In this work, we consider a microfluidic mixer that uses hydrodynamic diffusion stream to induce the beginning of the folding process of a certain protein. To perform these molecular changes, the concentration of the denaturant, which is introduced into the mixer together with the protein, has to be diminished until a given value in a short period of time, known as mixing time. In this context, this article is devoted to optimize the design of the mixer, focusing on its shape and its flow parameters with the aim of minimizing its mixing time. First, we describe the involved physical phenomena through a mathematical model that allows us to obtain the mixing time for a considered device. Then, we formulate an optimization problem considering the mixing time as the objective function and detailing the design parameters related to the shape and the flow of the mixer. For dealing with this problem, we propose an enhanced optimization algorithm based on the hybridization of two techniques: a genetic algorithm as a core method and a multi-layer line search methodology based on the secant, which aims to improve the initialization of the core method. More precisely, in our hybrid approach, the core optimization is implemented as a sub-problem to be solved at each iteration of the multi-layer algorithm starting from the initial conditions that it provides. Before applying it to the mixer design problem, we validate this methodology by considering a set of benchmark problems and, then, compare its results to those obtained with other classical global optimization methods. As shown in the comparison, for the majority of those problems, our methodology needs fewer evaluations of the objective function, has higher success rates and is more accurate than the other considered algorithms. For those reasons, it has been selected for solving the computationally expensive problem of optimizing the mixer design. The obtained optimized device shows a great reduction in its mixing time with respect to the state-of-the-art mixers.

中文翻译：

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建模和优化应用于蛋白质折叠快速流体动力聚焦微流体混合器的设计

在这项工作中，我们考虑使用流体扩散流来诱导某种蛋白质折叠过程开始的微流体混合器。为了进行这些分子变化，必须降低与蛋白质一起引入混合器中的变性剂的浓度，直到在短时间内称为给定时间的给定值为止。在这种情况下，本文致力于优化混合器的设计，着眼于混合器的形状和流量参数，以最大程度地减少其混合时间。首先，我们通过数学模型描述所涉及的物理现象，该数学模型使我们能够获得所考虑设备的混合时间。然后，我们以混合时间为目标函数，提出了一个优化问题，并详细介绍了与混合器的形状和流量有关的设计参数。为了解决这个问题，我们提出了一种基于两种技术混合的增强型优化算法：遗传算法作为核心方法和基于割线的多层线搜索方法，旨在改进核心方法的初始化。 。更准确地说，在我们的混合方法中，核心优化被实现为一个子问题，该子问题从多层算法提供的初始条件开始在多层算法的每次迭代中都要解决。在将其应用于混频器设计问题之前，我们通过考虑一组基准问题来验证该方法，然后，将其结果与其他经典全局优化方法获得的结果进行比较。如比较所示，对于大多数这些问题，我们的方法比其他考虑的算法需要更少的目标函数评估，更高的成功率并且更准确。由于这些原因，选择它来解决优化混频器设计的计算量大的问题。相对于现有技术的混合器，获得的优化装置显示出其混合时间大大减少。选择它来解决优化混频器设计的计算量大的问题。相对于现有技术的混合器，获得的优化装置显示出其混合时间大大减少。选择它来解决优化混频器设计的计算量大的问题。相对于现有技术的混合器，获得的优化装置显示出其混合时间大大减少。