Knowledge (XXG)

Knudsen paradox

Source đź“ť

217: 160: 68:
vanishes and a fully developed steady state channel flow shows infinite flux. On the other hand, the particles stop interacting for large Knudsen numbers. Because of the constant acceleration due to the external force, the steady state again will show infinite flux.
64:, one would expect the mass flux to decrease with increasing the Knudsen number. The minimum can be understood intuitively by considering the two extreme cases of very small and very large Knudsen number. For very small Kn the 142: 258: 126: 58: 201: 277: 251: 216: 307: 244: 23:
has been observed in experiments of channel flow with varying channel width or equivalently different pressures. If the normalized
194: 282: 302: 287: 90: 61: 297: 187: 84: 96: 292: 224: 144:, A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion. 159: 130: 102: 228: 171: 34: 127:"Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren" 78: 167: 122: 28: 271: 65: 24: 93: â€“ Equations describing the motion of viscous fluid substances 31:
based on the channel width a distinct minimum is observed around
105: â€“ List of statements that appear to contradict themselves 60:. This is a paradoxical behaviour because, based on the 232: 175: 99: â€“ Class of computational fluid dynamics methods 37: 81: â€“ Description of the time-evolution of plasma 52: 252: 195: 8: 259: 245: 202: 188: 36: 27:through the channel is plotted over the 115: 87: â€“ Partial differential equation 16:Apparently anomalous flow in channels 7: 213: 211: 156: 154: 231:. You can help Knowledge (XXG) by 174:. You can help Knowledge (XXG) by 14: 215: 158: 278:Partial differential equations 1: 91:Navier–Stokes equations 85:Fokker–Planck equation 308:Statistical mechanics stubs 324: 210: 153: 97:Lattice Boltzmann methods 62:Navier–Stokes equations 170:–related article is a 54: 53:{\displaystyle Kn=0.8} 283:Statistical mechanics 225:statistical mechanics 55: 303:Fluid dynamics stubs 35: 288:Transport phenomena 223:This article about 298:Physical paradoxes 133:333 (1909) 75–130. 131:Annalen der Physik 50: 240: 239: 183: 182: 103:List of paradoxes 315: 261: 254: 247: 219: 212: 204: 197: 190: 162: 155: 145: 140: 134: 120: 59: 57: 56: 51: 323: 322: 318: 317: 316: 314: 313: 312: 268: 267: 266: 265: 209: 208: 151: 149: 148: 141: 137: 121: 117: 112: 79:Vlasov equation 75: 33: 32: 21:Knudsen paradox 17: 12: 11: 5: 321: 319: 311: 310: 305: 300: 295: 293:Fluid dynamics 290: 285: 280: 270: 269: 264: 263: 256: 249: 241: 238: 237: 220: 207: 206: 199: 192: 184: 181: 180: 168:fluid dynamics 163: 147: 146: 135: 123:Martin Knudsen 114: 113: 111: 108: 107: 106: 100: 94: 88: 82: 74: 71: 49: 46: 43: 40: 29:Knudsen number 15: 13: 10: 9: 6: 4: 3: 2: 320: 309: 306: 304: 301: 299: 296: 294: 291: 289: 286: 284: 281: 279: 276: 275: 273: 262: 257: 255: 250: 248: 243: 242: 236: 234: 230: 226: 221: 218: 214: 205: 200: 198: 193: 191: 186: 185: 179: 177: 173: 169: 164: 161: 157: 152: 143: 139: 136: 132: 128: 124: 119: 116: 109: 104: 101: 98: 95: 92: 89: 86: 83: 80: 77: 76: 72: 70: 67: 63: 47: 44: 41: 38: 30: 26: 22: 233:expanding it 222: 176:expanding it 165: 150: 138: 118: 20: 18: 272:Categories 110:References 66:viscosity 25:mass flux 73:See also 227:is a 166:This 229:stub 172:stub 19:The 48:0.8 274:: 129:, 125:, 260:e 253:t 246:v 235:. 203:e 196:t 189:v 178:. 45:= 42:n 39:K

Index

mass flux
Knudsen number
Navier–Stokes equations
viscosity
Vlasov equation
Fokker–Planck equation
Navier–Stokes equations
Lattice Boltzmann methods
List of paradoxes
Martin Knudsen
"Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren"
Annalen der Physik

Stub icon
fluid dynamics
stub
expanding it
v
t
e
Stub icon
statistical mechanics
stub
expanding it
v
t
e
Categories
Partial differential equations
Statistical mechanics

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

↑