Turbulent oscillation in unbalanced T-junction flows

Abstract: The T-junction impinging flow occurs in many fluid dynamics systems. In particular, the T-junction micromixer has recently been widely used for nanoparticle production, where the two inlet streams operate at a significant flow-rate imbalance and the Reynolds number is in the turbulent regime. This operating condition exposes a gap in the existing literature on the fluid dynamics of the T-junction. In this study, we used high-fidelity numerical simulations to investigate high-Reynolds-number unbalanced T-junction flows. We discover a new oscillatory behavior between the two inlet streams at the T-junction, leading to a new turbulence-production mode. We will present detailed evidence of this new behavior, in contrast to the existing understanding of balanced turbulent T-junction flows. This oscillatory behavior also persists across a range of Reynolds numbers simulated, where the Strouhal number is approximately constant, indicating a self-similar phenomenon. As a result, many of the fluid dynamics parameters follow a power-law relation with the Reynold number. The discovery in this paper affects real-world applications, where process design and product quality are affected by turbulence and mixing dynamics.

• The paper identifies a previously unreported turbulence mechanism in 3:1 unbalanced T-junction flows, where a water-side vortex detaches, collides with the opposite wall, and drives interfacial oscillations and rapid mixing.
• Simulations across Reynolds numbers from 479 to 7658 find a nearly constant Strouhal number of 0.44, turbulence onset near Re=O(100), and power-law scaling of kinetic energy, dissipation, and mixing distance.
• The unbalanced configuration produces earlier interface breakup, junction-centered energy dissipation, and an approximately halved Kolmogorov scale compared with balanced flow, offering design guidance for nanoparticle manufacturing.

Motivation and context

T-junction impinging flows underpin a range of engineering systems, from heat exchangers and ventilation ducts to microfluidic mixers used in nanoparticle synthesis, including lipid nanoparticle production for mRNA vaccines. The established regime map for T-junction flows comprises segregated, vortex, and engulfment regimes at low Reynolds number ($Re \lesssim 400$), followed by unsteady turbulent flow at higher $Re$. This literature is dominated by balanced inlet flow rates, whereas the industrially relevant operating point for nanoprecipitation-based pharmaceutical production differs in two decisive ways: the mixer runs at turbulent conditions ($Re \sim O(1000)$) to ensure mixing times shorter than the particle formation time, and the antisolvent-to-solvent flow rate ratio (FRR) is typically 3:1 to suppress aggregation. The paper addresses this gap by simulating water–ethanol flows in an unbalanced T-junction at intermediate to high Reynolds numbers, reporting what the authors identify as the first study of turbulent unbalanced T-junction flow.

Numerical methodology

The simulations solve the compressible Navier–Stokes equations coupled with a mass-transport equation for the ethanol mass fraction, using the stabilized finite element solver MUPFES. Two physical subtleties are treated explicitly: because hydrogen bonding and molecular packing cause volume non-conservation upon water–ethanol mixing, the velocity field is not divergence-free; and the density-gradient term in the advection–diffusion equation is retained as non-negligible. Composition-dependent density follows a Jouyban-Acree model and viscosity a Grunberg-Nissan fit, both evaluated at 293 K.

Turbulence closure uses the residual-based variational multiscale (RBVMS) method, analogous to high-fidelity LES with analytically derived error bounds; the SUPG method stabilizes the scalar transport. Time integration employs a second-order generalized-$\alpha$ scheme ($\rho_\infty = 0.2$) with weakly-coupled Newton–Raphson iteration requiring four orders of magnitude residual reduction per step. The mesh contains roughly 6.27 million tetrahedral elements, with element edge lengths on the order of the Kolmogorov scale, which the authors argue yields near-DNS accuracy. The geometry consists of two collinear opposing inlets ($3d$ each) and a $15d$ downstream pipe, filleted by $d/10$. All cases run at a total flow rate of 80 mL/min, either balanced (40/40) or unbalanced (60/20, FRR 3:1); $Re$ is varied by rescaling the diameter. Each case runs on 125 cores for approximately 30 hours to statistical convergence, followed by at least five oscillation periods of saved data. A validation simulation at matched $Re$ but different $Re$0 supports the scaling choices.

The new oscillatory turbulence-production mode

The central result contrasts balanced and unbalanced operation at comparable $Re$1. In the balanced case ($Re$2), consistent with prior experimental and numerical work, turbulence arises from periodic formation and shedding of a vortex pair at the top of the junction plus downstream destabilization of the interfacial plane. Even here the flow is not fully symmetric because the two fluids differ in density and viscosity, producing slightly stronger turbulence on the water side.

Under 3:1 unbalanced flow ($Re$3), a qualitatively different mechanism emerges: a single vortex tube develops on the water side of the junction, detaches from the wall, and propagates along a direction combining axial and tangential components toward the ethanol side. The detached tube collides with the ethanol-side wall and splatters, generating intense, rapidly dissipating turbulence. This single-vortex cycle also drives an interfacial oscillation between the streams: the vortex trailing edge pulls ethanol toward the water side during detachment, while the higher-momentum water stream pushes the interface back as the next vortex forms. Consequences include much earlier breakup of the interfacial plane than in balanced flow, instantaneous turbulent kinetic energy production peaking at the junction itself (rather than one to two diameters downstream after a development period), and a substantially higher peak non-dimensional turbulent kinetic energy. The dissipation rate, computed directly from the Reynolds stress tensor, correspondingly peaks at the junction. These differences directly bear on nanoparticle synthesis, where local energy dissipation rates set the nucleation environment.

Self-similarity across Reynolds numbers

Five logarithmically spaced Reynolds numbers were simulated under unbalanced conditions:

$Re$4	$Re$5	$Re$6	$Re$7	$Re$8	$Re$9
479	0.4766	11.39	$Re \sim O(1000)$0	$Re \sim O(1000)$1	0.8344
957	0.4539	$Re \sim O(1000)$2	$Re \sim O(1000)$3	$Re \sim O(1000)$4	0.9255
1914	0.4255	$Re \sim O(1000)$5	$Re \sim O(1000)$6	$Re \sim O(1000)$7	0.9669
3829	0.4231	$Re \sim O(1000)$8	$Re \sim O(1000)$9	$\alpha$0	0.9729
7658	0.4047	$\alpha$1	$\alpha$2	$\alpha$3	0.9759

The Strouhal number remains nearly constant, with mean $\alpha$4 and 99% confidence interval $\alpha$5, indicating that the junction oscillation is self-similar across the simulated range. The onset lies between $\alpha$6 and $\alpha$7, i.e., at $\alpha$8—well below the turbulent threshold conventionally associated with T-junctions. Because $\alpha$9, $\rho_\infty = 0.2$0, the Kolmogorov scale $\rho_\infty = 0.2$1, and the mixing distance $\rho_\infty = 0.2$2 all follow power laws in $\rho_\infty = 0.2$3, the junction behavior admits predictable extrapolation across scales.

Downstream behavior is more nuanced: although the cross-sectional mean non-dimensional kinetic energy at $\rho_\infty = 0.2$4 is similar across cases, the downstream profile is not self-similar until $\rho_\infty = 0.2$5. Below that, instabilities seeded at the junction decay and the flow reverts toward laminar, exacerbated by the non-monotonic mixture viscosity, which halves the effective $\rho_\infty = 0.2$6 once the fluid homogenizes. Only around $\rho_\infty = 0.2$7 does the full geometry exhibit self-similar behavior combining the junction oscillation with classical turbulent pipe flow.

Implications for nanoparticle production

At comparable total flow rate, the unbalanced configuration produces a mean Kolmogorov length scale roughly half that of the balanced case, with the minimum local scale about two orders of magnitude below the plotted mean. The mixing index reaches $\rho_\infty = 0.2$8 substantially sooner downstream under unbalanced flow. Since micromixing scales govern nanoparticle size distribution in nanoprecipitation, these results imply that studies attributing product differences to T-mixer geometry must account for the distinct turbulence mode induced by flow imbalance. The self-similar, power-law character of the unbalanced flow further enables designed experiments that isolate individual turbulence and mixing parameters, supporting systematic kinetics–kinematics correlations for formulation optimization.

Limitations and open questions

Several caveats qualify the findings. The study is entirely computational; no experimental validation of the oscillatory mode or its Strouhal number is presented. The numerical clipping of the ethanol mass fraction to $\rho_\infty = 0.2$9 each step, while argued to negligibly affect mass conservation, introduces a small artificial constraint. The Reynolds-number sweep varies only the diameter at fixed flow rate, so the reported power-law scalings conflate geometric and dynamic effects to some degree, though the duplicate condition at $3d$0 partially controls for this. The onset Reynolds number is bracketed only coarsely (between 239 and 479), and the precise dependence on FRR beyond the single 3:1 ratio tested is not explored. Whether the wall-collision vortex breakup persists in geometries without the $3d$1 fillet, or with sharper edges typical of some devices, remains open, as does quantitative linkage between the computed dissipation fields and measured nanoparticle size distributions.

Conclusion

This paper identifies a previously unreported oscillatory interfacial instability in unbalanced turbulent T-junction flows, driven by single-vortex formation, detachment, and wall collision, active from $3d$2 and characterized by an approximately constant Strouhal number near 0.44. The resulting turbulence production is faster and more intense than in balanced flow, shifting energy production to the junction itself and halving the Kolmogorov scale. Combined with predictable power-law scaling of turbulence and mixing quantities with $3d$3, these results provide both a corrected fundamental picture of T-junction dynamics under realistic pharmaceutical operating conditions and a quantitative basis for process design in nanoparticle manufacturing.