Use of the Weibull equation to approximate diffusive release from particles in a closed system
Use of the Weibull equation to approximate diffusive release from particles in a closed system
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DOI：
10.1016/j.compchemeng.2011.09.012
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发表时间：
2012-04
期刊：
影响因子：
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通讯作者：
R. Farr;S. M. Goh;F. Y. S. Yong
中科院分区：
文献类型：
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作者：
R. Farr;S. M. Goh;F. Y. S. Yong
我们考虑的问题Fickian扩散的溶质（或热）进入或离开悬浮液的颗粒，在一个良好的混合溶剂。通过结合一个简单的数值方案与拉普拉斯变换方法，我们能够有效地解决这个问题，为不同的颗粒体积分数（包括在液相中的溶质的积累），形状（球，立方体和圆柱体的不同纵横比）和粒度分布（假设为对数正态分布）。我们近似的威布尔函数的结果，从而提供了一个物理校准的参数在这个功能时，作为我们的解决方案的近似。我们测试我们的计算通过测量盐的释放曲线从不同的尺寸分布的琼脂立方体，然后使用预测的威布尔方程推导出盐在这种材料中的扩散率。
We consider the problem of Fickian diffusion of a solute (or heat) into or out of a suspension of particles, in a well-mixed solvent. By combining a simple numerical scheme with a Laplace transform method, we are able to efficiently solve this problem for different particle volume fractions (including accumulation of solute in the liquid phase), shapes (spheres, cubes and cylinders of different aspect ratios) and particle size distributions (assumed to be log-normal). We approximate the results by a Weibull function, and thereby provide a physical calibration for the parameters in this function when used as an approximation for our solutions. We test our calculation by measuring salt release profiles from different size distributions of agar cubes, and then use the predicted Weibull equation to deduce the diffusivity of salt in this material.