Evaporation into Couette Flow

Danberg, James E.

doi:10.21236/ada478033

Cited by 3 publications

(19 citation statements)

References 1 publication

(1 reference statement)

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“…A similar development has been reported by Navez et al 1 The focus of previous reports 2 ' 3 in this series has been on the relationship between evaporation rate and the convective environment with the thought that if that were calculated correctly then the problem of the time history of the mass loss would be straightforward, which is only partially correct.…”

supporting

confidence: 68%

Halon Flightline Extinguisher Evaluation: Data Supporting Standard Development (Including Nov 2007 Addendum)

Hawk¹,

Carr²

2008

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supporting

confidence: 68%

Halon Flightline Extinguisher Evaluation: Data Supporting Standard Development (Including Nov 2007 Addendum)

Hawk¹,

Carr²

2008

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“…Stone, 1989;Bejan, 2013) or a flat droplet (see e.g. Baines and James, 1994;Danberg, 2008), the thickness of the diffusive boundary layer above the drop is related to the Schmidt number and the local Reynolds number such that <5c ~Sc~1/3 Re*1/3, then we can note that Sc increases with decreasing Reynolds number. Hence, the diffusive boundary layer thickness increases with decreasing velocity in the film: for instance, a decrease of 50% in the velocity corresponds to an increase of 25% in <5c-Further more, increasing the diffusive boundary layer thickness tends to decrease the mass transfer at the interface, which means a lower cleaning rate of the droplets.…”

Section: Discussionmentioning

confidence: 99%

“…One of the m ain assum ptions in Blount's (2010) model is to consider th a t the film velocity is n ot affected by the drop and the velocity in th e diffusive boundary layer rem ains linear w ith distance away from th e boundary. This com m on assum ption in theoretical m odels about the convective m ass transfer from a droplet into an external flow is also used by Baines and Jam es (1994) and Danberg (2008). To te st this assum ption we m easure the velocity field of th e film flow in the vicinity of a solid obstacle, representing a non-deformable drop.…”

Section: Introductionmentioning

confidence: 99%

Cleaning of viscous drops on a flat inclined surface using gravity-driven film flows

Landel¹,

McEvoy

Dalziel³

2015

Food and Bioproducts Processing

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We investigate the fluid mechanics of cleaning viscous drops attached to a flat inclined surface using thin gravitydriven film flows. We focus on the case where the drop cannot be detached either partially or completely from the surface by the mechanical forces exerted by the cleaning fluid on the drop surface. Instead a convective mass transfer establishes across the drop-film interface and the fluid in the drop dissolves into the cleaning film flow, which then transports it away. The characteristic time scale of dissolution is much longer than the advection time scale in the film flow. Thus, the shape and size of the drop can be considered as quasi-steady. To assess the impact of the shape and size of the drop on the velocity of the cleaning fluid, we have developed a novel experimental technique based on particle image velocimetry. We show the velocity distribution at the film surface in the situations both where the film is flowing over a smooth surface, and where it is perturbed by a solid obstacle representing a very viscous drop. We find that at intermediate Reynolds numbers the acceleration of the starting film is overestimated by a plane model using the lubrication approximation. In the perturbed case, the streamwise velocity is strongly affected by the presence of the obstacle. The upstream propagation of the disturbance is limited, but the disturbance extends downstream for distances larger than 10 obstacle diameters. Laterally, we observe small disturbances in both the streamwise and lateral velocities, owing to stationary capillary waves. The flow also exhibits a complex three-dimensional converging pattern immediately below the obstacle.

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“…This cleaning method tends to reduce water and energy consumption, and the volume of waste, due to lower wetting rates (Fuchs et al, 2013). The present study is also applicable to the decontamination of hazardous substances mixed in viscous liquid droplets (Fatah et al, 2007;Danberg, 2008). A liquid decontaminant can be delivered onto contaminated surfaces flowing over the hazardous droplets as a thin falling film.…”

Section: Introductionmentioning

confidence: 94%

“…Baines & James (1994) noted a very large scattering in the experimental data, which they attributed to the sensitivity of the measurements of the drop contact angle and the lack of consistency between the different experiments of Coutant & Penski (1982). Danberg (2008) studied experimentally, numerically and theoretically the same problem as Baines & James (1994): the evaporation of a small flat non-deformable liquid drop into a gas shear flow at large Péclet numbers. He found a similar theoretical prediction for the Sherwood number using an integral method and assuming a third-order polynomial distribution for the concentration in the diffusive boundary layer.…”

Section: Introductionmentioning

confidence: 99%

Convective mass transfer from a submerged drop in a thin falling film

et al. 2016

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We investigate the fluid mechanics of removing a passive tracer contained in small, thin, viscous drops attached to a flat inclined substrate using thin gravity-driven film flows. We focus on the case where the drop cannot be detached either partially or completely from the surface by the mechanical forces exerted by the cleaning fluid on the drop surface. Instead, a convective mass transfer establishes across the drop-film interface and the dilute passive tracer dispersed in the drop diffuses into the film flow, which then transports them away. The Péclet number for the passive tracer in the film phase is very high, whereas the Péclet number in the drop phase varies from Pe d ≈ 10 −2 to 1. The characteristic transport time in the drop is much larger than in the film. We model the mass transfer of the passive tracer from the bulk of the drop phase into the film phase using an empirical model based on an analogy with Newton's law of cooling. This simple empirical model is supported by a 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. We find excellent agreement between our experimental data and the two models, which predict an exponential decrease in time of the tracer concentration in the drop. The results are valid for all drop and film Péclet numbers studied. The overall transport characteristic time is related to the drop diffusion time scale, as diffusion within the drop is the limiting process. This result remains valid even for Pe d ≈ 1. Finally, our theoretical model predicts the well-known relationship between the Sherwood number and the Reynolds number in the case of a well-mixed drop Sh ∝ ReL 1/3 = (γL 2 /ν f ), based on the drop length L, film shear rate γ and film kinematic viscosity ν f . We show that this relationship is mathematically equivalent to a more physically intuitive relationship Sh ∝ Re δ , based on the diffusive boundary layer thickness δ. The model also predicts a correction in the case of a non-uniform drop concentration. The correction depends on Re δ , the film Schmidt number, the drop aspect ratio and the diffusivity ratio between the two phases. This prediction is in remarkable agreement with experimental data at low drop Péclet number. It continues to agree as Pe d approaches 1, although the influence of the Reynolds number increases such that Sh ∝ Re δ .

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Evaporation into Couette Flow

Cited by 3 publications

References 1 publication

Halon Flightline Extinguisher Evaluation: Data Supporting Standard Development (Including Nov 2007 Addendum)

Halon Flightline Extinguisher Evaluation: Data Supporting Standard Development (Including Nov 2007 Addendum)

Cleaning of viscous drops on a flat inclined surface using gravity-driven film flows

Convective mass transfer from a submerged drop in a thin falling film

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