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We present numerical simulations and laboratory experiments to study bulge formation at the trailing edge of an inclined surface and its inhibitory effect on particle removal during surface cleaning. We investigate the spatial variations in liquid films near the trailing edge and find that the Weber number can be used as a dominant parameter to determine bulge occurrence over the trailing edge. We divide the film region near the trailing edge at which the bulge occurs into two: the region where the surface linearly grows and the surface tension is negligible, and the region where the surface tension force becomes dominant and the film surface is curved. In the investigated cases in which the Reynolds number is O(10) or greater, the viscous forces are negligible, which allows for the derivation of the scaling laws for the length of the two regions according to the condition that the bulge height scales with the capillary length. In the resulting scaling law, the length scales depend on the Froude number and the inclination angle. The proposed scaling law allows for the prediction of the bulge shape and the prediction agrees with the simulation results, particularly at low Weber numbers (i.e., We < 0.5). Moreover, we construct a particle removability map to assess the removal of particles of different sizes at specific locations on the substrate. The map reveals a reduction of the removability for small-size particles or particles located in the bulge.

In this study, we investigate Rayleigh-Taylor instability in which the density stratification is caused by the suspension of particles in liquid flows using the conventional single-phase model and Euler-Lagrange (EL) two-phase model. The single-phase model is valid only when the particles are small and number densities are large, such that the continuum approximation applies. The present single-phase results show that the constant settling of the particle concentration restricts the lateral development of the vortex ring, which results in a decrease of the rising speed of the Rayleigh-Taylor bubbles. The EL model enables the investigation of particle-flow interaction and the influence of particle entrainment, resulting from local non-uniformity in the particle distribution. We compare bubble dynamics in the single-phase and EL cases, and our results show that the deviation between the two cases becomes more pronounced when the particle size increases. The main mechanism responsible for the deviation is particle entrainment, which can only be resolved in the EL model. We provide a theoretical argument for the small-scale local entrainment resulting from the local velocity shear and non-uniformity of the particle concentration. The theoretical argument is supported by numerical evidence. Energy budget analysis is also performed and shows that potential energy is released due to the interphase drag and buoyant effect. The buoyant effect, which results in the transformation of potential energy into kinetic energy and shear dissipation, plays a key role in settling enhancement. We also find that particle entrainment increases the shear dissipation, which in turn enhances the release of potential energy.

Transport of suspended sediment in high Reynolds number channel flows [Re=O(600 000)] is simulated using large-eddy simulation along with a dynamic-mixed model (DMM). Because the modeled sediment concentration is low and the bulk Stokes’ number (Stb) is small during the simulation, the sediment concentration is calculated through the use of the Eulerian approach. In order to employ the DMM for the suspended sediment, we formulate a generalized bottom boundary condition in a finite-volume formulation that accounts for sediment flux from the bed without requiring specific details of the underlying turbulence model. This enables the use of the pickup function without requiring any assumptions about the behavior of the eddy viscosity. Using our new boundary condition, simulations indicate that the resolved component of the vertical flux is one order of magnitude greater than the resolved subfilter-scale flux, which is in turn one order of magnitude greater than the eddy-diffusive flux. Analysis of the behavio...