Continuous flow magnetophoresis represents a common technique for actively separating particles within a fluid. For separation systems design, accurately predicting particle behaviour helps to characterise system performance, typically measured by the separation efficiency (SE). While finite element method (FEM) simulations offer high accuracy, they demand extensive computational resources. Alternatively, results can be achieved more quickly with simplified numerical models that use analytical descriptions of fluid flow, magnetic fields, and particle movement. In this research, we model a millifluidic system that separates magnetic particles using magnetophoresis. Therefore, we (1) develop a simple numerical model that can simulate continuous flow magnetophoresis for rectangular channels in two and three dimensions, (2) introduce a novel and simple approach to calculate the SE, and (3) quantify the effects of model assumptions in flow profile and dimensions on SE. Our method for estimating SE considers particle flux variation across the channel's cross-section due to the flow profile. The results are compared to an FEM model developed in COMSOL. The obtained three-dimensional simulation model computes results in seconds, around 180 times faster than the FEM approach, while deviating less than 2% from the FEM results. A comparison of the different two-dimensional and three-dimensional models underscores the significant influence of the flow profile and the SE calculation method on the result. The two dimensional models generally overestimate the SE of up to 15% due to their lower peak flow velocity. However, using a constant flow velocity leads to good agreement for high SE due to the overlap of differences in flow profile and SE calculation.

中文翻译：

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毫流体系统中磁泳的高效数值建模


连续流磁泳是一种主动分离流体中颗粒的常用技术。对于分离系统设计，准确预测颗粒行为有助于表征系统性能，通常通过分离效率 （SE） 来衡量。虽然有限元法 （FEM） 仿真提供了高精度，但它们需要大量的计算资源。或者，使用流体流动、磁场和粒子运动的解析描述的简化数值模型可以更快地获得结果。在这项研究中，我们模拟了一个使用磁泳分离磁性粒子的毫流体系统。因此，我们 （1） 开发了一个简单的数值模型，可以模拟二维和三维矩形通道的连续流动磁泳，（2） 引入一种新颖而简单的方法来计算 SE，以及 （3） 量化模型假设在流廓和维度中对 SE 的影响。我们估计 SE 的方法考虑了由于流动剖面而导致的通道横截面上的粒子通量变化。将结果与在 COMSOL 中开发的 FEM 模型进行了比较。获得的三维仿真模型可以在几秒钟内计算结果，比 FEM 方法快约 180 倍，同时与 FEM 结果的偏差不到 2%。对不同二维和三维模型的比较强调了流动剖面和 SE 计算方法对结果的显着影响。由于峰值流速较低，二维模型通常高估了高达 15% 的 SE。然而，由于流剖面和 SE 计算中的差异重叠，使用恒定流速会导致高 SE 的良好一致性。