A numerical study of heat and mass transport in fibre suspensions
A numerical study of heat and mass transport in fibre suspensions
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纤维悬浮液中传热传质的数值研究
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发表时间：
1994
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通讯作者：
R. Schiek
中科院分区：
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作者：
M. B. Mackaplow;E. Shaqfeh;R. Schiek
使用细长体理论，周期性的盒子，和周期解的拉普拉斯方程，我们开发了一组积分方程，数值求解，以确定高导电纤维的悬浮液的有效电导率和有效的反应速率系数的经典扩散控制反应问题。我们的问题公式明确考虑了所有的纤维-纤维相互作用。它适用于半稀释体系中的悬浮液浓度和各种纤维形状，包括钝头体。对于有效电导率问题，纤维-纤维相互作用在悬浮液浓度为nl 3·2 O（1）时大大提高了有效电导率，超出了稀释理论的预测，其中n是纤维的数量密度，l是特征纤维半长。扩散控制反应问题的相应条件是nl 3 ≠ O（10-5）。结果表明，对于nl ~ 3> O（1），无论是定向悬浮液还是各向同性悬浮液，悬浮液中的无量纲屏蔽长度都只取决于夹杂物的体积分数。我们相信这是第一次计算验证这个预测最初由E。S. G. Shaqfeh和G. H.弗雷德里克森通过稀/半稀过渡和充分进入半稀制度的悬浮液的电导率和反应速率系数很好地预测稀理论，考虑一些纤维-纤维相互作用。对于球状和圆柱形夹杂物的悬浮液，观察到相同的缩放行为的传输系数和筛选长度。
Using slender body theory, periodic boxes, and the periodic solution to Laplace’s equation we develop a set of integral equations that are numerically solved to determine the effective conductivity of suspensions of highly conducting fibres and the effective reaction rate coefficient for the classical diffusion-controlled reaction problem. Our problem formulation explicitly considers all fibre–fibre interactions. It is valid for suspension concentrations up through the semi-dilute régime and for a wide variety of fibre shapes, including blunt-ended bodies. For the effective conductivity problem, fibre–fibre interactions act to substantially enhance the effective conductivity beyond dilute theory predictions at suspension concentrations of nl3 ≽ O(1), where n is the number density of fibres and l is the characteristic fibre half-length. The corresponding condition for the diffusion-controlled reaction problem is nl3 ≽ O(10-5). It is shown that for nl3 > O(1), the non-dimensionalized screening length in the suspension depends only on the volume fraction of the inclusions both for aligned and isotropic suspensions. We believe this is the first computational verification of this prediction made originally by E. S. G. Shaqfeh and G. H. Fredrickson. The conductivity and reaction rate coefficients of the suspensions both through the dilute/semi-dilute transition and well into the semi-dilute régime are well predicted by dilute theories that consider some fibre–fibre interactions. The same scaling behaviour for the transport coefficients and screening lengths is observed for both suspensions of spheroidal and cylindrical inclusions.