A parametric study of droplet deformation through a microfluidic contraction: Shear thinning liquids

https://doi.org/10.1016/j.ijmultiphaseflow.2006.12.002Get rights and content

Abstract

Numerical simulations of a droplet passing through an axisymmetric microfluidic contraction are presented, focusing on systems where one of the two liquids present is shear thinning. The simulations are performed using a transient Volume of Fluid (VOF) algorithm. When the droplet is shear thinning and the surrounding phase Newtonian, droplets deform in a similar way to Newtonian droplets that have a viscosity equal to the average viscosity of the shear thinning fluid while it is within the contraction. When the surrounding phase is shear thinning and the droplet Newtonian, droplets deform in a similar way to droplets contained within a Newtonian liquid that has a viscosity that is lower than that of the droplet. In both cases the behaviour of the shear thinning fluid can be broadly described in terms of a ‘characteristic’ Newtonian viscosity: However, determining the exact value of this viscosity without performing a full shear thinning simulation is not possible.

Introduction

Microfluidic technology has the potential to revolutionise chemical and biological analysis and processing in the same way that integrated circuit technology revolutionised data analysis and processing three decades ago (Squires and Quake, 2005). As microfluidic processes operate on small length scales they generally consume smaller amounts of sample, require less time, and are easier to automate and control than more conventionally sized processes. How droplets behave within such microfluidic devices has application in the biotechnology, food, cosmetic and pharmaceutical industries. For example: reagents in chemical and biological assays that are constrained within droplets can be mixed by shear as the droplets move through a network (Song and Ismagilov, 2003); extrusion of liquid filaments through concentric contractions can be used to produce micron-sized fibres (Jeong et al., 2004); breakup of a liquid stream in a contraction (flow focusing) can be used as an emulsification technique (Anna et al., 2002, Utada et al., 2005).

A microfluidic contraction is chosen as the representative geometry in this study as it is simple, contains strong but distinct regions of extensional and shear strain, and is able to deform a droplet’s shape considerably. Previously, the authors presented numerical studies of droplet deformation for Newtonian fluids passing through a 4:1 axisymmetric contraction (Harvie et al., 2005, Harvie et al., 2006). In this study we continue our examination of droplet behaviour within a microfluidic contraction, but focus on systems that contain a shear thinning fluid. Such fluids are abundant in industrial and biological fields. They include various polymer suspensions and melts (Bird et al., 1987, Barnes et al., 1989, Tanner, 2000), as well as suspensions of organic products such as blood (Gijsen et al., 1998). Understanding how biological fluids behave within microfluidic devices has particular application to biomedical ‘Lab-on-a-chip’ design.

Previous works concerned with the movement of droplets through contractions have usually considered only Newtonian fluids. Typical of these are the numerical studies of Tsai and Miksis, 1997, Khayat et al., 1997, Khayat et al., 2000, Aboubacar et al., 2002, and the experimental studies of Anna et al., 2002, Sugiura et al., 2002. A more complete review of the literature in this field is given in Harvie et al. (2006). The authors are not aware of any studies involving droplets passing through contractions where one of the fluids present is shear thinning. The single phase problem of a shear thinning fluid moving into a contraction has been considered both experimentally and numerically (see for example Kim-E et al., 1983). Droplet deformation in general extensional and shear flows has been extensively studied. Eggers, 1997, Stone, 1994 give reviews of this topic.

The purpose of this study is to analyse the effect that the Reynolds number, surface tension strength and shear thinning fluid characteristics have on the deformation of a droplet as it passes through an axisymmetric contraction. We consider systems where either the disperse phase is shear thinning and the continuous phase is Newtonian, or where the continuous phase is shear thinning and the disperse phase Newtonian. We simulate parameter ranges that are relevant to liquid–liquid systems and characteristic of microfluidic applications, and perform the simulations using a transient Volume of Fluid (VOF) finite volume algorithm.

Section snippets

Mathematical model

Three non-dimensional equations are used to describe motion throughout the disperse (i.e., droplet) and continuous (i.e., surrounding) phases; a continuity equation, a volume-averaged incompressible Navier–Stokes momentum equation, and an advection equation which describes the evolution of the disperse phase volume fraction ϕ,·u=0ρut+·ρuu=-p+1Weκδ(x-xs)n+1Re·μ[u+(u)T]ϕt+·ϕu=0These equations are fairly conventional, except possibly for the second term on the right of Eq. (2) which

Problem description and simulation method

The deformation of a droplet passing through a 4:1 axisymmetric contraction was considered (Fig. 1). The inlet velocity profile was taken to be that of fully developed Poiseuille flow based on the continuous phase zero shear rate viscosity; droplet deformation behaviour was found to be quite insensitive to the choice of this profile however. The pressure gradient normal to the outlet was chosen to ensure overall mass conservation. No-slip boundary conditions were applied at the channel walls,

Results: shear thinning disperse phase

Fig. 2a shows images of a shear thinning droplet that is contained within a Newtonian continuous phase and passing through the contraction. For this simulation Re = 4.12 × 10−2 and S = 3.97 × 10−1, thus, viscous forces generally dominate inertial forces and surface tension forces are of a comparable magnitude to the other forces acting in the system. For the shear thinning disperse phase, the Carreau parameters used were μd,∞ = 0, λ = 1 and n = 0.6. As shown in Fig. 3, the viscosity of this fluid is

Results: shear thinning continuous phase

Fig. 6a shows a simulation conducted with the same Re and S as used in the simulations of Fig. 2, Fig. 5, but now with a shear thinning continuous phase and Newtonian disperse phase. The Carreau parameters are the same as those used in Fig. 5a, that is, μc,∞ = 0, λ = 1.0 and n = 0.2. The behaviour of this droplet is quite different to that observed in the shear thinning disperse phase simulations: The droplet deforms less prior to entering the contraction; appears to ‘contact’ the contraction ‘lip’

Conclusions

Simulations of a droplet passing through an axisymmetric contraction were performed using a Volume of Fluid algorithm. As a continuation to the companion studies of Harvie et al., 2005, Harvie et al., 2006, only liquid–liquid systems were considered and either the disperse or continuous phase was modelled as a shear thinning fluid.

In cases where the disperse phase was shear thinning, the local viscosity of the droplet decreased as it entered the contraction, remained low while within the

Acknowledgement

This research was supported by the Australian Research Council Grants Scheme.

References (22)

  • R.B. Bird et al.

    Dynamics of polymeric liquids

    (1987)
  • Cited by (28)

    • Three-dimensional simulation of droplet dynamics in planar contraction microchannel

      2018, Chemical Engineering Science
      Citation Excerpt :

      Effect of capillary number (Ca), Reynolds number (Re), Weber number (We) and viscosity ratio on the droplet dynamics in a two-dimensional contraction microchannel were studied in more detail later (Christafakis and Tsangaris, 2008). Droplet dynamics in an axisymmetric contraction microchannel has been studied by Harvie et al. (2005, 2006, 2007), where the influence of the Re, Ca, and viscosity ratios on droplet deformation was discussed. Regarding three-dimensional numerical simulation of the droplet dynamics in contraction microchannel, one can find only few works in the literature.

    • Numerical simulations of heat transfer characteristics of gas-liquid two phase flow in microtubes

      2014, International Journal of Thermal Sciences
      Citation Excerpt :

      Therefore, geometric reconstruction of interface (PLIC VOF) is employed to serve as a treatment to achieve interface that is as sharp as the level set method. This numerical method has proven to be appropriate to the study of mass and heat transfer characteristic related to air–water two phase flow in micro-scale [14]. In micro-scale, buoyant force is expected to be small comparing to the surface tension across the interface.

    • Heat transfer characteristics of alternating discrete flow in micro-tubes

      2014, International Journal of Heat and Mass Transfer
      Citation Excerpt :

      Therefore, geometric reconstruction of interface (PLIC VOF) is employed to achieve this sharp interface. This numerical method has proven to be appropriate to the study of mass and heat transfer characteristic related to air–water two phase flow in micro-scale [15]. Fig. 2 shows the flow pattern of the simulated result and the flow visualization experimental result performed by Lim et al. [13].

    View all citing articles on Scopus
    View full text