquid spreads from the top to the bottom of the sinusoidal wave (acceleration effect of surface). It slows down when the liquid spreads from the bottom to the top of the sinusoidal wave (deceleration effect of surface). If the wavelength of the surface is larger than the droplet diameter, the spreading process exhibits a periodic repetition of the acceleration-deceleration mode as the surface shape changes periodically, and ends when a violent breakup of liquid occurs (Figs. 3.14 and 3.16). If the wavelength of the surface is smaller than the droplet diameter, the surface hinders the droplet spreading (hindering effect), and the droplet breaks up and ejects from the surface in an irregular manner (Fig. 3.17). For Reynolds numbers ranging from 300 to 30000, the dimensionless deformation time changes from about 2.4 to nearly 3.6, and the dimensionless final splat diameter varies from about 2.8 to nearly 7.1.
It should be noted that the dynamic conditions of droplet impact processes discussed above cover a large range of the actual conditions in many industrial processes, such as spray forming, thermal spray, spray combustion, spray cooling, and aircraft flight. Under these conditions, the spreading behavior of droplets on a flat surface is essentially governed by inertia and viscous effects (Fig. 3.15). The surface tension effect on the deformation dynamics is not significant under these conditions (Fig. 3.18). However, with decreasing Weber number, surface tension force may become increasingly important to droplet deformation process. The effect of surface tension lies in that it makes the leading edge of the thin liquid film (splat) more rounded, and slows down the liquid velocity in the region of the leading edge.[335] This may cause some separation of the liquid edge from the surface.[371] It has been observed in experiments with high surface tension liquids[43] that splat edges indeed
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occur even during normal impact on a smooth, dry substrate surface if the droplet impact velocity exceeds a threshold value,[396] and/or the droplet undergoes a phase change during the impact process.[390] Detailed sequences of droplet splashing on a solid particle and liquid droplet, in shallow and deep pools have been presented by Liu et al.,[18][389] and Harlow and Shannon,[397] respectively.
In addition to the impact surface conditions, the fluid dynamic conditions of a droplet may also determine if the droplet will splash during impingement. To distinguish pure spreading from splashing, many studies have been performed with water or other normal liquids on dry, wetted and liquid surfaces,[396][398][399] and with liquid metals (Pb and Sn) at different impact angles on non-flat, dry, metal surfaces of different roughness values under a variety of dynamic and geometry conditions.[400] These studies showed that the amount of splashing mass increases with increasing impact velocity, droplet size, and roughness height of the impact surface. A large surface roughness corresponds to an earlier and more violent breakup of impact droplets and bounce-off of secondary droplets. The influence of impact angle on the amount of splashing mass did not appear to be significant under the experimental conditions,[400] although the impact angle may affect the final splat geometry.[401][402] The dependence of the number of secondary droplets on surface tension seemed to be week as well.[393][396] The splash limits for normal and oblique impact of molten metal droplets on different surfaces have been identified on the basis of experimental observations.[400] Generally, the correlation between the Weber number and Ohnesorge number according to Walzel[398] may be used to delimit the regimes of droplet spreading and splashing on a dry, solid surface in a We-Oh map (Fig. 3.21):
Eq. (43) |
We = 7.9 × 1010 Oh2.8 |
If the fluid dynamic conditions of a droplet are within the spreading regime, i.e., below the threshold curve in the We-Oh map, liquid splashing and ejection from the impact surface can be eliminated. The corresponding threshold velocity can be written as:
