Unstable two-phase flow rate in micro-channels and cracks under imposed pressure difference

This paper numerically investigates two-phase flow rate instabilities in micro-channels comprising localized geometrical restrictions (i.e., a convergent-divergent duct). A numerical Lattice Boltzmann method is used to model and simulate multiphase flow with an accurate treatment of the contact angle at the triple line. A pressure difference is imposed between the inlet and outlet sections of the channel. This induces flow and allows its time evolution to be followed. Indeed, the resulting flow exhibits strong time fluctuations as it is strongly influenced by the induced viscous forces acting at solid-fluid interfaces and by pressure discontinuities sustained across the curved fluid-fluid interfaces (i.e., across the curvatures of the menisci). Flow fluctuations are investigated parametrically for wetting and non-wetting fluids and for different micro-channel geometrical irregularities. For this purpose, an equivalent dimensionless formulation is adopted. Flow fluctuations are analyzed and related to the controlling dimensionless parameters (Reynolds number, Laplace number, Bejan number, contact angle and channel constriction ratio). This allows quantification of the coupled influence of physical fluid properties (surface tension and contact angle), channel geometry, and loading conditions (imposed pressure difference) on flow evolution. Numerical results show that, under particular conditions, capillary pressure jumps sustained across the fluid bridge (owing to flow rate, contact angle, and local orientation of channel walls) entirely compensate for the imposed pressure difference. This situation results in a no-flow state, i.e., the flow becomes impossible even under an imposed pressure difference.