Two- and three-dimensional modeling and optimization applied to the design of a fast hydrodynamic focusing microfluidic mixer for protein folding

Abstract

We present a design of a microfluidic mixer based on hydrodynamic focusing which is used to initiate the folding process (i.e., changes of the molecular structure) of a protein. The folding process is initiated by diluting (from 90% to 30%) the local denaturant concentration (initially 6 M GdCl solution) in a short time interval we refer to as mixing time. Our objective is to optimize this mixer by choosing suitable shape and flow conditions in order to minimize this mixing time. To this end, we first introduce a numerical model that enables computation of the mixing time of a mixer. This model is based on a finite element method approximation of the incompressible Navier-Stokes equations coupled with the convective diffusion equation. To reduce the computational time, this model is implemented in both full three-dimensional (3D) and simplified two-dimensional (2D) versions; and we analyze the ability of the 2D model to approximate the mixing time predicted by the 3D model. We found that the 2D model approximates the mixing time predicted by the 3D model with a mean error of about 15%, which is considered reasonable. Then, we define a mixer optimization problem considering the 2D model and solve it using a hybrid global optimization algorithm. In particular, we consider geometrical variables and injection velocities as optimization parameters. We achieve a design with a predicted mixing time of 0.10 μs, approximately one order of magnitude faster than previous mixer designs. This improvement can be in part explained by the new mixer geometry including an angle of π /5 radians at the channel intersection and injections velocities of 5.2 m s −1 and 0.038 m s −1 for the side and central inlet channels, respectively. Finally, we verify the robustness of the optimized result by performing a sensitivity analysis of its parameters considering the 3D model. During this study, the optimized mixer was demonstrated to be robust by exhibiting mixing time variations of the same order than the parameter ones. Thus, the obtained 2D design can be considered optimal also for the 3D model. C 2013 American Institute of Physics.

Modelling and optimization applied to the design of fast hydrodynamic focusing microfluidic mixer for protein folding

“…1. Furthermore, 3D,q can be approximated considering a two-dimensional projection, as suggested in previous works [3,16,29]. A representation of this projection, denoted by 2D,q , is shown in Fig.…”

“…Those parameters have been demonstrated to be suitable for solving similar optimization problems in [13,16,29,37]. Moreover, when the GMA ends, its solution is improved by performing 10 iterations of the Steepest Descent (SD) algorithm, in which the descent step size ρ is determined using 10 iterations of a dichotomy method starting from ρ 0 = 1.…”

“…Initialization is also of vital importance for meta-heuristic methods such as Genetics Algorithms (GA) [7,8], for which a lack of heterogeneity in the individuals of the initial population may yield to a early convergence to a local minimum of T [9]. From a general point of view, choosing suitable initial conditions can improve the efficiency of existing optimization algorithms by reducing the number of evaluations of the cost function, which is particularly worthy when dealing with expensive functional calculations, as it is the case in many industrial design problems [10][11][12][13][14][15][16][17][18]. There already exists several optimization algorithms which have been improved by choosing appropriate initialization techniques.…”

Modeling and optimization of activated sludge bioreactors for wastewater treatment taking into account spatial inhomogeneities

“…A typical representation of a bioreactor is a tank as depicted in Figure 2-(a), with a small inlet aperture at its top (through which polluted water enters the reactor) and a small outlet aperture at its bottom (through which the treated water leaves the reactor). In Section 2.2.2, following the model developed in [32] for fluidic mixers and for the sake of model simplification, we neglect the possible effects coming from the size and collocation of these apertures. To do that, we only model an intermediate part of the bioreactor, denoted by Ω * (dark part of Figure 2-(a)), assuming that the volume of the removed part is negligible compared to the total bioreactor volume.…”

“…Section 4.1) system (1) coupled with (10)- (12) with the flow rate Q = Q OL (·). We solve problem (21) with the Hybrid genetic algorithm (and its parameters) presented in [32].…”