Stokes flow paths separation and recirculation cells in X-junctions of varying angle

TL;DR

This study investigates how the angle of X-junctions influences fluid flow paths and recirculation cells in the Stokes flow regime, revealing counterintuitive flow behaviors and the critical role of junction geometry.

Contribution

It provides experimental and numerical analysis of flow separation and recirculation in X-junctions at varying angles, highlighting the impact of geometry on flow patterns in Stokes flow.

Findings

Flow preferentially bounces back into the outlet at low angles.

Recirculation cells appear below a 33.8° threshold angle.

Flow behavior is governed by energy dissipation minimization.

Abstract

Fluid and solute transfer in X-junctions between straight channels is shown to depend critically on the junction angle in the Stokes flow regime. Experimentally, water and a water-dye solution are injected at equal flow rates in two facing channels of the junction: Planar Laser Induced fluorescence (PLIF) measurements show that the largest part of each injected fluid "bounces back" preferentially into the outlet channel at the lowest angle to the injection; this is opposite to the inertial case and requires a high curvature of the corresponding streamlines. The proportion of this fluid in the other channel decreases from 50% at 90\degree to zero at a threshold angle. These counterintuitive features reflect the minimization of energy dissipation for Stokes flows. Finite elements numerical simulations of a 2D Stokes flow of equivalent geometry con rm these results and show that, below the threshold angle 33.8\degree recirculation cells are present in the center part of the junction and separate the two injected flows of the two solutions. Reducing further leads to the appearance of new recirculation cells with lower flow velocities.