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Three-dimensional advective–diffusive boundary layers in open channels with parallel and inclined walls
Non-expert summaryThe authors consider the steady laminar advective transport of a diffusive component released at the base of a narrow three-dimensional longitudinal open channel with non-absorbing side walls and rectangular or truncated-wedge-shaped cross-sections: the findings are relevant to heat and mass transfer applications in confined U-shaped or V-shaped channels (or trenches) such as might arise in the decontamination and cleaning of narrow gaps, crevices and boundary features on walls or other surfaces, and well as transport processes in chemical or biological microfluidic devices. The fluid flows along the channel in the laminar regime and there is no flux or slip on the side walls. Numerical simulations are conducted for various duct shapes and the rate of mass transfer from the base is calculated: this is used to evaluate the dimensionless mass transfer coefficient, the Sherwood number. The results for 3-D (constant cross section, long in the direction of flow) are compared favourably with results for a simplified, 2-D, calculation.
Non-expert summaryThis modelling study considers what happens after a droplet is set into motion by the action of an impose shear flow. Inertial effects and contact-angle hysteresis are both considered. A number of flow regimes are investigated, including steadily moving drops, partial and entire droplet entrainment. The critical conditions (capillary number) for the onset of entrainment are determined for pinned as well as for moving drops. The approach to breakup is then investigated in detail, including the growth of a ligament on a drop, and the reduction of the radius of a pinching neck. A model based on an energy argument is proposed for the rate of elongation of ligaments. The paper concludes with an investigation of detachment of a hydrophobic droplet from a solid wall.
Non-expert summaryThis is an experimental study of removal of dust particles from a hydrophobic surface by a rolling/sliding water droplet. The effect of surface inclination angle on droplet dynamics and dust removal is analyses and compared with a model. Droplet rolling dominates over sliding. Removal is mainly due to the droplet liquid coating the particles as it passes over the particle, and the removal efficiency is determined by the inclination of the surface.
Non-expert summaryThis is an experimental and modelling study of the removal of a passive tracer contained in small, thin, viscous drops attached to a flat inclined substrate using the flow of a thin gravity-driven film. The drop cannot be detached either partially or completely from the surface by the mechanical forces exerted by the cleaning fluid on the drop. Convective mass transfer is established across the interface between the drop and the flowing liquid film and the (dilute) tracer diffuses into the film flow, which takes it away. The Peclet number, comparing the rate of mass transfer in the drop to the rate in the liquid film, is small (< 1) . Two models are presented: a simple empirical model based on film mass transfer coefficients; and a fuller theoretical model solving the quasi-steady two-dimensional advection–diffusion equation in the film, coupled with a time-dependent one-dimensional diffusion equation in the drop. A range of values of the Peclet number (0.01 to 1) is considered in the fuller model. Good agreement is observed between the experimental data and the models.