We present a closed-form expression that allows the reader to predict the size of bubbles and droplets created in T-junctions without fitting. Despite the wide use of microfluidic devices to create bubbles and droplets, a physically sound expression for the size of bubbles and droplets, key in many applications, did not yet exist. The theoretical foundation of our expression comprises three main ingredients: continuity, geometrics and recently gained understanding of the mechanism which leads to pinch-off. Our simple theoretical model explains why the size of bubbles and droplets strongly depends on the shape of a T-junction, and teaches how the shape can be tuned to obtain the desired size. We successfully validated our model experimentally by analyzing the formation of gas bubbles, as well as liquid droplets, in T-junctions with a wide variety of shapes under conditions typical to multiphase microfluidics.

The high degree of uncertainty and conflicting literature data on the value of the permeability coefficient (also known as the mushy zone constant), which aims to dampen fluid velocities in the mushy zone and suppress them in solid regions, is a critical drawback when using the fixed-grid enthalpy-porosity technique for modelling non-isothermal phase-change processes. In the present study, the sensitivity of numerical predictions to the value of this coefficient was scrutinised. Using finite-volume based numerical simulations of isothermal and non-isothermal melting and solidification problems, the causes of increased sensitivity were identified. It was found that depending on the mushy-zone thickness and the velocity field, the solid–liquid interface morphology and the rate of phase-change are sensitive to the permeability coefficient. It is demonstrated that numerical predictions of an isothermal phase-change problem are independent of the permeability coefficient for sufficiently fine meshes. It is also shown that sensitivity to the choice of permeability coefficient can be assessed by means of an appropriately defined Péclet number.

Molten metal melt pools are characterised by highly non-linear responses, which are very sensitive to imposed boundary conditions. Temporal and spatial variations in the energy flux distribution are often neglected in numerical simulations of melt pool behaviour. Additionally, thermo-physical properties of materials are commonly changed to achieve agreement between predicted melt-pool shape and experimental post-solidification macrograph. Focusing on laser spot melting in conduction mode, we investigated the influence of dynamically adjusted energy flux distribution and changing thermo-physical material properties on melt pool oscillatory behaviour using both deformable and non-deformable assumptions for the gas-metal interface. Our results demonstrate that adjusting the absorbed energy flux affects the oscillatory fluid flow behaviour in the melt pool and consequently the predicted melt-pool shape and size. We also show that changing the thermo-physical material properties artificially or using a non-deformable surface assumption lead to significant differences in melt pool oscillatory behaviour compared to the cases in which these assumptions are not made.

Experimental observations of high-energy surface melting processes, such as laser welding, have revealed unsteady, often violent, motion of the free surface of the melt pool. Surprisingly, no similar observations have been reported in numerical simulation studies of such flows. Moreover, the published simulation results fail to predict the post-solidification pool shape without adapting non-physical values for input parameters, suggesting the neglect of significant physics in the models employed. The experimentally observed violent flow surface instabilities, scaling analyses for the occurrence of turbulence in Marangoni driven flows, and the fact that in simulations transport coefficients generally have to be increased by an order of magnitude to match experimentally observed pool shapes, suggest the common assumption of laminar flow in the pool may not hold, and that the flow is actually turbulent. Here, we use direct numerical simulations (DNS) to investigate the role of turbulence in laser melting of a steel alloy with surface active elements. Our results reveal the presence of two competing vortices driven by thermocapillary forces towards a local surface tension maximum. The jet away from this location at the free surface, separating the two vortices, is found to be unstable and highly oscillatory, indeed leading to turbulence-like flow in the pool. The resulting additional heat transport, however, is insufficient to account for the observed differences in pool shapes between experiment and simulations

The hydraulic permeability of single-layer fibrous media is studied through two-dimensional (2D) and three-dimensional Navier-Stokes based flow simulations. As simple representations of such materials, one-dimensional arrays of parallel cylinders as well as two-dimensional arrays of perpendicularly crossing cylinders were used. The distance between the cylinders was either constant (ordered layers) or variable (disordered layers). For both 1D and 2D ordered layers, we propose a geometrical scaling rule for the hydraulic permeability as a function of cylinder radius and solid volume fraction (porosity), which is a modification of a scaling rule previously reported by Clague and co-workers. The proposed modification is based on theoretical considerations and leads to significantly improved correspondence with simulation results. The hydraulic permeability of unstructured layers is found to be higher than that of structured layers of equal porosity for both 1D and 2D arrays. We propose a single parameter that can be easily determined experimentally to characterize the degree of disorder, as well as a generally valid correction factor in the proposed geometrical scaling rule to account for the influence of disorder on the hydraulic permeability.

Flows in low Prandtl number liquid pools are relevant for various technical applications and have so far only been investigated for the case of pure fluids, i.e., with a constant, negative surface tension temperature coefficient ∂γ/∂T. Real-world fluids containing surfactants have a temperature dependent ∂γ/∂T > 0, which may change sign to ∂γ/∂T < 0 at a critical temperature T_c. Where thermocapillary forces are the main driving force, this can have a tremendous effect on the resulting flow patterns and the associated heat transfer. Here we investigate the stability of such flows for five Marangoni numbers in the range of 2.1 × 10⁶ ≤ Ma ≤ 3.4 × 10⁷ using dynamic large eddy simulations, which we validate against a high resolution direct numerical simulation. We find that the five cases span all flow regimes, i.e., stable laminar flow at Ma ≤ 2.1 × 10⁶, transitional flow with rotational instabilities at Ma = 2.8 × 10⁶ and Ma = 4.6 × 10⁶, and turbulent flow at Ma = 1.8 × 10⁷ and Ma = 3.4 × 10⁷.