iii TABLE OF CONTENTS Chapter Page LIST OF FIGURES xi LIST OF TABLES xvii I. SUMMARY 1 II. INTRODUCTION 7 III. REVIEW OF THE LITERATURE 10 A. STATIC ENCOUNTERS 10 Gas-liquid Systems 10 Liquid-liquid Systems 20 B. DYNAMIC ENCOUNTERS 25 Liquid-liquid Systems 25 Theory for drop collisions in gas-liquid Systems 28 Experiments with clouds of droplets 42 Studies of drops impacting on flat surfaces 50 EXPERIMENTS WITH PAIRS OF DROPS COLLIDING IN GASEOUS MEDIA 59 Qualitative studies 59 Studies which took impact angle into account 77 Studies in which impact angle was measured 89 C. METHODS OF UNIFORM DROP GENERATION 111 D. TECHNIQUES OF DROP PHOTOGRAPHY 112 IV. OBJECTIVES OF THE INVESTIGATION 114 V. PRELIMINARY EXPERIMENTS 117 A. DEVELOPMENT OF DROP COLLISION CONTROL 117 Drop generation system 117 iv Control of gas and water temperatures 120 Control of charges on the drops 121 Calibrations 123 B. EARLY DROP COLLISION WORK 125 Attempts to produce rebound 125 Tests on the influence of relative humidity . 130 Tests on the influence of drop charge 131 Investigation of sunderance 131 C. DEVELOPMENT OF PHOTOGRAPHIC TECHNIQUE 135 Still photographs 135 Motion pictures 138 VI. DESCRIPTION OF THE APPARATUS 143 A. EQUIPMENT USED 143 Chamber for control of ambient conditions 143 Drop generators 146 Systems of mechanical support 152 General 154 B. PERFORMANCE CHARACTERISTICS 158 Uniform generation of drops 158 Range of drop sizes 168 Range of relative velocities 168 Control of other factors 170 VII. EXPERIMENTAL PROCEDURE 171 A. CONTROL OF COLLISION CONDITIONS 171 Drop liquid 171 v Drop size 172 Relative velocity 173 Impact angle 175 Charges on the drops 177 Water and gas temperatures 180 Chamber atmosphere 182 B. PHOTOGRAPHY 182 Motion pictures 183 Still photographs 186 C. SAMPLE RUN 187 Promotion of collisions at the desired conditions 188 Motion pictures 191 Collision-control data readings 193 Still photographs 196 Additional series of still photographs 198 Results 199 D. ANALYSIS OF THE DATA 202 Data from the motion pictures 202 Data from the still photographs 209 Other data 212 VIII. EXPERIMENTAL RESULTS 214 A. TERMS AND SYMBOLS 214 Collision 215 Rebound 215 Coalescence 215 vi Partial coalescence 216 Disruption 216 Reflex disjection 216 Spatter 216 Delay time 217 Relative velocity and impact angle 217 Mapping symbols and practices 218 B. LARGE DROPS OF 1:1 DIAMETER RATIO 219 Collision results by runs 219 Delay times 224 Illustrative composite photographs 224 C. SMALL DROPS OF 1:1 DIAMETER RATIO 244 Collision results by runs 244 Delay times 246 Illustrative composite photographs 247 D. LARGE DROPS OF 2:1 DIAMETER RATIO 266 Collision results by runs 266 Delay times 273 Illustrative composite photographs 273 E. SMALL DROPS OF 2:1 DIAMETER RATIO 290 Collision results by runs 290 Delay times 292 Illustrative composite photographs 293 F. LARGE DROPS OF 3:1 DIAMETER RATIO 305 Collision results by runs 305 vii Delay times 310 Illustrative composite photographs 311 C. SMALL DROPS OF 3:1 DIAMETER RATIO 325 Collision results by runs 325 Delay times 327 Illustrative composite photographs 328 H. DROPS OF OTHER SIZES 336 Rebound between drops of 3:2 diameter ratio 336 Attempted illustrative films of partial coalescence 339 Illustrative photographs of spatter 342 Impacts between drops and flat surfaces 345 IX. DISCUSSION OF RESULTS 360 A. THE POSSIBLE COLLISION OUTCOMES 360 B. INFLUENCE OF MINOR FACTORS ON COLLISION OUTCOMES 363 Relative humidity and electrical fields or charges 364 Physical properties 365 Dissolved gas and impurities 368 Effects on mapping 369 C. EXPERIMENTAL ERROR 370 Drop diameters and diameter ratio 370 Relative velocity 373 Impact angle 375 Damping of drop oscillations 379 Charges carried by the drops 380 Water conductivity 382 viii Temperatures 383 Particles in the water and gas 385 Relative humidity 385 Pressure 387 Gaps in the data 388 D. DISCUSSION OF EXPERIMENTAL RESULTS 390 Positioning of boundary curves 390 Correlation of the data 391 Convetitions adopted for the combined mapping of outcomes 393 Results of mapping at Wes > 5 394 Results of mapping at Wes < 5 398 Influence of drop size 400 Influence of drop diameter ratio 402 Delay times 406 Aerodynamic conditions of collision 413 E. COMPARISON WITH QUANTITATIVE RESULTS OF OTHER EXPERIMENTERS 419 Plotting of data collected from the literature 419 The collected results 423 Studies utilizing a supported drop 426 Studies in which pairs of drops collided in free flight 435 F. POSSIBLE APPROACHES TO THE THEORETICAL PREDICTION OF BRIDGING 452 Intervening gas film 453 Flat-plate models for film thinning 455 ix Damon's model 459 Surface microphysics 463 Bridging-stage ratios 465 Impact-induced oscillations 468 G. SUNDERANCE THEORY 472 Partial coalescence 472 Theoretical treatments of disjection 478 Model for the coalescence-disruption transition 490 H. IMPLICATIONS OF RESULTS 506 X. CONCLUSIONS 517 XI. RECOMMENDATIONS FOR FUTURE RESEARCH ON DROP COLLISION BEHAVIOR 522 A. FURTHER MAPPING OF OUTCOMES 522 Variation of relative velocity and impact angle 522 Variation of drop size and diameter ratio 524 B. SIMILAR INVESTIGATIONS YIELDING INFORMATION IN OTHER AREAS 525 Influence of minor factors 526 Other liquids 528 Delay times 528 Post-bridging data 529 C. OTHER RELATED INVESTIGATIONS 530 Surface microphysics 530 Theory and related experiments 531 BIBLIOGRAPHY 534 APPENDIX 565 x A. DERIVATIONS OF EQUATIONS 565 Equivalent spherical diameter of a spheroidal drop 565 Relative velocity and the angle β 566 Impact-angle measurement in high-velocity collisions 567 Actual impact angle in an out-of-plane collision 568 B. DATA TABLES 570