Taylor dispersion in systems of sedimenting nonspherical brownian particles. I. Homogeneous, centrosymmetric, axisymmetric particles
Taylor dispersion in systems of sedimenting nonspherical brownian particles. I. Homogeneous, centrosymmetric, axisymmetric particles
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沉积非球形布朗颗粒系统中的泰勒色散。
DOI：
10.1016/0021-9797(79)90232-7
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发表时间：
1979
影响因子：
9.9
通讯作者：
H. Brenner
中科院分区：
文献类型：
--
作者：
H. Brenner
最近的广义泰勒色散现象的理论适用于相同的，非中性浮力，轴对称，布朗粒子在斯托克斯定律制度的沉降。一般表达式推导出的平均（取向平均）沉降速度U的颗粒和这个平均值的分散在一般情况下，轴对称的颗粒可能缺乏前后对称性，他们可能拥有一个不均匀的质量分布。对于粒子具有对称中心（例如，在长球体和扁球体的情况下）并且是均匀的情况，进行具体的计算。在这种情况下，没有重力力偶作用于粒子，因此它们相对于重力场的方向不具有优先取向。颗粒在平行和垂直于重力场方向运动时的弥散系数D_i= D+ K_i λ_2（U_i）~ 2 d_r，其中U_i为颗粒的平均沉降速度，d_r为颗粒的旋转扩散系数，和D =（1 3）×（D + 2D）粒子的平均平移扩散系数-其中D和D分别是粒子对于平行于和垂直于其对称轴的平移的取向特异性分子扩散系数。此外，λ是无量纲参数λ=| D − D|/D = 1 2，κ B = 2 135，κ B = 1 90。这些横观各向同性色散的形式与Goren最近通过Langevin方案得到的结果一致，但κ i值与他的不同。一个根本性的错误，在戈伦的分析是来源的差异。在这些计算的基础上，Smoluchowski的众所周知的方程扩散在外部力场中被证明是一般不适用于非球形粒子。色散结果的潜在应用进行了讨论。
A recent theory of generalized Taylor dispersion phenomena is applied to the sedimentation of identical, nonneutrally buoyant, axisymmetric, Brownian particles settling in the Stokes-law regime. General expressions are derived for the mean (orientation-averaged) settling velocity U ̄∗ of the particles and the dispersion about this mean in the general case where the axisymmetric particles may lack fore-aft symmetry and where they may possess an inhomogeneous mass distribution. Specific calculations are carried out for the case where the particles possess a center of symmetry (as, for example, in the case of prolate and oblate spheroids) and are homogeneous. In such circumstances no gravitational couple acts upon the particles and they therefore possess no preferred orientations relative to the direction of the gravity field. The dispersion coefficients, D ̄‖∗ and D ̄⊥∗, for motion of the particles parallel and perpendicular, respectively, to the direction of the gravity field are found to be of the forms D∗ i= D+ K i λ 2 (U∗) 2 d r with U ̄∗ the mean settling velocity of the particle, d r its rotary diffusion coefficient, and D ̄=(1 3)×(D‖+ 2D⊥) the mean translational diffusion coefficient of the particle—wherein D‖ and D⊥ are the orientation-specific molecular diffusivities of the particle for translation parallel and perpendicular, respectively, to its symmetry axis. In addition, λ is the dimensionless parameter λ=| D‖− D⊥|/D ̄ 1 2, and κ‖= 2 135 and κ⊥= 1 90. The forms of these transversely isotropic dispersivities agree with those recently obtained by Goren via a Langevin scheme, but the κ i values differ from his. A fundamental error in Goren's analysis is shown to be the source of the discrepancy. On the basis of these calculations, Smoluchowski's well-known equation for diffusion in an external field of force is shown to be generally inapplicable to nonspherical particles. Potential applications of the dispersion results are discussed.