(368g) Repressing Spurious Currents in the Modelling of Two-Phase Flows in Microfluidics

Multiphase flows are widely encountered in microfluidic applications, and the design of micro-scale two-phase contacting geometries (e.g. T-junctions) are often aided by the predictive modeling capability of computational fluid dynamics (CFD) methods. The challenge associated with two-phase CFD at the micro-scale is that interfacial effects outweigh inertial effects, resulting in a changing and developing phase interface, which needs to be accurately predicted during the simulation. To accomplish this, most CFD methods implement an interface capturing technique, in which an indicator function is used to describe the interface location.

However, almost all implicit interface capturing methods, including the volume-of-fluid (VOF) method, are susceptible to the generation of spurious currents at the interface. These currents are unphysical and arise entirely due to numerical flaws, even in the absence of external forces. Even though spurious currents are not a major issue in inertia-dominated systems, they may introduce errors in the simulation of capillary-driven flows up to a point where the solution has no relevance anymore. In order to increase the predictive capabilities of the VOF method in simulating two-phase flows at the microscale, which are often governed by interfacial forces, several methods are investigated to suppress the generation of spurious currents. Three sources of spurious currents in the VOF method have been identified: (1) the inaccurate calculation of the interface curvature, (2) the lack of a discrete force balance and (3) the presence of complex solid boundaries.

The first source relates to the fact that interface curvature and surface normals are determined from a sharp jump in the VOF function. These abrupt changes may induce instabilities that translate in the generation of unphysical flows in a region close to the interface. A smoothing operation performed on the indicator function prior to the calculation of the interface curvature has been implemented. This method, although simple in principle, was found to mitigate these errors and maintain the simulation in a stable state. The second source refers to the consistent coupling of surface tension and pressure. Although in the VOF method as implemented in OpenFoam an exact balance between pressure and surface tension has been established, imbalances may still exist due to errors in the iterative procedure. The first two sources of spurious currents have been observed to present issues especially in situations where the fluid interface is smeared over a few computational cells. A method has therefore been investigated that reduces the thickness of the interfacial region by sharpening the indicator function. As such, the effect of surface tension is confined to a single grid cell. Finally, complex solid boundaries can also give rise to spurious currents. This phenomenon has been observed to play a significant role in the simulation of droplet break-up in microfluidic T-junction channels. In order to eliminate this source of instabilities, a Gaussian smoother has been applied to the solid wall normal vectors that essentially replaces the sharp solid edges with slightly rounded versions.

We will report in detail on the implementation of the improved VOF method in OpenFOAM^®, and will benchmark our obtained results with literature data for droplet generation in microfluidic T-junctions at different Capillary numbers.