CFD analysis of microfluidic droplet formation in non-Newtonian liquid

TL;DR

This work develops and validates a 3D volume‑of‑fluid CFD model to study Newtonian droplets formed in a non‑Newtonian continuous phase within a microfluidic T‑junction. The continuous phase obeys a power‑law rheology $ar{\tau}=\eta(\dot{\gamma})\dot{\gamma}$ with $\eta(\dot{\gamma})=K\dot{\gamma}^{n-1}$, enabling systematic exploration of how $n$, $K$, and interfacial tension $\sigma$ influence drop formation, deformation, and regime transitions (squeezing, dripping, jetting). The study provides quantitative scalings of droplet size with modified Capillary number $Ca'$ and dispersed‑phase Reynolds number $Re_w$ across multiple parameter regimes, and demonstrates near‑spherical droplets in dripping/jetting but plug shapes in squeezing. These results offer practical guidelines for tuning flow rates, rheology, and interfacial tension to achieve desired droplet sizes and shapes in non‑Newtonian microfluidic systems, complementing experimental efforts with a validated computational framework.

Abstract

A three-dimensional, volume-of-fluid (VOF) based CFD model is presented to investigate droplet formation in a microfluidic T-junction. Genesis of Newtonian droplets in non-Newtonian liquid is numerically studied and characterized in three different regimes, viz., squeezing, dripping and jetting. Various influencing factors such as, continuous and dispersed phase flow rates, interfacial tension, and non-Newtonian rheological parameters are analyzed to understand droplet formation mechanism. Droplet shape is reported by defining a deformation index. Near spherical droplets are realized in dripping and jetting regimes. However, plug shaped droplets are observed in squeezing regime. It is found that rheological parameters have significant effect on the droplet length, volume, and its formation regime. The formation frequency increases with increasing effective viscosity however, the droplet volume decreases. This work effectively provides the fundamental insights into microfluidic droplet formation characteristics in non-Newtonian liquids.

Figures (16)

• Figure 1: (a) Considered 3D T– junction geometry, and (b) 2D schematic of droplet formation in a T– junction microchannel.
• Figure 2: Comparison of the model predictions with the experimental results of garstecki-2006 (figures reprinted with permission from the publisher, Royal Society of Chemistry) for (a) $Q_w = 0.14$$\mu L/s$ and $Q_o$ = 0.124 $\mu L/s$, (b) $Q_w = 0.14$$\mu L/s$ and $Q_o$ = 0.408 $\mu L/s$, (c) $Q_w$ = 0.004 $\mu L/s$ and $Q_o$ = 0.028 $\mu L/s$, (d) $Q_w$ = 0.006 $\mu L/s$ and $Q_o$ = 0.028 $\mu L/s$. Comparison of droplet length with (e) experimental results of garstecki-2006 and numerical predictions by raj-2010 at $Q_w$ = 0.14 $\mu L/s$, $\sigma$ = 0.0365 N/m, $\eta_o = 0.01~ Pa.s$, $\eta_w = 0.001~ Pa.s$, and (f) experimental as well as LBM results of van-2006 at $Q_w$ = 0.055 $\mu L/s$, $\sigma$ = 5 mN/m, $\eta_o = 6.71~ mPa.s$ and $\eta_w= 1.95~ mPa.s$.
• Figure 3: Droplet formation mechanism for Newtonian and power-law liquids at a fixed operating condition of $Q_o = 0.408$$\mu L/s$, $Q_w = 0.14$$\mu L/s$, K= 0.01 $Pa.{s^n}$, $\eta_w = 0.001$ Pa.s and $\sigma$ = 0.0365 N/m.
• Figure 4: Droplet formation mechanism (a) squeezing regime ($n$=0.80) and (b) dripping regime ($n$=1.10) at a fixed operating condition of $Q_o = 0.408$$\mu L/s$, $Q_w = 0.14$$\mu L/s$, K= 0.01 $Pa.{s^n}$, $\eta_w = 0.001$ Pa.s and $\sigma$ = 0.0365 N/m.
• Figure 5: Effect of power– law index on (a) non-dimensional droplet length (b) droplet velocity and volume, (c) deformation index ($D.I$), and (d) pressure profiles along the channel centerline at fixed $K= 0.01~Pa .s^n$, $\eta_w = 0.001~Pa.s$, $\sigma = 0.0365~N/m$, $Q_o = 0.408 ~\mu L/s$, and $Q_w = 0.14~\mu L/s$.