Elsevier

Chemical Engineering Journal

Volume 343, 1 July 2018, Pages 54-60
Chemical Engineering Journal

3D MRI velocimetry of non-transparent 3D-printed staggered herringbone mixers

https://doi.org/10.1016/j.cej.2018.02.096Get rights and content

Highlights

  • 3D MRI velocimetry quantifies complex vortex flows in a non-transparent device.

  • Staggered herringbone mixers (SHM) embedded in channel by additive manufacturing.

  • High channel surface shear rates identified and quantified by shear rate analysis.

  • Developed 3D MRI pulse sequence is faster than conventional MRI pulse sequences.

  • CFD simulations validate our 3D MRI data.

Abstract

In microfluidics confocal microscopy and PIV are well-suited instruments to analyze laminar and complex fluid dynamics. However, these analysis methods require transparent devices made of e.g. glass or silicon rubber. This prerequisite of transparency precludes investigations of complex geometries generated by modern 3D printing techniques. Yet, 3D printing enables the engineer to free-form fabricate chemical engineering devices of any complex fluidic architecture. Based on a 3D printed meandering channel reactor with incorporated staggered herringbone structure we exploit the limits of 3D flow magnetic resonance imaging (MRI) for the analysis of fluid dynamics on a sub-millimeter scale. We visualize the 3D flow field, in particular the secondary eddy flows and derive shear rate maps. CFD simulations of the virtual shadow are in agreement with our experimental findings and proof that flow MRI gives reliable experimental access to non-transparent flow geometries.

Introduction

Small-scale and microfluidic systems become increasingly important in many branches of science such as chemistry, cell biology, biotechnology [22], [34] as well as chemical reaction engineering where small volumes can be handled reliably, reaction times can be shortened and costs reduced [23], [31], [29]. In contrast to macroscale systems, diffusion and molecular transport mostly dominate transport phenomena in laminar flow regimes on the microscale [32], [30], [26]. Although laminar flow is predictable and easy to control, its fluid mechanical conditions are inefficient for the molecular mixing of different components. In laminar flow, viscous forces affect the hydrodynamics more than inertia. For example, a simple T-mixer operated at low Re numbers requires a long mixing channel because both inlet streams flow parallel and show only diffusive mixing between the layers [23]. Static mixers overcome this drawback by introducing secondary flows to a linear laminar flow and thus effectively combine the advantages of both, laminar and turbulent flow regimes [23], [28].

Staggered herringbone mixers (SHM) are known to induce transverse flow to overcome the drawbacks of laminar flows [28]. The introduction of higher vorticity in the channel enhances transport normal to the main flow field and avoids diffusion limitations for surface reactions [28] and mass transfer if the channel wall is permeable and transports gas into the fluid phase [13]. The staggered herringbone mixer’s (SHM) particular efficiency motivates us to further investigate and visualize the fluid conditions under such geometric conditions.

Computational fluid dynamics (CFD) simulations allow the rigorous prediction of the flow patterns and overall mixing performance [4], [15], [32], [25]. Numerical evaluation of such simulations mainly target the optimization of the staggered herringbone structure with respect to maximal surface interaction [16] and well developed transverse flow [33], [20], [5]. Any manipulation of the herringbone’s structure such as groove dimensions and tip orientation greatly effects the flow conditions. Extensive studies of engineered microstructures enable the precise control of flow patterns within a channel [3], [30].

Yet the biggest challenge in numerical evaluations is the significant gap between the real device and the corresponding virtual model. Especially in micro- and mesoscale systems, high fabrication accuracy is crucial for matching model predictions. Even slight fabrication imperfections in the channel height or width, or the structure of the staggered herringbones can lead to flow conditions forcing the fluid into directions not predicted by the virtual shadow. This issue becomes critical for small systems: to the person experienced in microfluidics experimentation, it is well known that even a dust particle or a trapped bubble leads to unforeseen fluid behavior. CFD simulations do not take these effects into account. In fact, the CFD-modelled virtual shadow represents an idealized situation only. The comparison of CFD simulation data with experimental data becomes also complex when dealing with realistic devices as opposed to precisely manufactured lithography-based microfluidic channel systems [8].

One of the most appreciated experimental procedure to map the real flow in channels with complex channel topology is confocal microscopy. Confocal microscopy uses dispersed fluorescent molecules or fluorescent particles to reveal the mixing behavior in the herringbone channels [28], [32], [3]. The optical method of Particle Imaging Velocimetry (PIV) produces high-resolution 3D flow maps based on the motion of the fluorescent particles in the fluid. One or more cameras capture images of flow tracers (e.g. density matched colloidal particles) enabling a resolution in short time depending on the lens size and particle size [9]. However, confocal microscopy and PIV necessarily require transparent devices, e.g. made of PDMS or glass [12]. This drawback ultimately excludes powerful manufacturing techniques like 3D printing due to the fact that most printing materials are not transparent. Yet, with modern 3D printing devices the manufacture of almost every geometry for a chemical engineering device is possible no matter the complexity of the geometry [14].

An alternative experimental procedure to quantitatively measure fluid dynamics in opaque or even non-transparent devices is magnetic resonance imaging (MRI) velocimetry. Using 3D MRI velocimetry we exploit below the limits for this technique in microfluidic systems. To showcase the methodology, we designed a microfluidic device with incorporated staggered herringbone structure suitable for MRI analysis. The whole device was fabricated via 3D printing, allowing for simple and flexible incorporation of herringbones within the channel. The layout of the staggered herringbones is based on the findings of Stroock et al. [28]. Below, we describe the visualization of eddy development due to the herringbone geometry and analyze the effect on shear stress patterns. These measurements are complemented with computational fluid dynamics simulations on the virtual shadow to compare fluidic phenomena experimentally determined with those predicted from simulations.

Section snippets

3D printed staggered herringbone mixer

Fig. 1 depicts the device design of the staggered herringbone mixer used for MRI and COMSOL studies. At the front of the device two inlets are provided to allow for two-phase flow and for studies of the inlet length, however such conditions are not reported here. In this study only one inlet is connected to the pump while the other one is sealed. The meandering channel has a total length of approximately 70 mm, a width of 2 mm and a height of 0.5 mm. The dimensions chosen here enable imaging

Velocity vector maps

From MRI data, we derive 2D velocity vector maps to describe the influence of the staggered herringbones on the fluid dynamics (Fig. 4). The CAD drawing of the negative structure of the mixer, shown in an isometric perspective, illustrates the original solid structure and the direction of flow. The solid structure consists of the narrow channel and the grooves of the staggered herringbones as shown in the enlargement of Fig. 4a. There, two colored lines define the heights (y-position) of two

Conclusion

In this study, we found that 3D MRI velocimetry is a profound tool to quantify complex and rapidly changing fluid dynamics in a non-transparent device with incorporated staggered herringbones. The latter causes steady but periodically changing eddy flows in the transversal plane that enhance mixing throughout the channel. With 3D MRI velocimetry we determined the direction and magnitude of these secondary flows that are especially predominant in the herringbone grooves and at the channel

Acknowledgement

Matthias Wessling acknowledges support through an Alexander von Humboldt Professorship. Financial support of the German Research Foundation (DFG) is acknowledged. Furthermore the authors kindly acknowledge financial support from Gerätezentrum Pro2NMR, a DFG supported joint instrumental NMR facility of RWTH Aachen University and KIT Karlsruhe. The authors acknowledge Monika Barth, Hans Breisig and Deniz Rall for fruitful discussions on the shear rate calculation method. Jonas Lölsberg is

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