Scaling Laws of Droplet Coalescence: Theory and Numerical Simulation

<div>Time evolution of the neck heights <svg height="11.5564pt" id="M475" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 33.0346 11.5564" width="33.0346pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z"></path></g><g transform="matrix(.013,0,0,-0.013,6.101,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,10.599,0)"><path d="M611 455L576 464C561 440 550 438 518 438L239 441C97 441 44 363 21 321L47 295C85 345 137 358 192 358C168 240 96 67 42 10L49 -12C69 -12 118 -4 140 10C190 88 228 266 247 357L379 355L318 105C314 87 313 71 313 58C313 5 339 -12 369 -12C434 -12 505 45 546 101L525 129C501 102 464 82 451 82C440 82 439 103 449 160C458 209 476 300 490 353C510 352 552 352 565 358C580 378 602 419 611 455Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.781,0)"><path d="M114 412C81 412 58 388 58 355C58 321 81 297 113 297S169 321 169 355C169 388 145 412 114 412ZM95 130C70 130 46 114 46 88C46 72 54 65 59 64C93 56 121 33 121 -3C121 -41 93 -68 45 -88L56 -118C117 -99 186 -56 186 22C186 91 131 130 95 130Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.924,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z"></path></g><g transform="matrix(.013,0,0,-0.013,28.357,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg> in the inertial-viscous regime. The<i> circular markers </i><svg height="7.35473pt" id="M476" style="vertical-align:-0.3499303pt" version="1.1" viewbox="-0.0498162 -7.0048 4.94072 7.35473" width="4.94072pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M326 255C326 330 263 391 186 391S46 330 46 255S109 119 186 119S326 180 326 255ZM274 255C274 204 235 163 186 163S98 204 98 255S137 347 186 347S274 306 274 255Z"></path></g></svg> indicate the numerical experiment results and the solid line represents the fitted curve.</div>

Advances in Mathematical Physics

Scaling Laws of Droplet Coalescence: Theory and Numerical Simulation

Figure 6