Gravity-induced coalescence of drops at arbitrary Péclet numbers
Gravity-induced coalescence of drops at arbitrary Péclet numbers
复制标题
任意佩克莱数下液滴的重力诱导合并
DOI：
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发表时间：
1994
影响因子：
3.7
通讯作者：
Robert H. Davis
中科院分区：
文献类型：
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作者：
A. Z. Zinchenko;Robert H. Davis
考虑了考虑颗粒布朗运动和货车德瓦耳斯吸引力的情况下，沉降液滴稀悬浮液的碰撞效率。假设液滴具有相同的密度，但它们的大小不同。忽略液滴变形和流体惯性。由于小颗粒的体积分数，分析仅限于二元相互作用，并包括对分布函数的全准稳态福克-普朗克方程的解决方案。与以前的研究不同，液滴或固体颗粒碰撞，数值解任意Péclet数，Pe，从而涵盖了整个范围内的颗粒尺寸在典型的水溶胶。我们的技术主要是基于一个解析延拓到平面的复杂Péclet数和一个特殊的保角映射，表示的解决方案作为一个收敛的幂级数的所有真实的Péclet数。这种有效的算法被证明适用于各种对流扩散问题。对分布函数展开为勒让德多项式，并使用有限差分格式相对于粒子分离。从精确的双球坐标解和近场渐近性，提供了流体动力学相互作用的两滴迁移率函数。碰撞效率计算的尺寸比，液滴介质粘度比，和Péclet数的宽范围内，有和没有interdroplet力。固体球被认为是一个限制的情况下，有吸引力的货车范德华力在这种情况下，非零碰撞率所需的。对于Pe [Gt ] 1，渐近极限Pe → ∞的修正是O（Pe−1/2）。对于Pe [Lt ] 1，碰撞效率渐进展开式中的前两项为C/Pe + ½C2，其中常数C由Pe → 0极限下的布朗解确定。数值结果与这些限制非常吻合。对于中间Pe，数值结果表明，当Pe ≤ O（102）时，布朗运动是重要的.对于Pe = 10，Pe → ∞的轨迹分析可能会低估碰撞率两倍。一个更简单的，近似的解决方案的基础上忽略横向扩散也被认为是相比，精确的解决方案。对于所有研究条件，一致性在2-3%范围内。研究了货车吸引力对液滴碰撞效率的影响。除了非常高的液滴与介质粘度比，影响相对较小，特别是当考虑电磁阻滞时。
The collision efficiency in a dilute suspension of sedimenting drops is considered, with allowance for particle Brownian motion and van der Waals attractive force. The drops are assumed to be of the same density, but they differ in size. Drop deformation and fluid inertia are neglected. Owing to small particle volume fraction, the analysis is restricted to binary interactions and includes the solution of the full quasi-steady Fokker—Planck equation for the pair-distribution function. Unlike previous studies on drop or solid particle collisions, a numerical solution is presented for arbitrary Péclet numbers, Pe, thus covering the whole range of particle size in typical hydrosols. Our technique is mainly based on an analytical continuation into the plane of complex Péclet number and a special conformal mapping, to represent the solution as a convergent power series for all real Péclet numbers. This efficient algorithm is shown to apply to a variety of convection—diffusion problems. The pair-distribution function is expanded into Legendre polynomials, and a finite-difference scheme with respect to particle separation is used. Two-drop mobility functions for hydrodynamic interactions are provided from exact bispherical coordinate solutions and near-field asymptotics. The collision efficiency is calculated for wide ranges of the size ratio, the drop-to-medium viscosity ratio, and the Péclet number, both with and without interdroplet forces. Solid spheres are considered as a limiting case; attractive van der Waals forces are required for non-zero collision rates in this case. For Pe [Gt ] 1, the correction to the asymptotic limit Pe → ∞ is O(Pe−1/2). For Pe [Lt ] 1, the first two terms in an asymptotic expansion for the collision efficiency are C/Pe + ½C2, where the constant C is determined from the Brownian solution in the limit Pe → 0. The numerical results are in excellent agreement with these limits. For intermediate Pe, the numerical results show that Brownian motion is important for Pe ≤ O(102). For Pe = 10, the trajectory analysis for Pe → ∞ may underestimate the collision rate by a factor of two. A simpler, approximate solution based on neglecting the transversal diffusion is also considered and compared to the exact solution. The agreement is within 2–3% for all conditions investigated. The effect of van der Waals attractions on the collision efficiency is studied for a wide range of droplet sizes. Except for very high drop-to-medium viscosity ratios, the effect is relatively small, especially when electromagnetic retardation is accounted for.