Abstract Colloid suspensions commonly exhibit a distribution of sizes, but most transport models only consider a single colloid size. A mathematical model was therefore developed to describe the advective and dispersive transport and first-order retention and release of a stable or aggregating polydispersed colloid suspension in porous media. The colloid size distribution was described using a unimodal or a bimodal lognormal probability density function (PDF), and Brownian aggregation was considered by making lognormal PDF parameters a function of time. Filtration theory was used to predict the retention rate coefficients for the various colloid sizes. The amount of retention for a stable polydispersed suspension was highly dependent on the colloid size distribution parameters, especially for a bimodal lognormal PDF. Increasing the distribution variance produced hyper-exponential retention profiles and an increase or a decrease in colloid retention depending on whether the medium colloid size was close to the optimum size for transport. Aggregation produced a similar decrease in the breakthrough concentrations with injection time as ripening, especially when the sticking efficiency was low. Aggregation effects were much more pronounced at higher input concentration levels, which also produced retention profiles that were increasingly hyper-exponential. Simulation results indicate that the colloid size distribution of stable and aggregating polydispersed suspensions always becomes more uniform and approaches the optimum transport size with increasing distance, suggesting that consideration of polydispersed suspensions is of primary importance near the injection surface.

中文翻译：

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多孔介质中多分散胶体悬浮液的传输和保留建模

摘要 胶体悬浮液通常表现出尺寸分布，但大多数传输模型只考虑单一胶体尺寸。因此开发了一个数学模型来描述多孔介质中稳定或聚集的多分散胶体悬浮液的平流和分散传输以及一级保留和释放。使用单峰或双峰对数正态概率密度函数 (PDF) 描述胶体尺寸分布，并通过使对数正态 PDF 参数成为时间的函数来考虑布朗聚合。过滤理论用于预测各种胶体尺寸的保留率系数。稳定的多分散悬浮液的保留量高度依赖于胶体尺寸分布参数，尤其是双峰对数正态 PDF。增加分布方差会产生超指数保留分布和胶体保留的增加或减少，这取决于中等胶体尺寸是否接近于运输的最佳尺寸。随着注射时间的推移，聚集产生了类似的突破浓度降低，尤其是当粘附效率低时。在较高的输入浓度水平下，聚集效应更加明显，这也产生了越来越超指数的保留曲线。模拟结果表明，随着距离的增加，稳定和聚集的多分散悬浮液的胶体尺寸分布总是变得更加均匀并接近最佳传输尺寸，