Formation characteristics of Taylor bubbles in power-law liquids flowing through a microfluidic co-flow device

TL;DR

This study addresses Taylor bubble formation in circular co-flow microchannels with power-law PAAm solutions by implementing a coupled LS-VOF (CLSVOF) framework to accurately capture gas–liquid interfaces and non-Newtonian rheology. The approach combines level-set interface tracking with mass-conserving VOF, using CSF for surface tension and a power-law constitutive model for the continuous phase, enabling detailed analysis of bubble length $L_B$, film thickness $oldsymbol{ his$delta}$, and pressure drop, across varying PAAm concentration, inlet velocities, and surface tension $oldsymbol{oldsymbol{ abla}}$. Key findings include a decrease in $L_B$ with increasing PAAm concentration and liquid velocity, an increase in $L_B$ with higher surface tension and gas velocity, and the development of flow regime maps that distinguish non-Taylor, Taylor, and elongated Taylor bubbles; a modified Capillary number $Ca' = K U_B^n D^{(1-n)}/oldsymbol{ abla} oldsymbol{ ext{sigma}}$ governs bubble scaling, with $L_B/D$ collapsing onto a single relation across PAAm concentrations. The results provide practical guidelines for controlling Taylor bubble generation in non-Newtonian flows and advance understanding of Newtonian-like bubble behavior in complex rheology environments.

Abstract

Formation and dynamics of Taylor bubble in power-law liquids flowing through a circular co-flow microchannel are numerically investigated using coupled level set and volume-of-fluid method. Aqueous solutions of polyacrylamide (PAAm) are used as power-law liquids. Influences of PAAm concentration, gas-liquid velocities, and surface tension on bubble characteristics are explored. Various mechanism of bubble breakup are observed in different concentration of PAAm. Based on the bubble length with respect to the channel diameter, two different flow regimes are identified. Flow pattern maps are constructed based on inlet velocities, and scaling laws are proposed to estimate the bubble length.

Figures (16)

• Figure 1: Schematic of (a) 3D cross-sectional view of Taylor bubble formation in a circular co– flow geometry, (b) 2D depiction of bubbles surrounded by a thin liquid film, and separated by liquid slug, (c) 2D axisymmetric representation of computational domain with imposed boundary conditions, and (d) mesh refinement near the wall.
• Figure 2: (a) Comparison of interface tracking by two different mesh element sizes, (b) grid independence study of the bubble length for air-PAAm 1.25% system at $U_G$ = 0.5 m/s, $U_L$ = 0.5 m/s, (c) comparison of model predications with experimental and numerical (VOF) results of deng2017 at $Q_o$ = 0.03 $mL/h$, $\sigma$ = 19.45 mN/m, $\eta_{oil}$ = 49.50 mPa.s, and $\eta_{water}$= 1.04 mPa.s, and (d) comparison of Taylor bubble shape for air-water system at $U_G$ = 0.5 m/s, $U_L$ = 0.5 m/s with the results of gupta-2009.
• Figure 3: Effect of PAAm concentration on (a) effective viscosity, (b) bubble length and formation frequency, (c) liquid film thickness and bubble velocity, and (d) bubble volume at $U_{L}$ = 0.5 m/s and $U_{G}$ = 0.5 m/s.
• Figure 4: Taylor bubble evolution in a co– flow microchannel having different PAAm solution for (a) PAAm 0.1 %, (b) PAAm 0.25%, (c) PAAm 0.50%, (d) PAAm 0.75 %, (e) PAAm 1.0%, and (f) PAAm 1.25 % at $U_{L}$ = 0.5 m/s and $U_{G}$ = 0.5 m/s.
• Figure 5: The scaling relation of non– dimensional bubble length with the modified Capillary number ($Ca^{'}$) for different PAAm concentration solutions at $U_{L}$ = 0.5 m/s and $U_{G}$ = 0.5 m/s.