Transient Marangoni convection induced by an isothermal sidewall of a rectangular liquid pool

Chen, Enhui; Xu, Feng

doi:10.1017/jfm.2021.795

Cited by 10 publications

(10 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the right side of Figure 3, the capillary number is shown to not have much effect on the velocity profile. The previous CFD shows some minor disagreement as the problem was modeled with a fixed flat interface and Marangoni forces were applied along the flat boundary [8,27]. Previous CFD results and (29) give a maximum U * = 0.49 while results from STAR-CCM+ in S6 give a maximum U * = 0.386.…”

Section: Effect Of Capillary Numbermentioning

confidence: 96%

“…Chen and Xu [27] found various transient regimes in the single-phase problem by analyzing the velocity and time scales of Marangoni convection and viscous effects. The model was validated by comparing the predicted velocity profile with the theory from Sen and Davis [7] and the experimental work from Villers and Platten [8].…”

Section: Literature Reviewmentioning

confidence: 99%

“…while possibly controversial to use multiple velocity scales, (30) is a physical velocity scale that represents the magnitude of convection in the problem based on the balance of forces. Whereas ( 28) is more of a numerical scaling factor to apply to the analytical expression in (27).…”

Section: Analytical Modelmentioning

confidence: 99%

“…All cases were laminar and used a 600 × 100 isotropic hexahedral grid for the L × 2h domain. Previous work found grid independence on this flow problem with coarser grids [27]. While some results are presented as nondimensional (or scaled dimensionally when relevant for comparison), the CFD models solve the dimensional form of the governing equations, and a domain size of 1 × 2/12 m was used, giving a grid sizing ∼1.66 mm.…”

Section: Cfdmentioning

confidence: 99%

See 3 more Smart Citations

Free Surface Motion of a Liquid Pool with Isothermal Sidewalls as a Benchmark for Marangoni Convection Problems

Ciccotosto,

Brooks

2023

Energies

View full text Add to dashboard Cite

In single phase flows, benchmarks like the lid driven cavity have become recognized as fundamental tests for newly developed computational fluid dynamics, CFD, codes. For multiphase free surface flows with variable surface tension, the presently studied pool with isothermal sidewalls is suggested as it is the simplest domain where Marangoni effects can dominate. It was also chosen due to its strange sensitivity to the initial setup which is discussed at length from a chosen number of ‘scenarios’. It was found that the fluid interface can reverse deformation by a change in the top boundary condition, the liquid equation of state, and the gravity level. For the top boundary condition, this reversal is due to vapor expansion within the closed volume, creating an additional convection mechanism. Not only does the interface reverse, but the peak height changes by more than an order of magnitude at the same Marangoni number. When including gravity, the peak velocity can increase significantly, but it can also cause a decrease when done in combination with a change in the top wall boundary condition. Finally, thermal expansion of the liquid phase causes the peak velocity to be reduced, with additional reductions from the gravity and top wall condition. The differences in each scenario could lead to significant errors in analyzing a practical application of Marangoni flows. Therefore, it is important to demonstrate that a new CFD code can not only resolve Marangoni convection, but also has the capability to resolve the scenario most relevant to the application at hand.

show abstract

Section: Effect Of Capillary Numbermentioning

confidence: 96%

Section: Literature Reviewmentioning

confidence: 99%

Section: Analytical Modelmentioning

confidence: 99%

Section: Cfdmentioning

confidence: 99%

See 2 more Smart Citations

Free Surface Motion of a Liquid Pool with Isothermal Sidewalls as a Benchmark for Marangoni Convection Problems

Ciccotosto,

Brooks

2023

Energies

View full text Add to dashboard Cite

show abstract

“…The onset of such non-equilibrium is considered here as mainly initiated by two factors: (i) temperature gradient imposed axially along the channel in the direction, as described by Chen & Xu (2021); (ii) non-uniform coating of the soluble surfactant gradient lining the inner walls of the channel . By surfactants here we mean a substance that changes the surface tension of liquids (increase/decrease).…”

Section: Surface Tension Transfigurationmentioning

confidence: 99%

Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

et al. 2022

View full text Add to dashboard Cite

The unsteady effects of transitioning surface tension, $\gamma (t)$ , on the dynamics of capillary imbibition in channels of arbitrary shape are analytically investigated with a focus on rectangular and circular channels. With proper scaling, two unsteady models for $\gamma (t)$ are defined and used to highlight this transient behaviour. The convoluted dynamics at the flow front are correctly captured in the governing equations, which are rigorously analysed using unsteady eigenfunction expansion. Then, the final solution and data are obtained by employing the Runge–Kutta fourth-order scheme elegantly applied simultaneously to two derived nonlinear ordinary differential equations. Ultimately, the results are more accurate compared with previous studies. Dynamics and kinematic similarity between rectangular and circular channels are investigated and discussed and the conditions for equivalence in both channels are highlighted. Using a small parameter ( $\epsilon$ ) that stretches the time scale, we successfully use a robust asymptotic analysis to develop and capture the long-time dynamics. Ultimately, we recover the Lucas–Washburn regime analysed in Washburn (Phys. Rev., vol. 17, 1921, pp. 273–283), Lucas (Kolloidn. Z., vol. 23, 1918, pp. 15–22) for steady surface tension where the variations of depth and rate with time result in $h\thicksim t^{1/2}$ and $v \thicksim t^{-1/2}$ . In the end, the three forces, namely the inertia, $F_{v}$ , the viscous, $F_{\mu }$ , and the surface tension, $F_{\gamma }$ , are briefly analysed and used to highlight three main distinct regimes. We show that at early times, $F_{v}/F_{\gamma } \thicksim 1$ , whereas at a long time, $F_{\mu }/F_{\gamma } \thicksim -1$ .

show abstract

The “Effect of Marangoni Convection on Heat Transfer in Phase Change Materials” experiment

et al. 2023

View full text Add to dashboard Cite

Transient Marangoni convection induced by an isothermal sidewall of a rectangular liquid pool

Cited by 10 publications

References 50 publications

Free Surface Motion of a Liquid Pool with Isothermal Sidewalls as a Benchmark for Marangoni Convection Problems

Free Surface Motion of a Liquid Pool with Isothermal Sidewalls as a Benchmark for Marangoni Convection Problems

Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension

The “Effect of Marangoni Convection on Heat Transfer in Phase Change Materials” experiment

Contact Info

Product

Resources

About