Spurious velocities in the Volume of Fluid method: modeling a sub-millimeter bubble

In both industrial and natural processes, such as electrochemical gas evolution and atomization of fuel, understanding the dynamics of gas-liquid interfaces is critical in designing more efficient processes. For example, in electrochemical systems, the bubbles produced at the electrodes must be removed as it reduces the area for electrochemical reaction and the spray characteristics of fuel effects the engine performance in vehicles. In these systems, the characteristic diameters of bubbles and droplets are typically smaller than a millimeter, tens of micrometer for atomization of fuels and few micrometer to hundreds of micrometer for electrochemical gas evolution. Due to the small length scales that are relevant in these processes, surface tension governs the dynamics of the flow. To model these two-phase flow scenarios, the Volume of Fluid (VOF) method is widely adopted to capture the interface dynamics. Due to the popularity of open source solvers, in the current paper we focus on interFoam, the VOF based solver available in OpenFOAM (OF). The VOF method advects the volume fraction of the liquid phase and prevents the excessive smearing of the interface using interface compression method [1]. The discontinuous nature of the interface that is produced with this approach introduces errors when computing the curvature which along with imbalance in the surface tension and pressure forces generates spurious velocities near the interface [1,2]. These spurious velocities can sometimes be strong enough to render some simulations inaccurate (like in [3]). Typically in literature that uses interFoam, the diameters of bubbles or droplets which are modeled are a millimeter and larger [2]. It is worth pointing out that the studies that use ANSYS Fluent has reported a more stable behavior of smaller bubbles which could be attributed to the advanced interface reconstruction methods used in its VOF approach [4]. Recent developments in interFoam has replaced the original formulation that used the Continuum Surface force [1] with more advanced models like Sharp Surface Force and others (see [2]) to reduce the spurious velocities but so far no approach has managed to eliminate them [2].As modeling small bubbles that are less than a millimeter in diameter has not been shown reliably using OF in literature, we attempt to address this in the current study. The interFoam solver, available in OF 6, is modified to include the Sharp Surface force model, which uses a three step smoothing of the interface curvature and a sharpened volume fraction of liquid. The sharpening of the volume fraction is computed based on a user defined coefficient (Csh), where 0≤Csh