Droplet-Wall Collisions_ Experimental Studies of the Deformation and Breakup Process

Int. J. Multiphase Flow Vol. 21, No. 2, pp.151 173, 1995 Perga,.o. 0301-9322(94)00069-7 Copyright !~ 1995ElsevierScienceLtd Printed in Great Britain.All rights reserved 0301-9322/95 $9.50+ 0.00 D R O P L E T - W A L L COLLISIONS: E X P E R I M E N T A L S T U D I E S OF THE D E F O R M A T I O N A N D B R E A K U P PROCESS CHR. MUNDO, M. SOMMERFELD and C. TROPEA Lehrstuhl fiir Str6mungsmechanik, Universitfit Erlangen-Nfirnberg, Cauerstr. 4, 91058 Erlangen, Germany (Received 3 April 1994; in revised form 1 October 1994) Abstract--Experimental studies of liquid spray droplets impinging on a flat surface have been performed with the aim of formulating an empirical model describing the deposition and the splashing process. Monodisperse droplets with a known viscosity and surface tension, produced by a vibrating orifice generator, were directed towards a rotating disc and the impingement was visualizedusing an illumination synchronized with the droplet frequency. A rubber lip was used on the rotating disk to remove any film from previous depositions. The test matrix involved different initial droplet diameters (60 < do < 150~m), velocities (12 < w < 18 m/s), impingement angles (4° < ~ < 65°), viscosities (1.0 </1 < 2.9 mPas) and surface tensions (22 < a < 72 mN/m). The liquids used to establish the different viscositiesand surface tensions were ethanol, water and a mixture of water-sucrose-ethanol. One major result from the visualization is a correlation of the deposition splashing boundary in terms of Reynolds number and Ohnesorge number. Noteworthy is that a distinct correlation between the Re and Oh number, K = Oh. RC 25, is only achieved if the normal velocity component of the impinging droplets is used in these dimensionless numbers. For the case of a splashing droplet, a two-component phase Doppler anemometer was used to characterize the size and velocity of the secondary droplets. The obtained droplet size distributions and correlations between droplet size and velocity around the point of impingement constitute the basis of an empirical numerical model. Key Words': spray systems, droplet-wall interaction, impact models I. I N T R O D U C T I O N The fluid mechanics of spray droplets i m p i n g i n g on a rigid surface is of great i m p o r t a n c e in m a n y different technical applications, including thin film coatings, spray painting, spray coating, injection systems a n d in the spraying of m o l t e n metal for the p r o d u c t i o n of semi-finished articles with a special metallurgical structure. A l t h o u g h n u m e r o u s studies have been performed in the past on d r o p l e t - w a l l interactions, most of these are qualitative in nature, o b t a i n i n g i n f o r m a t i o n from the visualization of droplet i m p i n g e m e n t a n d d e f o r m a t i o n . A short s u m m a r y of previous studies is given in the following section. In general there are two possible outcomes of droplet i m p i n g e m e n t on a solid a n d dry surface, each of which m a y be desirable for a particular application. O n the one h a n d the droplet may deposit on the surface a n d form a liquid film. F o r more energetic impacts however, the droplet splashes a n d secondary droplets are formed. Some general correlations exist describing this d e p o s i t i o n - s p l a s h i n g limit a n d its governing parameters, however virtually no i n f o r m a t i o n exists describing the size a n d velocity distributions of the secondary droplets a n d the splashed mass fraction with reference to the i m p i n g e m e n t parameters. This i n f o r m a t i o n is, however, essential if d r o p l e t - w a l l interactions are to be modelled with the intent of i n c o r p o r a t i n g such models into an E u l e r i a n - L a g r a n g i a n a p p r o a c h for calculating two-phase flows. The goal of the present investigation is to provide such i n f o r m a t i o n in a form suitable to formulate empirical models o f the d r o p l e t - w a l l interaction. F o r this purpose the secondary droplets m u s t be measured in size, c o n c e n t r a t i o n a n d velocity. Therefore, a phase D o p p l e r a n e m o m e t e r ( P D A ) has been employed, in a d d i t i o n to more traditional visualization techniques. F o l l o w i n g a brief literature review of previous experimental studies, some theoretical considerations of the d r o p l e t - w a l l interaction are given in section 2. In particular, dimensionless analysis uMv2~ 2-B 151 152 CHR. M U N D O et a l can help to identify important governing parameters and also guide the layout of the experimental equipment and procedures. Details of the experimental equipment are given in section 3 before presenting the measurement results in section 4. A summary of the most important conclusions is given in section 5. 1.1. Previous investigations of droplet impact on surfaces The outcome of a droplet impact on a solid surface depends on the properties of the liquid, the surface conditions and the kinematic parameters, i.e. velocity and momentum. Following the Buckingham II-theorem, the number of independent parameters can be reduced by the number of fundamental dimensions which are present. Usually the remaining number of parameters which are important for a particular experiment is, however, relatively large. Therefore, it is often difficult to obtain simple relations from dimensional analysis and results reported in previous investigations are often not comparable to one another. Nevertheless, the major dimensionless groups governing droplet impact include Reynolds number Re - #do wo [I] Ohnesorge number O h - ,~pfP~d0 ,tl [2] and surface roughness S~ = R~ d(~ [3] where p, g and ~r are the liquid density, the viscosity and the surface tension for a fluid-air interface. Furthermore, do is the initial droplet diameter and R~ the mean roughness height of the wall surface. Note that the droplet initial velocity w0 used in the Reynolds number is the component normal to the surface. The Weber number is also commonly used We = (Oh. Re) 2 - pd~,w~ O" [4] as well as the Bond number Bo - dopg O" [S] where g is the gravitational force, in cases in which a film on the surface may have an influence on the impact event. Previous investigations which have been performed on droplet impingement on surfaces may conveniently be divided into three main groups (Rein 1992): • Investigations of droplet impingement on heated surfaces, in which the temperature is above the evaporation temperature of the fluid. • Investigations of droplet impingement on cold surfaces. • Investigations of droplet impingement on films. 1.1. I. Impact on heated surfaces. Obviously the most important technical application in this area is the spray cooling of hot surfaces and the impingement of injected fuel droplets onto the heated surfaces of a combustion engine. The early work by Wachters & Westerling (1963) considered the heat transfer of single droplets impinging on a heated surface. They determined the heat flux and evaporation rate for surface temperatures above the evaporation temperature. Furthermore, they found that, for low Weber numbers of the impinging droplet, the droplet could experience a reflection from the surface, as indicated in figure 1. This can be explained by the vapour layer, which is generated due to the sudden evaporation of the liquid immediately above the solid surface, and which expels the droplet from the surface. These observations were supported by the investigations of Anders et al. (1993) who observed a reflection of a sequence of 90 # m droplets on a heated surface for a small velocity .. Stow & Hadfield (1981) tried to evaluate the size distribution of splashed droplets more precisely than Levin & Hobbs (1971). .. If the kinetic energy of the primary droplets was high enough. Using the Buckingham II-theorem he obtained a set of two non-dimensional parameters which determine whether splashing or deposition took place.00.. Weiss (1993) found similar relations for droplets impinging on a surface film with a high repetition frequency. the droplets were deformed during the impact but splashing did not occur. 60. .00'.6 .00 O 63 O 0 2. . viscosity and density) and kinematic parameters (velocity normal to the wall and diameter). the droplets splashed into secondary droplets. ' . Chandra & Avedisian (1991) employed photographic measuring techniques to evaluate the deformation stages of a single droplet impinging on both heated and unheated surfaces at low Reynolds numbers.. .00. ' . . ...DROPLET-WALL COLLISIONS [ 53 8. Impact on unheated surfaces.. For evaluating the diameter distribution of the splashed droplets only those droplets greater than 50/~m in size could be counted. They used photographic emulsion paper on which the splashed droplets were collected. . 16 .1. . . . . When the kinetic energy was relatively low..2. They found that the splash-product sizes were distributed according to a log-normal distribution function and that the number averaged diameter was about 10% of the primary droplet diameter. 40.. The number averaged diameter was between 10 and 20% of the primary droplet diameter. '60 .00 0 0 8 0 8o 0 0 O ~4. For higher Weber numbers the droplet was deformed and the reflection velocity vector decreased. . . Levin & Hobbs (1971) used a copper hemisphere on which water droplets of about 2.00 6. one finds that an increase of the surface tension led to an increase of the size of the generated droplets. due to the insufficient resolution of the photographs. The non-dimensional parameters include fluid properties (surface tension. Walzel (1980) analysed the splashing of wate~glycerin mixtures on dry and wetted surfaces. component normal to the wall. 1.00 Weon Figure 1. For Weber numbers above a critical value. .9 mm in diameter impinged at a low velocity normal to the surface. '2'6'6o • . Often this sheet was unstable and tiny droplets appeared at its upper rim. This occurrence was called corona formation. Bolle & Moureau (1982) extended these investigations to polydisperse spray-wall interaction. . increasing the resolution to droplets smaller than 50/~m. Relationship between the normal velocity components at arrival and departure for a droplet impinging on a heated plate (Wachters & Westerling 1963). and that an increase of the diameter of the primary droplets also led to an increase of the size of the splashed droplets. In this case. the fluid was completely deposited on the surface. Comparing the results for different impingement conditions.. then the droplets were deformed to a cylindrical sheet that rose around the point of impingement.00 0 c 0"000. . . 8 ' 6 ' 6. . the influencing parameters were not varied in a wide range to obtain an empirical model or a numerical model that could be implemented into a two-phase flow simulation code. M U N D O et al. In section 4. one can conclude that an attempt was made to characterize the outcome of the splashing. be obtained solving the Navier-Stokes equations. For the case that . Foote (1974) solved the equations with the Marker-and-Cell-method (MAC) and obtained a solution for low Re and We numbers for the impinging primary droplet. However. Deformation process A full description of the fluid motion during the impact and the deformation process can. + [81 before impact and mass conservation m = after impact m' [9] have to be solved.154 C H R . indicating that a second size fraction was generated by the impact. the droplet-wall collision has not been simulated. 2.2 it will be shown that the data of Schmidt & Knauss (1976) agree well with the correlations found in the present study. Van der Geld & Sluyter (1987) used the collocation method to determine the motion of discrete surface points of a droplet that rests on a surface with w0 = 0. with a deformation that leads to a corona and subsequent breakup. Impact on fluid films. Here. The background of these experiments was the atomization of molten metal which is used for metal products with a special metallurgical structure. The investigations of Jayaratne & Mason (1964) show that for very low impingement m o m e n t u m (and therefore low Weber number normal to the wall). For the case of higher Re and Oh numbers. E~ and Ed are the kinetic. Ozdemir & Whitelaw (1992) investigated the spray impingement on an unheated surface covered by a fluid film and found that the impact on the wall generates a new fraction of larger droplets which are spattered out of the liquid film. Brunello et al. T H E O R E T I C A L APPROACH 2. o [6] x/We d~' [7] Schmidt & Knauss (1976) investigated the splashing of mercury droplets in a rotary atomizer.3. (1991) investigated the impingement of a spray for a defined inclination angle with respect to the surface using a phase-Doppler anemometer. surface and dissipated energies. In principle the equations of energy conservation + + = + e.1. water droplets can rebound from a water surface. and a number of authors have numerically studied the deformation of an impinging droplet on this basis. Deposition-splashing of the droplet Another i m p o r t a n t .2. potential. Ep.. In their experiments they showed that the size distribution of splashed droplets depended on the inclination angle of the primary spray. In recent years the development of laser-diffraction and laser-Doppler measuring techniques have provided an opportunity to measure both the velocity and the size of spray droplets. respectively. They found a bimodal diameter distribution in the vicinity of the wall. 1. 1. and m and m ' are the mass of the droplets before and after impact. Summarizing the studies on droplet-wall interactions performed by various investigators. Hardalupas et al. Ek. (1991) measured the droplet size and velocity distribution of a fuel spray near the surface of a disc. in principle. + e. 2. d* - dopa p2 Wop.a n d maybe easier--problem to solve is the quantification when breakup or complete deposition occurs. because the velocity distribution inside the deforming droplet is not known. [I 6] Re 2 _ 4 . as sketched in figure 2. it becomes zero at the maximum extension of the liquid on the surface. The dissipated energy is very difficult to determine. 7F [12] The contact angle ® is defined using the tangent line at the liquid gas interface at the point where the meniscus begins. introducing the Re and We numbers with /~m. surface tension and diameter of the impacting droplet.v ~dV dt ~ @ V t e.~= d~.~ -Introducing the Ohnesorge number Oh = ~ / R e Oh=q yields Re [17] We + 4 ) = 0. . is estimated by te ~ do/wo. Combining [8]-[15].DROPLET WALL COLLISIONS 155 E~ ~ E k + Ep + E~ splashing does not occur and complete deposition of the fluid mass takes place. for the case that a corona is not formed and full deposition takes place. do are the liquid density. the surface energy can be described as (Chandra & Avedisian 1991) E~ = -4 d?~. 5 f l 4 / h/ gas / F i g u r e 2. The kinetic and surface energy before impact can be described by Ek = ~ 1 pL Wond6 2 3 [10] E. At the maximum extension diameter d.~/do and E o = E~ the following equation for the splashing-deposition boundary is obtained R~ fl 4~x + (1 . The kinetic energy upon impact is expended in deforming the droplet and. The volume of the fluid V when it is flattened out in the shape of a disc is 7~ V~d~. a. [11] where PL. the time for deformation.~ax. Chandra & Avedisian (1991) used a very simple model to determine E~ E'd = f0. [13] The dissipation per unit mass of the fluid is given by @=p ~¢.cos ®). = nd~a.cos ®)fl m.xh E15] where h represents the height of the disc. D e f i n i t i o n o f the c o n t a c t a n g l e O.~a (1 . + ~ x i~/~ [14] where te. A vibrating orifice generator (TSI Model 3450) was used to generate a stream of monodisperse droplets (Berglund & Liu 1973). The geometrical factor /~m~xand the contact angle ® are constant for a given fluid and surface material. Schematic overviewof the test rig. The outflowing jet was perturbed by a piezo quartz actuator acting on the orifice plate in the frequency range of 28 65 kHz. . as expected from the dimensional analysis.. E X P E R I M E N T A L S E T . The droplets were formed by forcing liquid through an orifice of 50 ~m diameter. Rotating Disc ... The normal component of the velocity remains independent of the disc rotational speed and is determined by the operating conditions of the droplet generator.3 39. This theoretical approach will be compared to the measured splashing-deposition data presented in section 4.. the impingement and deformation process of droplets on a rigid cold wall has been investigated by directing a stream of monodispersed droplets towards a rotating disc. Apparatus A schematic diagram of the experimental set-up is shown in figure 3. • A rotating disc with which the circumferential velocity can be varied in the range of 1.tr--n o o o ] Power Supply Speed Control Figure 3. 3.3. The rotational speed of the disc determines the effective collision angle and the velocity of impingement. and mean velocity w0 of the monodispersed droplets after disintegration can be evaluated using [18] and [19] do=3 / 6 0 x/~J dsyringc [18] [19] /I'0 ~ [?syringe dorific ¢ Piezo-(" . otherwise the fluid droplet will deposit completely on the surface.M o t o r Q) ~ ] [ ] Droplet-Generator I .U P In the present investigation. 1. Equation [17] determines the splashing deposition boundary as a function of the Ohnesorge and the Reynolds numbers of the impinging droplet.3 m/s. For an Ohnesorge number above the value given in [17] splashing will occur.150 t~m and a repetition rate of 28 65 kHz. 3. The mean diameter d~.156 C H R MUNDO et al. • A rubber lip to remove the film of fluid that was deposited on the surface. This equation confirms that the deposition-splashing depends only on the Re and Oh numbers. leading to perturbations of a defined wavelength and thus to a jet disintegration at a defined frequency and with a defined droplet volume. The main components are: • A droplet generator which produces a stream of monodisperse droplets in the size range of 60. pictures were taken with a Canon T90 camera (film: K o d a k Tmax 400). Co-ordinate system.5 mW/sr at a dominant wavelength of 2 = 637 nm (red light). The repetition rate for the C C D camera readout was 50 Hz. the impingement occurred at a distinct impact angle and at a distinct impact velocity which was dependent on the rotational speed of the disc. droplets of 100/~m diameter and a velocity of I0 m/s could be measured with a spatial resolution of r s = woAt/do = 5%. The L E D (Hewlett-Packard Type HLMP-8150 15 Candela) was triggered at the frequency of the droplet generator (28-65 kHz) with a pulse duration of 500 ns. so that the vertical and tangential velocity components of the impinging and reflected spray droplets could be measured. this measuring technique gave an integral view of the deformation process.86). 3. The camera was equipped with a 90 mm f4 macro lens and an extension bellows. R. The co-ordinate system and the definition of the velocity components is shown in figure 4. A non-dimensional roughness number can be defined as St = Rt/do (disc 1: St = 0. so that each frame consisted of 560-1300 events. For determining the boundary between droplet deposition and splashing a visualization technique was used. Therefore. velocity vectors -Vo coordinate s y s t e m Y w C V0 Figure 4. Therefore.8/~m) and disc 2 had a roughness height in the range of the impinging primary droplet diameter (i.DROPLET WALL COLLISIONS 157 where Q is the total volume flow rate defined by the feed syringe velocity Vsyring¢ and the diameter dsyring e and f is the piezo quartz actuator frequency. 3.2. Instrumentation 3. The rise time of the LED-light pulse was determined as Az = 45 ns. The technical data of the PDA are summarized in table 2 and in the user's manual (Dantec 1992).c a m e r a (Type Hitachi KP-M1) with a high spatial resolution of 756 x 581 pixels was used for acquiring the pictures.1. In figure 5 the surface profile of the two discs is shown. The maximum intensity of light of the L E D was 423. For qualitatively analysing the outcome of a splashing collision a commercially available two-colour phase Doppler anemometer (PDA) was used. each video frame represents an average over many single droplet impacts all at the same impact phase. From this videotape. The surface temperature of the disc was kept constant at 25°C. Visualization techniques. A C C D .e. The PDA was aligned normal to the plane of impingement. . Therefore. Phase Doppler measurements.e. The instrumentation set-up is shown schematically in figure 6.2. The experimental test conditions are summarized in table 1. Statistical fluctuations are eliminated or blurred on single frame pictures. This stream of droplets impinged on a rotating disc made of stainless steel.03. Rt = 78/~m). Therefore. The impact angle ~ is defined as the angle between the absolute velocity vector and the normal on the surface. This visualization technique synchronizes an illuminating L E D with the droplet impact. disc 2: St = 0. = 2. Two different rotating discs were used during the experiments. The pictures from the CCD-camera were recorded using a SVHS-videorecorder (Panasonic).2.2. Disc 1 had a technically smooth mean roughness height (i. .3 × 10 ~-5..00 -50. T a b l e 1.3 .00 -150. MUNDO et aL a) 10.... ..--velocity component Re n u m b e r We number Oh number Frequency -mPas mN/m kg/m ~ t~ m m/s ---k Hz Test rig M a t e r i a l o f the disc Size o f disc v0--velocity component Impact angle -mm m/s Stainless steel 150 9 30 4..0 2000...00 200.00 100.158 CHR..00 -250.1~55.00 O -I00.00 50. .. [.00 0...00 -10...00 0.18 195-2694 94-2204 6.0 1000. S u r f a c e profile o f disc I (a) a n d disc 2 (b)...0 ..4 × 10 2 27.00 5.0 Length (tzm) b) 250..00 -200.4 water-ethanol sucrose 1-2..0 1500..0 Length (/zm) F i g u r e 5.00 CD 0 0.00 150.0 20000.. 500....0 10000.9 22 72 7 8 9 998 60-150 12.........00 0..00 ~ -5. Test c o n d i t i o n s Generated droplets Fluid Viscosity Surface tension Density Diameter w0. I . I ..2-64. 86 for disc 2. indicating that the surface roughness is negligible in the case of the smooth surface.8 240 . 4.03 for disc 1 and 0. .1. . whereas in the case of the rough surface a strong influence is expected. P D A transmitting.37 55.1. Table 2.10 -.17. . . . . receiving optics and measurement range Transmitting and receiving optics Laserpower Wavelength Vertical component Horizontal component Focal length of the transmitting optics Focal length of the receiving optics Diameter of the measured volume Measurement range Focal length Droplets: Refractive index Diameter range w velocity v--velocity mm -/lm m/s m/s 310. .5 488. . .45 52. . RESULTS 4. . . High Reynolds numbers : figure 7 shows a photograph of droplet splashing on disc 1. but also on the ratio of the surface roughness compared to the droplet diameter. The non-dimensional surface roughness number St is 0. spreading and splashing of the droplets depend not only on the kinematic and fluid parameters of the primary droplets. . . 4.306 1. . Smooth surface. . . .367 13~307 18. the results for the smooth and rough surfaces are discussed in different sections.8 1.35 mW nm nm mm mm /~m 400 514.1 310.DROPLET-WALL COLLISIONS I59 CCD Camera Extension Bellows Macro Lens V] LED [ / . . . Therefore. averaged over many individual events at the same phase. Schematic overview of the experimental instrumentation for visualization. .8 309. 1. . iPmOipltn~ment L_I I~ I ooo Connected to the Piezo Quartz I 188MRRRB ~1 Q~) I oo I IZZ] --[I Monitor Videorecorder Droplet Generator Frequency Generator Time Delay Unit Figure 6. . . In figure 8 the derived schematical view of the splashing process is shown. . Visualization of the deformation process The deformation. 0.160 CHR. Figure 11 shows the splashing of a droplet with Re = 589.0492.9 and Oh = 0. Once the lower half of.0518. respectively. K . disc 2 with a surface roughness approximately equal to the diameter of the primary droplets was used. Furthermore. effective angle of impingement ~ 36 . as indicated by the dark area. MUNDO et ~tl. Rather. Low Reynolds numbers: The deposition of a droplet on a rough surface at low Reynolds number (figure 12) is similar to the deposition process for the technically smooth surface. . the nature of the surface target is an important factor in determining the outcome of a splashing event. the total volume flow rate into the wall film begins to decrease.153. also now has less fluid feeding the film and hence becomes thinner. A corona around the deforming droplet is formed and grows in time as the droplet fluid continues to feed the film. the liquid film spreads around the point of impingement.2. High Reynolds numbers: as pointed out by Weiss (1993). the concentration of the secondary droplets is much higher in front of the impingement point. Splashing of a liquid droplet with Re . O O Figure 7. To investigate this effect. Obviously the surface roughness in this range does not promote the splashing of the primary droplet. The high tangential momentum of the incident droplet leads to a sudden and rigorous disintegration into secondary droplets. An instability develops and leads to a circumferential wreath which propagates upward in the corona and finally results in a disintegration into secondary droplets.5and S~. the kinetic energy necessary to overcome surface tension and gravity to form a corona is dissipated during the deformation process. having been stretched in its radial expansion. ~ ~ o o o o Figure 8. in which the kinetic energy of the droplet is dissipated in the deformation process. a liquid film spreads outwards.0518. indicating that the time for the formation of the corona is much larger than the time for the deformation of the primary droplet. 4.598. 1. Rough surface. Oh = 0. but there is not enough momentum normal to the wall to form a corona. Hence the time evolution of the deformation process is recognizable in a single frame. As the droplet touches the surface. The deformation of the droplet upon impact is much more irregular than in the case of the smooth surface. The deformation process can be summarized as follows. At low Re numbers. Thus the corona. the droplet has undergone deformation. Low Reynolds numbers: figure 9 shows a sequence of photographs describing the steps of the droplet deformation at a Re and Oh number of 215.4 and 0. Three coronas are visible on the frame. demonstrating the high repeatability of the deformation process. A number of secondary droplets appear behind the impact location as a result of the surface roughness.03 on a smooth surface. A corona and the associated instabilities before atomization are no longer identifiable. The corresponding schematic view of the deposition process with respect to time is presented in figure 10.8. Schematic view of the splashing process. S c h e m a t i c view o f the d e p o s i t i o n process.86 o n a r o u g h surface. effective a n g l e o f i m p i n g e m e n t ~¢ = 3 6 .0492.DROPLET WALL COLLISIONS 161 F i g u r e 9.7 leads to incipient splashing. K = 153.4. ~Y//////////7///Y/////~7~/. O h . whereas K less than 57. 4. F i g u r e 10. F i g u r e 11. A remarkably strong correlation can be observed and is given by the relation K = Oh Re E2s.3 a n d S~ = 0. .5 a n d S~ = 0. D e p o s i t i o n o f a liquid d r o p l e t w i t h Re = 251.8. O h = 0. the influencing factor is the momentum of the primary droplets in the direction normal to the surface and not the total momentum vector. Correlation o f the splashing and deposition event in terms o f the Oh and Re number The observed limits of deposition and splashing for both the smooth and the rough surface can be correlated in terms of the Re and Oh numbers. A value of K exceeding 57.0. as illustrated by the results presented in figure 13 (Mundo et al. 1993b). The strong correlation shown in figure 13 indicates that in the case of splashing. S p l a s h i n g o f a liquid d r o p l e t w i t h Re = 598. K = 49. This indicates that the same physical process is responsible for the generation of the secondary spray.0518. effective a n g l e o f i m p i n g e m e n t 2 . The boundary line which separates deposition and splashing is parallel to the line that describes the decay of a liquid film from a nozzle. the so-called Ohnesorge line (Ohnesorge 1936).2.7 leads to complete deposition of the liquid.3 6 ' .03 o n a s m o o t h s u r f a c e . 7: S p l a s h i n g ~ "- "-.0 h = 1 3 2 ... described briefly in section 3.2 [17]. Comparison with the theoretical approach The correlation for incipient splashing obtained in figure 13 can be compared with the theoretical approach presented in section 2. 2 5 ) 0 h n e s o r g e K=Oh Re .~ to the diameter of the primary droplet do must be evaluated.3 a n d S. ++'~-e 2 \ I / 0. = dm~. However.7: D e p o s i t i o n K=57. .l .162 (HR.2s K<57. = 0. This relation matches the experimentally obtained correlation very well for Re numbers above 150. K = 49.3. O h = 0. Splashing K increasing 7~ region " "4{--V~+~"m. Additionally the theoretical correlation deviates from the experimentally obtained correlation for Re > 2000.7: I n c i p i e n t Splashing K>57.001 Deposition region i i i J l r l ~ t i i ~ i ill I i i J i i ill I i i 10 100 1000 Re (-) 10000 Figure 13. 4.4. ~ 2.3 (Mundo et al. 2 5 ) C o r r e l a t i o n --. For Re numbers less than 150 the solution of [17] becomes irregular..~/d. Limits lbr splashing a n d d e p o s i t i o n o f p r i m a r y droplets.n.2. M U N D O et ul. 4. r measurements The secondary spray that occurs due to the splashing at sufficiently high K numbers was measured by means of a phase Dopper anemometer. " .. 7 0 Re e x p ( .2..1 . 1993a). effective angle o f i m p i n g e m e n t x = 36 . In figure 14. From the measurements this was determined with fl.4.1 0 0. [17] for these parameters is shown as "theoretical approach". D e p o s i t i o n o f a liquid d r o p l e t with Re = 251. The contact angle does not necessarily have to be the equilibrium angle. Phase Dopph. indicating that for low Re numbers the assumption for the dissipative term in the momentum equation is not appropriate.01 0.86 on a r o u g h surface.. Figure 15 ooooo Splashing: Measurements []rq[][nn S p l a s h i n g : S e h m i d t & K n a u s s (1976) zxt~zxLxzxS p l a s h i n g : Walzel (1900) [ [ I t ~ Deposition: Measurements xxxx× Deposition: S c h m i d t & Knauss (1976) 0 h = 5 7 . Figure 12.0492. but it is considered to be fixed at ® ~ 75'. 3 Re e x p ( . to solve the equation the relation of the maximum diameter d. Schmidt (1976) Breakup: P.259) 1 ~ 0 region I 0. .01 0. This was done by computing the autocorrelation function [20] of the secondary droplet velocities and sizes over 50..50 mm 0. .000 samples. indicates the matrix of measurement locations around the point of impingement in order to characterize the spatial distribution of the secondary spray... a (z) = (z (i) -.DROPLET-WALL COLLISIONS 163 ooooo ODODO annna +++++ xxxxx . The result reveals that for both Measurement Volume 0. the size distributions of the corresponding three measurement positions were averaged in their number distribution weighted with their rate of events. Breakup: Measurements Breakup: P. The measured autocorrelation functions.2 Breakup Re exp(-l. This is in contrast with conventional autocorrelation functions.001 Deposition region 1oo 1o'oo .£ ) a"2 [20] Note that the autocorrelation was performed over the sequence of droplets as they arrived in the measurement volume. Oh = 132. . independent of their arrival time.1 o o 0 " " ~ °°~ ~o 0 0.~)(z (i + Ai ) -.50 mm ~ © O O © / Figure 15. In estimating the statistical reliability of the measured distributions first the statistical independence of individual droplet samples was investigated. in which a time lag is used as an abscissa.Walzel (1980) Depositlon: Measurements Deposition: P..Schmidt (1976) Theoretical approach . Re (-) Figure 14. Measurement locations for the PDA measurements. For obtaining a size distribution in front of and behind the point of impingement. Empirical and theoretical correlations for incipient splashing. . using the velocity or size of the secondary droplets is given in figure 16. . velocity components each individual droplet is statistically independent since the autocorrelation function approaches zero at about two samples. A comparison of the size distributions obtained in front of the point of impingement with those behind the point of impingement reveals only minor differences.00 --0.40 -0.20 C H R MUNDO et al. water. ~2=1( -N ) [2l] where c is the normalized standard deviation. For completeness. a minimum number of samples must be measured as given by. with the latter leading to slightly smaller mean size statistics.00 5. 40.~.124 Diameter 1. The distributions in figure 17 and the derived size statistics dr0. Re L25=4 / P N / 0"2// [-° 3d 3u 5 [22] The droplet size distribution has been normalized with the diameter of the primary droplets. ~0 and d32 are shown in figure 18. a~ is the standard deviation of the measured quantity.4.i.212 Minimum number of samples for ~ = 1% r--velocity component 6420 w--velocity component 2652 Diameter 1782 .106 w velocity component 1. water-sucrose-ethanol) are summarized in figure 17.1.i 0. .164 1.x/Re=Oh.00 20. . ethanol.000 samples were measured. [22] shows the parameters influencing the K value.80 a(-) 0..~. Autocorrelation function for the secondary spray. Results of the statistical analysis Number of samples over which an integral correlation exists v--velocity component 1. For a statistically reliable distribution with a deviation of 1% therefore.00 Samples (-) 15.00 i0. K= ~ee . Smooth surface: the size distributions corresponding to different values of the parameter K between 133 and 186 for three different liquids (i. These indicate that especially the larger secondary droplets are absent at higher K values. diameter 0.. Z is the mean value of the process and N the number of samples. --==e-.qt~l~. 4.e.40 ~t~t~l~tf~J. associated with a decrease of the mean particle size. . Table 3 summarizes the results of this statistical analysis and the required minimum number of secondary droplet observations. The result indicates that the size distribution of the secondary droplets becomes narrower with increasing K value. . In the present investigations a minimum number of 10.v-velocity w-velocify .00 Figure 16. Diameter distributions.. Table 3. The mean diameters shown in figure 20 vary only slightly with K... ..~Z_~---:-Z ... both in front of and behind the impingement point. Rough surface: in figure 19 the size distributions of secondary droplets are shown for the rough surface (i. determines the distributions.5 891. r . .....9 .6 We 620. . indicating that the normal and tangential momentum of the primary droplet is almost directly transformed into surface energy in the case of a rough surface. . .. • .80 1..5 186. = 0.00 0.2 147. .2 1182... Secondarydroplet diameter distribution for the smooth surface (a) in front of and (b) behind the point of impingement._ 0. a) 15. ~:. 10. As described in section 4.20 0.. roughness factor S. Similar trends are observed for an increase in the viscosity of the liquid.00 0..00 . ~..00 0.... .0 5.....2 147.oo K 133. .40 d/dprim 0..5 891. .80 1. .6 We 620..e.. . . .. ....00 (-) b) 15.00 I **~* . K 133.~.DROPLET-WALL COLLISIONS 165 Increasing the surface tension results in a smaller K value and therefore a narrower size distribution.. .2 11[}2.9 162. a splash corona could not be observed for the rough surface.~-'Z2-.2..86).60 0.. 162.00 0.60 0.20 0.00 (--) Figure 17.. In this respect the splashing phenomenon resembles the decay of a liquid sheet (Lefebvre 1989).00 K-Value of t h e p r i m a r y d r o p l e t s ~=~= .40 d/dprim 0. . .0 5.1 579.. but that the non-dimensional surface roughness number S...1.. The distributions show only minor differences for an increasing K value.00 K-Value of t h e p r i m a r y d r o p l e t s ~=~== T io. .. The disintegration of the droplet appears to be more immediate.1 579.00 0. This indicates that the fluid properties and the kinematic parameters are not the most influential factors for the size distributions. .5 186. 00 ~ . 4..166 CHR.. Smooth surface: figures 21 and 22 show the orientation and length of the velocity vectors for three size classes of the secondary droplets for a K number of 131.. For formulating a statistical model of the droplet-wall impingement it is also necessary to determine the velocity of the secondary spray.. Characteristic m e a n d i a m e t e r s for the s m o o t h surface (a) in front of and (b) behind the point of i m p i n g e m e n t .00 180.00 b) aooco dlo/do 0.40 0.. both incident and reflection angle are measured with respect to the normal on the surface).4.00 ~ ..00 180. MUNDO et ~d..00 140... 36 ° and 65 ° impingement angle) are presented.80 d~oXdo ¢ ¢ ~ ~ 0 ds2/do ~0.... 140. The momentum of impingement is partially conserved and determines the flight a) dto/. The orientation of the velocity vector of the secondary spray depends strongly on the incident angle of the primary droplet.2.e.. Velocity distributions.e.. and a large incident angle leads to a large reflection angle..00 K (-) Figure [8.00 K(-) 160.do cocoo :~aaa 0. The most important result which can be obtained from figures 21 and 22 is that a small incident angle of the primary drop leads to a small reflection angle (i..00 II~llll~lll~ll11~qllltLtlllll 120.. ... therefore the outcome of two impact conditions (i.do = = = c = d~o~..00 ..80 ¢¢~¢0 d ~ / d o "'• 0... 160.40 0. Therefore.. 120. in this section the velocity distributions are investigated in a plane that includes the impingement and reflection velocity vector. .5 186.2 147. . . the flight direction does not depend strongly on the size of the droplets.5 779.. .00 ... The velocity distributions for three impact angles and various K values are summarized in figure 23 for the two velocity components.. Moreover.00 0. The velocity components are presented in non-dimensional form to obtain comparable results for a) 15.00 0. .00 d/dpri~ b) 15.20 0. .10. r. . .20 "r .. 0. .. expressed by the K number as a function of the Ohnesorge and Reynolds numbers.60 0. since the orientation of the velocity vectors are similar for the three size classes. ..00 d//dprim (--) Figure 19. On the other hand. . . .9 162. . The reflection angle of the secondary droplets as a function of the impingement angle of the primary drop for a variation of the impact angle is summarized in figure 24. . . the fluid properties.DROPLET-WALL COLLISIONS 167 direction of the secondary spray.. .40 0. From a least square fit a linear correlation can be determined. . . 0..2 1182. Secondary droplet diameter distribution for the rough surface (a) in front of and (b) behind the point of impingement.00 0. ..5 891. .000 samples.00 I ~o o ~ *~.0 ~ 10. .6 droplets We 579. . . I / M F 31 2 ~ .00 I K 133. .1 1092.× 162..9 .6 ===='~ 5. the dependency of the flight kinematics of the secondary spray on the impact conditions has to be analysed more closely.1 579. ..00 K-Value of the primary droplets We 620.00 K-Value (-) of the primary K 133. .. are important influencing factors. .2 147.. .80 1. Each point represents an average of 30. .60 0.8 967. .80 1.. . . . .._.~ * ×~×~ ~ C~w 5. . However.00 j ....00 0... 0.40 0.8 . .5 ~ ::::e 186. 20 0. .00 150. K = 131. Velocity vectors for the impact on the smooth surface.00 150.m (~) 15-30gm 30-45 gm # . impingement angle 65 . ~ .00 K (-) Figure 20. K . . . . in front behind of the point of impingement Figure 22. ~rrrrr~ 130.00 1 6 0 .00 160.60 '7~ 0.. .00 . . 10 m/s J I . i . .00 170.00 140.20 0.~~ dzo~do ¢ ¢ 0 ~ 0 dzz/do 0. . 0 0 1 7 0 . for three size classes of the secondary spray. .00 i i i i i i i i i i 1777-FTTTI [ I I I I I I I ~ I I I I I E I ~ I IT77~q~r7-r-FTT 1:30.n--rrrvrqT~rrrrr. . . Characteristic mean diameter for the rough surface (a) in front of and (b) behind the point of impingement. 0 0 i 8 0 .60 ¢D " ~ 0.40 N --0 0. . 0 0 b) 0.00 180. .168 CHR MUNDO et aL a) 0. / 10 rn/s © (~ 0-15 gin 15-30 gm 30-45 gm © 0-15 p. i . impingement angle 3 6 . Velocity vectors for the impact on the smooth surface.80 o c c c o dlo//do c ~ m. .40 N N 0.. i.00 140. . for three size classes of the secondary spray. .80 oooco dlo/d o ~ c ~ = d~o/do ~r~ d~o/(do 0.131.~ in front behind of the point of impingement Figure 21. 00 1.DROPLET-WALL COLLISIONS 169 different impingement velocities. .00 6.....60 2. .5 0. 2. A 0.00 i. ..60 e. W/W. 1.00 1 ~.00 oo] . .z .. 1 I .00 I .00 V/Vo 1. . 1.. a large impingement angle and therefore a large ratio of tangential to normal momentum of the primary drop leads to a narrow distribution for 6.00 0.00 0. W/Wo 0.60 1.60 0.. ...60 .00 6.00 A .00 -0.00 1. .50 1..00 .. .00 ~11|11.. .°°! ~ .86) for the s e c o n d a r y spray (v = tangential velocity c o m p o n e n t : w = n o r m a l velocity component). . .60 0.00 0... . . w/wo a=65 0. . ... .00 .00 "~'4. 2.00 . 0 0 .oo 0..00 0.00 ° ° ° Figure 23.00 - 0.50 0. However.00 W/Wo a 0. 0..00 -0..00 1.~'.00 1.00 O..60 . . . .00 0.~. .~ 0. ...0 : : : : ~ K=145. . 2. . .00 -0.150 V/Vo 1. .oo - ~'4..00 .00 O. Obviously the fluid properties (viscosity and surface tension) do not influence strongly the velocity and direction of secondary droplet motion..00 . .. ... 0..OO A I=. OAO I W/Wo a=30 i~60 00J k 0 .8 ~ : : : ~ X=157.00 1.00 -0....00 1. .00 0. . ... W/Wo 0..00 I:~.00 6. . . 1. .00 0.~ -0.00 I ""'4.. ....00 . .2..5 0. . .00 I .. ..50 ~ 0. .00 • . A V/Vo 1.00 1.00 . Velocity distribution for the s m o o t h surface (a) in front o f and (b) behind the point o f i m p i n g e m e n t (S~ = 0.00 1. .00 "•4.00:1 (a) "•4.. a=50 0. . .. . .00 -o. 0.0~ 0. ~..00 2.. 1..00 .00 .00 V/Vo 1. . . 1.. . .00 00o 1 6.0 : : : : ± K:145. .00 [ 0...00 v ~2.00 V/Vo v/vo 1.00 I 1:~2.00 I] 0.00 0.00 0.00 I ..DO .60 1..60 .00 (b) "•'•4.. ...00 ~4..00 ~9.00 0... .00 1 0. . .. . : K=lSl... .oo -t 0.. the distributions are nearly identical for the three K values.B :~ K=157.. 0.00 2.00 0..60 0.. .. .60 a = 30 ° a = 50 ° = 65 ° : : : : o X=131..do ~ 6 ~ A "~4. . . .170 90. impingement angle 65 .. MUNDO et al. in front behind of the point of impingement Figure 25.. Rough surface: considering the velocity vectors for the secondary droplets obtained for the impingement on the rough surface...00 '''' 60 . K = 131.. It is surprising that in front of the impingement point the ratio of the tangential velocity of the secondary to the primary droplets is slightly larger than one. .00 . an almost linear relationship between the impingement angle and the reflection angle exists. 1993). for three size classes of the secondary spray. A similar effect was observed for the interaction of a solid particle with rough walls (Sommerfeld et al. because the tangential velocity component is reduced. In comparison to the velocity vectors presented in figures 21 and 22 for the impact on the smooth surface.00 . Velocity vectors for the impact on the rough surface. In fact.. • .~ j t f A ~A o ~-. This can be explained by the surface roughness which leads to a dissipation of the tangential momentum..'00 ' ' ' Impingement angle (o) Figure 24. it is obvious that the roughness influences strongly the direction of the droplet motion (figures 25 and 26).00 ... smooth rough surface surfac~ ?_~80.. especially for small impingement angles.. impingement angle 36.00 70. 0 0 50.. for three size classes of the secondary spray. • • • .00 CHR.. 20.. but compared to the results obtained for a smooth surface the reflection angles are shifted to smaller values.r. K = 131.. the reflection angle with respect to the normal becomes smaller. The reflection angle correlation with the impact angle of the primary droplet is given in figure 24. both measuring points (in front of and behind the point of impingement) and for both velocity components. Velocity vectors for the impact on the rough surface. 40. 6 0 . Dependency of the reflection angle on the impingement angle for the smooth and the rough surface (angles measured normal to the surface). indicating that the momentum of the impinging drop in the normal direction is partially transformed into tangential momentum. indicating that the normal velocity component is 10 m/s F I © C) ~ 0-15 gm 15-3(I gm 30-45 gm ~ % / / ~c~ ~e" / 10 m/s [ I © 0-15 gm C ) 15-30 gm ~ 3(.. .-45 gm . and to a transformation of tangential momentum into normal momentum. in front behind of the point of impingement Figure 26.~ Aee. . o. o ' - . .00 . ~:~6 . i:++ . . the mean normal velocity component of the splashed droplets ::::~ ::::: ==::: X=157... ..oo i c~+z. ~ .. V e l o c i t y d i s t r i b u t i o n for the r o u g h surface (a) in f r o n t o f and (b) b e h i n d the p o i n t o f i m p i n g e m e n t ( S t = 0. .~ . 0.oo 4.0o ~ . .. ...... . . . + A 0. 6 : ~ . .00 j .00 1. . .. . o °'°°. . .):mi . The possibility of an impinging droplet hitting the "windward" side of the surface roughness element is greater than hitting the "leeward" side.. . leading to a transfer of tangential momentum into normal momentum (figure 28). . .00 0.00 0.. .... This can be explained by the influence of the local surface roughness. . . . . . .o... . i:d~ .. .00 V/Vo 0. -ox. . ...ooI ~2. .. W/Wo a = 50 ° = 65 ° 6..6o 1 -t . i:.00 • I 2..oo I 1 -T-...00o. . .oo . .00 U J .. .oo "T"°° v ..... .. Therefore. ' ~:66" "l+ "i2~ c~ = 30 ° c~ = 50 ° c~ = 65 ° F i g u r e 27. w = n o r m a l v e l o c i t y component). .O0 0. .50 .o+ .6o 0..1 0..oo ' .+o. . . .00 5"0° C~e..~ ..85) f o r the secondary spray (v = tangential velocity c o m p o n e n t ..O0 (b) ~ "~4..00 v Iv'~4"O0 'T'+. . .. .. .50 V/Vo 6..00.00 a. . ..6+. ...oo- 4t. . LOO. . V/Vo i:5o e.. . i:66 . . o a = 30 ° z.. : .. . . i 6o i: 0100 -0:00 o.00 : ~2. .~0 i O. .00 7-. W o'. .00 0.00 "00 1 (a) ~:. . . i'.O0 -4 i °'°°-o.9 K:150.~O |..DROPLET-WALL COLLISIONS 171 increased. . . ..' ~ ' .o e: V/Vo 6. c:::: K=157. .00 . . .. ) V/Vo L. . .~2.. .o.. . . .' ' ' .... . o... I:+. . .00 . . i:~o J + .9 0.. .00 6. . .6o °'°°-o:e-o: ' : O : d 6 . . i. . .~4. .00 ~. ..7 ===== X=141.00 1 ~<z. . o:d+ .. .50 W/Wo ' .00 V/Vo 1. .... o. o.oo -3 ! °'00o. .~..7 X:141. . .00 W/Wo a .2. . .00 0. . .oo " 0 : 0 6 . 0 0 -J 0.. . . . . i:00 0 1 0 0 :/ -0:00 - "4 0.. . .+0 .00 i ~.00 o.60 .oo I ' . . ~'. i:i 0. i'.. . However. An increase of the impingement angle of the primary drop leads to a narrower velocity distribution. For rough surfaces the splashing occurs under the influence of the local surface angle. K. which is the subject of further investigations. Influence of the surface roughness profile on the impingement process. the ratio of the normal velocity component to the tangential is slightly larger than that obtained from the smooth surface. the mean reflection angle to the normal of the secondary droplets decreases. C O N C L U D I N G R E M A R K S In this work the principal physical process of deformation and splashing of single droplets on surfaces was visualized and described. The normal momentum is only partially conserved. 1993 The velocity change of ethanol droplets during collision with a wall analysed by image processing. The distributions are very similar for the three K numbers. The fluid properties and the kinematic parameters were varied. indicating that the flight direction does not depend on the fluid viscosity and surface tension in the case of a rough surface. For the derivation of a numerical droplet impact model it is necessary to measure the spatial mass flux around the point of ir. for the impingement on the smooth and the rough surface. For the case of splashing. Regarding the deformation and splashing when a liquid droplet impacts on a rough surface (roughness in the range of the diameter of the primary droplet). N. leading to a transfer of tangential momentum into normal momentum. The distribution does not depend strongly on the fluid properties. 5. Fluids 15. & FROHN. The diameter distribution of the secondary droplets depends on the fluid properties (viscosity and surface tension) and kinematic parameters (velocity and size of the primary droplets) in the case of an impingement on a smooth surface. A. Exp. The influence of the fluid properties on the velocity probability density function are presented in figure 27. Acknowledgement--The authors are grateful to the Deutsche Forschungsgemeinschaft (DFG). for an impact on the rough surface must be larger than the normal component for an impact on the smooth surface. ROTH. The tangential impact velocity is nearly completely transferred to the secondary droplets. The outcome of an impact--whether splashing or deposition occurred--depends on the Re and Oh numbers. one finds that no splash-corona is formed and the diameter distribution of the secondary droplets becomes narrower with a smaller mean diameter. Therefore. similar to the results obtained from the smooth surface. through grant TR194/7. REFERENCES ANDERS. and in front of the impingement point the ratio of the tangential velocities of the secondary droplets to the primary droplets is slightly larger than one. because the energy is dissipated during the impact and in the formation of the corona. 91-96.. The velocity distributions show a remarkable strong dependence on the impingement kinematics. MUNDO et ul. for financial support of these investigations. which represent the fluid properties and kinematic impact parameters. the diameter and velocity distributions of the product droplets were measured around the point of impingement using a phase Doppler anemometer.172 CHR.@ingement. Figure 28. It was shown that the splashing occurs due to the decay of the cylindrical sheet ('corona') which arises around the point of impingement for a smooth surface. Atm. C. F. 48. T. 419-441.M. Czech. Phil. J. 338-339. REIN. SOMMERFELD. H. WATKINS. 1990 A new model for diesel impaction on walls and comparison with experiments. 21. 1987 Numerical simulation of liquid drop collision with a rigid flat plate.-Soy. Lond. 1992 Application of a phase-Doppler anemometer to a spray impinging on a disc. 62. D. & SLUYTER. 147-153. Lond.A. I.H.S. 1991 LDV and PDA analysis of spray-wall interaction. WACHTERS. Ing. 1936 Die Bildung von Tropfen an Diisen und die Aufl6sung flfissiger Strahlen. 983-994. Proc. WEISS. A. Ph. 6th Int. A S M E Fluids Engng Conf. 32. FADDEYEV.G. BOLLE. M. & L~u. A 373. Sci. & GAMMA. W. Portugal. WALZEL. & MASON. R. (~)ZDEMIZ. 1973 Generation of monodispersed aerosol standards. O. J. Mech. 1981 An experimental investigation of fluid flow resulting from the impact of a water drop with an unyielding dry surface. & WHITELAW.D. ICLASS-91. 1993 Periodischer Aufprall monodisperser Tropfen auf eine feste Wand. 1988 Fuel impingement in a direct diesel engine.A.I.. Technol. 1971 Splashing of drops on solid and wetted surfaces: hydrodynamics and charge separation. New York.J. 21. 1989 Modelling engine spray/wall impingement. LSTM Bericht 373/E/1993. Soc. University of G6ttingen. Lisbon. R. NABER. HARDALUPAS. Envir.P. 1989 Atomization and Sprays. Prague. & HOBBS. VAN DER GELD.S. . L. COSSALI. 8.W. Soc.B. 8. D. 503-532. & AVEDISIAN. Soc. H. Lond. 7. 1047-1056. COGHE. STow. 1974 The water rebound problem: dynamics of collision. Germany. J. Tech. 545-565. B. P.M. FOOTE. A 280.W. Chem. MUNDO.J. D. Tech. R.C. 12. & TROPEA. SCHMIDT. SOMMEREELD. OKAMOTO. 483-503.G. 240. Proc. In Multiphase Science and Technology. Washington. P. MD. 1990 Zerstfiuben von Flfissigkeiten.. 1993 Particle-wall collisons: experimental studies and numerical models. 1992 Impingement of an axisymmetric jet on unheated and heated flat plates. G. S. Engng 880107. 1991 On the collision of a droplet with a solid surface. R. H. ICLA SS 1994. Republic. 1993.. A 432. Chem. Soc.J. 1964 The coalescence and bouncing of water drops at an air/water surface. & HADFIELD. P. University of Erlangen-Nfirnberg. Washington.M.DROPLETWALL COLLISIONS 173 BERGLUND..P. NABER. Y.. Tech.. & WANG. C. Soc. A. Syrup. of Laser Technol. J. 355-358. Sci.~ MOSENZHNIK. R. 1. Norway. Gaithersburg. Chem. W. 8L TROPEA.A... Ing. on Appl. Ing. Lehrstuhl f/Jr Str6mungsmechanik. D. K. C. Denmark. S. DANTEC. Fluid. P. Lond. 1047-1056. No. Z.. P. Y. Hemisphere. & KNAUSS.A. 52. Chem. thesis. to Fluid Mech. A 269. Proc. • MOUREAU. V.J. B. MUNDO. WALZEL. Ing. R. DC. E.N. KHAVIYA. B. Sci. CH. 1980 Zerteilgrenze beim Tropfenprall.J. M. DC. 1992 Particle Dynamics Analyzer. COHEN. Vol. Hemisphere. Fluid Mech. CH. B. A 435. HUBER.P. 1993 Phenomena of liquid drop impact on solid and liquid surfaces. Trondheim. 390-402. Automot.N.S. A. 1976 Prallzerstfiubung von Flfissigkeiten bei Nichtbenetzung. C. Soc. Fluid Dynam. SOMMEREELD. Lond. B. R. L. 1991 Shattering of a liquid drop due to impact. Automot. LEEEBVRE. O. 13-41. 1988 Oblique impingement of a spherical liquid droplet on a solid wall. OHNESORGE. CHANDRA. 555-585. 17.R. LEVIN. Skovlunde.M.2 REITZ. CALLERA. 1993b Experimental studies of the splashing and deposition of small liquid droplets impinging on a fiat surface. BRUNELLO. C. G. J. U. European Two-phase Flow Group Meeting. & W~CHTER. & WESTERLING. 1982 Spray cooling of hot surfaces. Proc. Chem. 1963 The heat transfer from a hot wall to impinging water drops in a spherical state. 61-93. Soc. & FARELL. M. ENRIGHT. 1993a Deposition von Flfissigkeitstr6pfchen an Wandoberflfichen. JAYARATNE.. TAYLOR. & WHITELAW. Z A M M 16. Engng Sci. 3. Res. 7.G.. D. B. P. Engng 8801316. Res.