Numerical investigation of mixing performance in microchannel T-junction with wavy structure

Highlights

• We evaluate mixing performance of micromixer T-junction with wavy structure.

• Mixing performance is compared in terms of mixing index performance index (PI).

• Mixing performance is superior as compared to conventional T-junction.

• PI improves up to 2 order-of-magnitudes at higher Reynolds numbers.

• Effect of Dean number is investigated.

Abstract

Mixing in chemical microreactors is a multi-scale processes as the transport mechanisms occur at different length scales. Since the small scale mixing depends mainly on molecular diffusion, a relatively long channel is necessary to achieve the desired mixing. To improve the mixing quality whilst keeping easy and simple manufacturing, an innovative design of microchannel T-junction with wavy structure is proposed to trigger secondary flow for enhanced chaotic mixing. To gain better understanding of the interplay of transport mechanism, we develop numerical model for micro-mixing in micro-channel T-junction with wavy structure; the model considers single phase mixing of laminar Newtonian miscible fluid and it solves for conservation of mass, momentum and species. To ensure robust and accurate solutions, several discretization methods and mesh sizes were tested and compared; while to ensure fidelity of the comparison of mixing performance, we introduce the performance index (PI) concept for the first time in micromixing area. The numerical results suggest that the mixing quality and PI improves significantly for microchannel T-junction with wavy structure, especially at higher Reynolds number. The performance enhancement is also seen for all range of Schmidt numbers, wavy frequencies and amplitudes considered, which shows potential for several practical applications.

Introduction

Over the past decade, micro-mixers have gained considerable attention especially in the chemical processes, pharmaceutical industries, reactive polymerization and nanoparticle precipitations. Apparent advantages of microreactors are highly efficient micromixing, a high area-to-volume ratio, efficient heat transfer ability, the avoidance of hot spots by effective temperature control, and high operational safety for highly exothermic or explosive chemical reactions, compact design and simpler process control. The main concept underlying these mixers is the impinging of two reactants streams in a confined space where mixing proceeds without stirring devices, i.e. passive mixing; however, since small scale mixing depends mainly on molecular diffusion, a relatively long channel is necessary to achieve the desired mixing. Here, mixing is a multiscale processes as it involves various scales phenomena, ranging from microchannel length in the order of ∼1 cm, width and height of microchannel ∼1 mm, flow advection ∼10 μm, diffusivity of liquid ∼1 nm, and chemical reaction ∼0.1 nm.

Numerous experimental [1], [2], [3], [4], [5], [6] and numerical investigations [7], [8], [9], [10], [11], [12] on mixing processes in micro-channel T-junction have been conducted and reported. Extensive reviews on the mixing processes in micro-channel have also been published [13], [14], [15], [16]. Mixing in T-junction has been studied regarding factors such as the influence of the aspect ratio of the mixer, fluid speed, flow regimes and approaches to enhance mixing performance. Sultan et al. [6] identified four flow regimes in the T-junction microchannel:

• Segregated flow regime: a steady flow regime for which two parallel streams of fluid flow from inlet to outlet with hardly mixing; typically, it occurs at the very low Reynolds number.

• Vortex flow regime: this is characterized by the existence of vortices inside each jet and their rotation axis is aligned with the mixing channel axis.

• Engulfment flow regime: steady flow where the flow patterns are not parallel; but, there is a rotation of the jets over the channel axis that transports fluid from one half of the channel to the other half.

• Chaotic flow regime: this is characterized by the formation of a vortex street evolving through mixing channel, which promotes fast mixing of the two jets. The chaotic flow regime is a dynamic flow regime where the jets are engulfed by action of vortices that have a diameter close to half of the mixing channel width and are formed immediately downstream the jet impingement point. The fluids from the two inlet jets are engulfed in the vortex street that evolves from the jet impingement point towards the outlet.

Good mixing performance in a micromixer is an important design factor as it is particularly suited for fast complex chemical reaction where the reaction yields is strongly affected by the mixing quality [17]. In order to enhance mixing, two approaches can be implemented, i.e., passive and active mixing enhancement [13], [16]. For the former, we can make use of the energy of the flow itself by, for example, designing the shape of the channel to stretch and fold the flow [18], and generate chaotic advection in cross-channel micromixer [19]. Moreover, several geometries have been proposed by many researchers, e.g. channel of zigzag shape [20], omega shape [17], converging–diverging shape [21], splitting-recombination configurations [22], [23] and SZ shape mixer [24]. In short, the mixing enhancement can be achieved by carefully designing the channel so that the reactants are forced to flow through channels of special shapes and create vortices and disturb the flow stability which, in turn, leads to the chaotic flow regime. These can increase the interfacial area between fluid segments thus created, and by reducing the diffusion length for heat and mass transport without any additional equipment or energy added to the system.

In an active micromixer, on the other hand, external forces and artifact is added to help enhance mixing [25]; this external force can be introduced using mechanical rotation [26], pulsation of the flow [27], vibration or electrical excitation of the flow [28] and microwaves [29]. Most of the proposed approaches, however, add complexities to the design and manufacturing processes/cost which can be impractical for some applications. Tonkovich et al. [30] showed that the most economical method for mass manufacturing of microreactor is stamping method; however, this method is unable to create complex geometry in three-dimensional shapes as proposed by many researchers to enhance mixing performance. There is thus a need for improved yet easy-to-manufacture design for mixing in micro-channel T-junction with the focus of achieving chaotic flow regime at relatively low Reynolds number with a simple geometry modification. Here, we propose to use microchannel T-junction with wavy structure to create chaotic advection which is expected to improve the mixing performance. The objectives of the work presented here are twofold: (i) to evaluate mixing performance of micro-channel T-junctions with wavy structure relatives to conventional straight microchannel T-junction; and (ii) to study the effect of Reynolds and Schmidt number to the mixing performance at microchannel T-junction with wavy structure.

The layout of the paper is as follows. First, the model development is introduced; it comprises conservation equations of mass, momentum and species for mixing. The mathematical model is then solved numerically utilizing finite-volume based CFD software. The sensitivity of numerical solutions to the grid and discretization scheme is evaluated. Fluid flow and mass transfer (mixing) performance of various designs are evaluated in terms of a “mixing index” (MI) and “Performance index” (PI) defined later. Parametric studies are then carried out for the effect of Reynolds, Schimdt number and Dean number (wavy frequency and amplitude). Finally, advantages and limitations of the design are highlighted, and conclusions are drawn based on the results presented.