Computational fluid dynamics (CFD) software tools for microfluidic applications – A case study

Abstract

This paper reports on an exemplary study of the performance of commercial computational fluid dynamic (CFD) software programs when applied as engineering tool for microfluidic applications. Four commercial finite volume codes (CFD-ACE+, CFX, Flow-3D and Fluent) have been evaluated by performing CFD-simulations of typical microfluidic engineering problems being relevant for a large variety of lab-on-a-chip (LOAC) applications. Following problems are considered as examples: multi lamination by a split and recombine mixer, flow patterning on a rotating platform (sometimes termed “lab-on-a-disk”), bubble dynamics in micro channels and the so called TopSpot^® droplet generator for micro array printing. Hereby mainly the capability of the software programs to deal with free surface flows including surface tension and flow patterning of two fluids has been studied. In all investigated programs the free surfaces are treated by the volume-of-fluid (VOF) method and flow patterning is visualised with a scalar marker method. The study assesses the simulation results obtained by the different programs for the mentioned application cases in terms of consistency of results, computational speed and comparison with experimental data if available.

Introduction

Today CFD methods are well described in many textbooks [1], [2] and applied routinely in engineering science. They serve as valuable tools for design and engineering of components and systems in turbo machinery, aerospace and many other fields [1]. In this paper we focus on the application of CFD as engineering tool for microfluidic devices and the particularities associated with it [3]. In micro dimensions, for example, surface forces dominate over body forces requiring special attention for problems involving two phase flows with free surfaces which are often driven by capillary forces. Typical flow situations are capillary wicking or formation of droplets which are characterised by low Weber and Reynolds numbers [4], [5], [6]. To model free surface flows including surface tension effects – amongst others – the so called volume-of-fluid method (VOF) has been established [7] and is still being refined [8], [9], [10], [11]. Another particularity in microfluidics is the increased importance of diffusion for mixing phenomena. Since in microfluidic flow problems the Reynolds numbers are typically very small, turbulence is hardly ever observed and mixing is driven by diffusion only at low Peclet numbers [12]. Effective mixing within short times can thus only be achieved by decreasing the diffusion length of the fluids which can technically be realized by multi lamination or chaotic advection [13], [14], [15], [16], [17], [18]. On the one hand the absence of turbulence in microfluidics simplifies the CFD treatment substantially but on the other hand diffusion is difficult to account for with the required accuracy in practical cases. High order discretisation schemes are required to suppress the so called “numerical diffusion” which is nothing else than numerical errors being accumulated by the algorithm.

Both of the described particularities, free surfaces as well as diffusion have been dealt with in length in the CFD-literature from a numerical point of view. In principle there are many approaches known to simulate these types of problems in more or less specific situations at various degrees of accuracy (see for example [11], [13], [19], [20]). In this paper however, we want to assess the topic from an engineering perspective and ask the question: How helpful are the software tools being available for the micro engineer to address these problems in practice? As it is the nature of the selected engineering problems, they can not be solved analytically and thus have to be considered numerically with CFD. The crucial points in this context are the availability and the applicability of CFD-tools for engineering purposes in the considered cases. To do so a case study of various commercial CFD codes has been performed with respect to experimental results, where available. Due to the variety of commercial software tools and the limited resources for performing such case studies the authors restricted their choice to the four previously mentioned Finite Volume codes. A comparison to well established Finite Element codes like COVENTOR [21] or COMSOL [22] was not possible in the framework of this work.

Benchmarking in general is an essential part of CFD research and code validation [23], [24], [25], [26], [27], [28]. However, due to the commercial nature of the software applied for the presented study, the algorithms are not in the public domain and are not know in detail. Therefore the presented case study can only be descriptive instead of analytic i.e. the outcome of the simulations can be documented and discussed but not be analysed in detail. Nevertheless, the state of the art of CFD simulation in microfluidics is presented by this approach and the question is addressed which tools are available and well suited for a specific purpose, if any. The devices studied in this paper were not selected for the purpose of driving certain numerical codes into problems, but are a representative selection of the problems encountered by the authors over the years in microfluidic research. Indeed, the major part of the paper deals with the application of simulation methods to these microfluidic devices that have not been published before. The results hopefully will provide guidance to micro engineers applying CFD as engineering tool as well as support for developers of CFD code in search of even faster and more accurate algorithms.