Abstract:It is known that the dripping of a liquid film on the underside of a plate can be suppressed by tilting the plate so as to cause a sufficiently strong flow. This paper uses two-dimensional numerical simulations in a closed-flow framework to study several aspects of this phenomenon. It is shown that, in quasi-equilibrium conditions, the onset of dripping is closely associated with the curvature of the wave crests approaching a well-defined maximum value. When dynamic effects become significant, this connection … Show more
“…We note the striking qualitative similarity between the interfacial profile seen in figure 5 and that computed for a viscous film flowing on the underside of an inclined plate (see e.g. Kofman et al 2018;Zhou & Prosperetti 2022).…”
Section: Physical Discussionsupporting
confidence: 56%
“…Kofman et al. 2018; Zhou & Prosperetti 2022). Figure 5.( a ) Flow configuration and ( b ) interfacial curvature for and parameters , , fixed to the same values as in figure 1.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…Examples of fully nonlinear waves in related unstably stratified problems include travelling waves on fluid films flowing down the underside of an inclined plane – see, for example, Kofman et al. (2018) and Zhou & Prosperetti (2022).…”
The Rayleigh–Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated in the absence of inertia. The dynamics of the flow is described by a nonlinear lubrication equation which is solved numerically for adverse density stratifications. The early-time dynamics features a number of finger-like protrusions of different heights at the interface. The fingers travel at different speeds leading to a sequence of merging events after which the interface eventually settles to a near-saturated state, comprising only one finger that includes most of the lower fluid. For sufficiently large density stratifications, the final state spans the height of the channel and includes two thin fluid films at each wall, both of which undergo chaotic dynamics, but finite-time touch-down/touch-up is shown to be precluded by the shear flow. An asymptotic analysis in the large-Bond-number limit (intense density stratification) reveals the finer structure of the final state including Landau–Levich-type connection regions. The asymptotic solutions are compared with numerical results of the lubrication model as well as direct numerical simulations, and excellent agreement is observed between the three in terms of interfacial structure, wave speed and film thicknesses.
“…We note the striking qualitative similarity between the interfacial profile seen in figure 5 and that computed for a viscous film flowing on the underside of an inclined plate (see e.g. Kofman et al 2018;Zhou & Prosperetti 2022).…”
Section: Physical Discussionsupporting
confidence: 56%
“…Kofman et al. 2018; Zhou & Prosperetti 2022). Figure 5.( a ) Flow configuration and ( b ) interfacial curvature for and parameters , , fixed to the same values as in figure 1.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…Examples of fully nonlinear waves in related unstably stratified problems include travelling waves on fluid films flowing down the underside of an inclined plane – see, for example, Kofman et al. (2018) and Zhou & Prosperetti (2022).…”
The Rayleigh–Taylor instability at the interface of two sheared fluid layers in a horizontal channel is investigated in the absence of inertia. The dynamics of the flow is described by a nonlinear lubrication equation which is solved numerically for adverse density stratifications. The early-time dynamics features a number of finger-like protrusions of different heights at the interface. The fingers travel at different speeds leading to a sequence of merging events after which the interface eventually settles to a near-saturated state, comprising only one finger that includes most of the lower fluid. For sufficiently large density stratifications, the final state spans the height of the channel and includes two thin fluid films at each wall, both of which undergo chaotic dynamics, but finite-time touch-down/touch-up is shown to be precluded by the shear flow. An asymptotic analysis in the large-Bond-number limit (intense density stratification) reveals the finer structure of the final state including Landau–Levich-type connection regions. The asymptotic solutions are compared with numerical results of the lubrication model as well as direct numerical simulations, and excellent agreement is observed between the three in terms of interfacial structure, wave speed and film thicknesses.
“…It is known from the two-dimensional analogue of this configuration that a sufficient downward tilt of the plate can hinder the development of the Rayleigh-Taylor instability: as they propagate downward, surface waves grow under the combined effect of the Kapitza and Rayleigh-Taylor instabilities but, in suitable conditions, they can stabilize at a finite amplitude (see e.g. Indeikina, Veretennikov & Chang 1997;Brun et al 2015;Kofman et al 2018;Zhou & Prosperetti 2022). The same phenomenon is observed for three-dimensional drops sliding down the underside of an inclined surface (Jambon-Puillet et al 2021).…”
Section: Reverse Gravitymentioning
confidence: 99%
“…2015; Kofman et al. 2018; Zhou & Prosperetti 2022). The same phenomenon is observed for three-dimensional drops sliding down the underside of an inclined surface (Jambon-Puillet et al.…”
This paper addresses several aspects of the axisymmetric flow of a liquid film over the surface of a downward-sloping cone. The study is rooted on a validated computational tool the results of which are interpreted with the help of a hyperbolic time-dependent reduced-order model also derived in the paper. The steady version of the model demonstrates the weakening and ultimate disappearance of the circular hydraulic jump as the cone surface transitions from planar to downward sloping. Mathematically, this evolution is reflected in a change of the model's critical point from spiral to node. A significant advantage of the time-dependent model is that, when it is integrated in time, the flow regions upstream and downstream of the critical point are connected. Due to this feature, when a hydraulic jump exists, its position can be sharply captured automatically with a good agreement with Navier–Stokes simulations. Surface-tension effects are properly accounted for and, in steady conditions, are shown to have a marginal effect on the flow, including the position of the hydraulic jump. A correlation is obtained for the jump radius as a function of the flow rate, liquid viscosity, gravitational acceleration and the angle of inclination of the cone surface. In a suitable limit, the model reduces to the optimal two-dimensional, first-order model for liquid film flow down an inclined plane and, in a different limit, it describes an axisymmetric thin liquid film falling down the surface of a vertical cylinder. Some results are also presented for the waves induced by a pulsating jet on the surface of the liquid film and for a jet impinging on the surface of a cone from below.
Water flow on plant canopies determines the partitioning of intercepted rainfall between stemflow and throughflow, yet understanding of these flow processes remains minimally developed. Plant canopies may concentrate intercepted water into rivulets that flow beneath branches. If the rivulets remain attached to branches until they encounter the main tree trunk, they form stemflow. If the rivulets detach from branches, however, they form ‘pour points’, regions of concentrated throughfall. Here, rivulet flow below uniform cylinders was studied experimentally. Experimental observations were interpreted using hydrodynamic theory to predict the likelihood of a rivulet detaching based on a critical rivulet height (). Predictions of rivulet detachment were explored for a simplified case where water is introduced at known flow rates at a discrete point above a uniform, cylindrical ‘branch’. Where the branch was straight, the percentage of trials forming a rivulet, or the rivulet formation rate, increased with increasing branch inclination angle to the horizontal axis. Rivulet formation rates did not vary with flow rate. However, the volume of water collected at the end of the branch, analogous to stemflow, decreased with a higher flow rates due to the formation of flow instabilities. Rivulets forming on straight branches did not detach. Instead, the rivulet stream accelerated and reduced in height as it flowed along the cylinder. Rivulets formed on curved branches detached only when the branch axis after the curve approached the horizontal. Future theoretical and experimental studies can extend this work to improve understanding of more complex surfaces and branch architectures to mechanistically understand canopy interception.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
