Non-expert summaryMany cleaning and decontamination operations employ a flow to detach or move a particle or foreign element (e.g. a piece of dust, baterium or a spore) from a surface. The presence of the element disturbs the flow near the wall. Knowledge of the flow field and the forces imposed on the element is useful for predicting or quantifying removal. This paper considers a simple shear flow of a Newtonian fluid over an axisymmetric protuberance (with uniform shape) on a plane wall. The full 3-D problem is formulated in terms of three scalar Fredholm integral equations of the first kind and is solved using a boundary-element method. The hydrodynamic force and torque exerted on the protuberance, and distribution of shear stresses, are calculated. There is good agreement with previous analytical computations for hemi-spherical and spherical shapes.
Non-expert summaryThe Navier-Stokes equations for the three-dimensional flow of a Newtonian fluid around a hemispherical bubble simultaneously sliding along a flat wall and growing are solved. The forces experienced by the bubble (lift, drag and added mass) are calculated for bubble Reynolds numbers greater than or equal to 0.01 and flow Reynolds numbers < 2000. The bubble does not change shape. The scenarios studied are (i) an immobile bubble in a linear shear flow; (ii) a bubble sliding along the wall in an otherwise stagnant fluid; and (iii) a bubble sliding in a linear shear flow. The results are presented in the form of dimensionless coefficients.
Non-expert summaryThis is a review of the fluid mechanics associated with blistering, which occurs when a thin solid layer locally separates from an underlying substrate through cracking of a bulk material, delamination of a composite material, or peeling of a thin layer (membrane) adhered to the substrate by a thin layer of viscous fluid. The focus of the review is on the latter case, where the expansion of the newly formed blister by fluid injection occurs via a displacement flow, which peels the adhered surfaces apart through a two-way interaction between flow and deformation. These blisters are prone to fluid- and solid-mechanical instabilities. If the injected fluid is less viscous than the fluid already occupying the gap, patterns of short and stubby fingers (fingering) form on the propagating fluid interface. Buckling/wrinkling instabilities of the delaminated layer can arise for sufficiently thin membranes and can interact with the fluid mechanical fingering instability.
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 summaryThe displacement of one liquid by another in a channel of constant height occurs in flushing and cleaning operations. The authors study the effect of buoyancy (arising from different fluid densities) on a pressure-driven flow of two miscible fluids in inclined channels using direct numerical simulations DNS). The flow dynamics are governed by the continuity and Navier–Stokes equations, without the Boussinesq approximation for buoyancy, coupled to a convective-diffusion equation for mass transfer between the two liquids. The effect of concentration on viscosity and density is modelled. The effect of varying the density ratio, Froude number, and channel inclination on the flow dynamics is examined, for moderate Reynolds numbers. These detailed simulations give insights into mixing and cleaning behaviour.
Non-expert summaryWhen one liquid is pumped into a channel containing a second liquid, the behaviour depends on the properties of the two fluids and pressure driving force. This paper considers the stability of a flow of two miscible fluids in a horizontal channel. The flow dynamics are governed by the continuity and Navier–Stokes equations, with mass transfer between the two. An analysis of the flow in the linear regime delineates the presence of convective and absolute instabilities, and shows that vertical gradients of viscosity perturbations (caused by mixing) are the main destabilizing influence of the interface (in agreement with previous work). Previous work in the area is reviewed as well. Transient numerical simulations demonstrate the development of complex dynamics in the nonlinear regime, characterized by roll-up phenomena and intense convective mixing.
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 summaryThe authors conduct a comprehensive numerical study of convective mass transport from 2-D rectangular cavities in low‐Reynolds‐number flows, i.e. the flow set up in a long rectangular trench by the motion of a steady shear flow across the top. They calculate the velocity field in the trench and the associated mass transport (enhancement of diffusion). The flow field is calculated by a high‐order implementation of the boundary‐integral method, while the convective diffusion equation is solved using the spectral‐element method. Results are presented in the form of concentraton contours and local mass fluxes, for cavity aspect ratios from 1:1 to 4:1 and for Péclet numbers from 0 to 100,000. They investigate the effects of inlet flow profile and system boundaries on the system.
Non-expert summaryWhen a steady shear flow passes over a long (2-D) cavity it sets up a circulation cell in the cavity, where the flow in the cavity is contained within the cavity (with a boundary called the separatrix) and mass transport into and out of the cavity is predominantly by diffusion. This is particularly true at small scales. The authors investigate numerically and experimentally two methods for enhancing mass transport from these 'cells' - by geometrically modifying the boundary driving the flow, and making the driving flow time-dependent. Both modifications destabilize one of the wall attachment points of the separatrix, allowing fluid exchange between the cavity and channel. The range of Reynolds and Reynolds-Strouhal numbers studied is 7.7 <= Re <= 46.5 and 0.52 <= ReSr <= 12,55 in the spatially dependent mode and 12 <= Re <= 93 and 0.26 <= ReSr <= 5.02 in the time-dependent mode. The transport is described theoretically via lobe dynamics, which characterizes the instability of the separatrix. They find that the resulting mass transfer between the cavity and the outer shear flow, through the distabilized separatrix is enhanced by several orders of magnitude compared to a diffusive mass transfer.
Non-expert summaryThe flushing of a viscous fluid from a pipe or cavity by a less viscous one is widely used in cleaning operations. This paper reports the numerical modelling of the transient displacement of a viscoplastic material from straight or suddenly constricted (square entry) concentric cylindrical tubes of finite length, simulating a gas at higher pressure displacing the geometry initially filled with liquid. A mixed finite element method is coupled with a quasi-elliptic mesh generation scheme in order to follow the very large deformations involved. The gas bubble grows in length and leaves a thin liquid film on the duct wall (so it does not remove all the liquid). The shape of the bubble is computed for various Reynolds and Bingham numbers (ratio of yield stress to viscous stress). The 'tip splitting' instability that can arise in flow of a gas along a tube filled with a viscous Newtonian fluids is suppressed with viscoplastic fluids at higher Bingham numbers. The shape of the bubble as it passes through the constriction is also studied.
Non-expert summaryThe use of a gas to purge a viscous liquid from a straight cylindrical pipe of finite length is investigated for the case where the liquid is viscoelastic. The rheology of the liquid is described using the Giesekus and the Phan-Thien-Tanner (PTT) models. The focus of the work is on the numerical aspects of the simulations. A parametric analysis is made in order to determine the effects of elastic and inertial forces, and the Newtonian viscosity, on the process.
Non-expert summaryThe use of pressurised air to displace a viscoplastic liquid from a complex duct geometry is simulated using detailed numerical modelling. The transient displacement of Newtonian and viscoplastic liquids by air in cylindrical tubes of finite length with a concentric expansion followed by a contraction in their cross section is considered. The change in diameter is not sudden. Various expansion and contraction ratios are studied. Papanastasiou's formula is employed to regularize the discontinuous Bingham model. Results are presented for a range of fluid and geometrical parameters, and some cases are compared to analytical results.