An augmented Young-Laplace model of an evaporating meniscus in a microchannel with high heat flux

Schonberg, Jeffrey A.; DasGupta, Sunando; Wayner, Peter

doi:10.1016/0894-1777(94)00085-m

Cited by 89 publications

(61 citation statements)

References 9 publications

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“…Further reducing the value to zero does not significantly change the resulting film profile. Since δ''(0) cannot be specified directly, a far-field boundary condition is used as in [6,23]. In [23], the far-field condition is set by assuming that the film slope approaches a constant value (i.e., the meniscus radius R approaches infinity).…”

Section: Solution Methods and Boundary Conditionsmentioning

confidence: 99%

“…Since δ''(0) cannot be specified directly, a far-field boundary condition is used as in [6,23]. In [23], the far-field condition is set by assuming that the film slope approaches a constant value (i.e., the meniscus radius R approaches infinity). For a meniscus in a channel, however, R should approach the constant radius R* in the intrinsic meniscus, which is approximately half of the channel height H when the liquid is completely wetting [26,27].…”

Section: Solution Methods and Boundary Conditionsmentioning

confidence: 99%

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Characteristics of an evaporating thin film in a microchannel

Wang

Garimella

Murthy

2007

International Journal of Heat and Mass Transfer

322

210

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An evaporating meniscus in a microchannel is investigated through an augmented Young-Laplace model and the kinetic theory-based expression for mass transport across a liquid-vapor interface. The complete expression for mass transport is employed without any approximations and boundary conditions for the film profile are developed. The thin-film and the intrinsic-meniscus regions are distinguished based on the disjoining pressure variation along the meniscus. While heat transfer in the thin-film region is found to be relatively insensitive to channels larger than a few micrometers in radius, that in the intrinsic meniscus is quite sensitive to channel size. The role of evaporation suppression due to capillary pressure in both regions is discussed. Compared to the relatively small contribution to overall heat transfer from the thin-film region, the micro region (defined here as extending from the non-evaporating region to a location where the film is 1 m thick) is found to account for more than 50% of the total heat transfer.

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Section: Solution Methods and Boundary Conditionsmentioning

confidence: 99%

Section: Solution Methods and Boundary Conditionsmentioning

confidence: 99%

Characteristics of an evaporating thin film in a microchannel

Wang

Garimella

Murthy

2007

International Journal of Heat and Mass Transfer

322

210

View full text Add to dashboard Cite

show abstract

“…Subsequent models (Demsky and Ma 2004;Jiao et al 2005) have been developed based on the force balance for a variety of geometries. Continual advancements in modeling include an augmented YoungLaplace model by Schonberg et al (1995) which accounts for the pressure drop across the liquid-vapor interface due to capillarity and disjoining pressure. Other phenomenon associated with thin film evaporation such as Marongoni instabilities, which is a wave-like motion of the interface due to temperature gradients, has been investigated by Sultan et al (2005).…”

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confidence: 99%

Fluid flow and heat transfer in the evaporating thin film region

Cheng

Borgmeyer

et al. 2007

Microfluid Nanofluid

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The evaporating thin film region is an extended meniscus beyond the apparent contact line at a liquid/solid interface. Thin film evaporation plays a key role in a highly efficient heat pipe. A detailed mathematical model predicting fluid flow and heat transfer through the thin film region is developed. The model considers the effects of inertial force, disjoining pressure, surface tension, and curvature. Utilizing the order analysis, the model is simplified and can be numerically solved for the thin film profile, interfacial temperature, meniscus radius, heat flux distribution, velocity distribution, and mass flow rate in the evaporating thin film region. The prediction shows that while the inertial force can affect the thin film profile, interfacial temperature, meniscus radius, heat flux distribution, velocity distribution, and mass flow rate, in particular, near the non-evaporating region, the effect can be neglected. It is found that a maximum velocity, a maximum heat flux, and a maximum curvature exist for a given superheat, but the locations for these maximum values are different.friction factor, f ¼ 4s w 1 2 q l u 2 h lv latent heat of vaporization (J/kg) k thermal conductivity (W/m K) K curvature (m -1 ) _ m mass flow rate (kg/s) p pressure (N/m 2 ) P R reference pressure (N/ m) 2 q heat transfer (W) q¢¢ heat flux (W/ m 2 ) Re Reynolds number, Re ¼ q l ud l l t time (s) T temperature (K) u velocity in the x-direction (m/s) " u mean velocity in the x-direction (m/s) v velocity in the y-direction (m/s) x coordinate (m) y coordinate (m) d film thickness (m) d 0 non-evaporating film thickness (m) l viscosity (N s/m 2 ) q density (kg/m 3 ) r surface tension (N/m) s shear stress (N/ m 2 )

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“…(25) Schonberg et al (1995); Stephan et al (1992), without much discussion. An accommodation coefficient of unity implies that for every liquid molecule emitted, none are rebounded and re-absorbed, giving a perfect evaporative capacity.…”

Section: Accommodation Coefficientmentioning

confidence: 99%

Numerical Investigation of an Evaporating Thin Film on a Heated Surface

Ball¹,

Polansky²,

Kaya³

2013

Frontiers in Heat and Mass Transfer

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The fluid flow and heat transfer in an evaporating extended meniscus are numerically studied. Continuity, momentum, energy equations and the Kelvin-Clapeyron model are used to develop a third order, non-linear ordinary differential equation which governs the evaporating thin film. It is shown that the numerical results strongly depend on the choice of the accommodation coefficient and Hamaker constant as well as the initial perturbations. Therefore, in the absence of experimentally verified values, the numerical solutions should be considered as qualitative at best. It is found that the numerical results produce negative liquid pressures under certain specific conditions. This result may suggest that the thin film can be in an unstable state of tension; however, this finding remains speculative without experimental validation. Although similar thin-film models proved to be very useful in gaining qualitative insight into the characteristics of evaporating thin films, the results shown in this study indicate that careful experimental investigations are needed to verify the mathematical models.

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An augmented Young-Laplace model of an evaporating meniscus in a microchannel with high heat flux

Cited by 89 publications

References 9 publications

Characteristics of an evaporating thin film in a microchannel

Characteristics of an evaporating thin film in a microchannel

Fluid flow and heat transfer in the evaporating thin film region

Numerical Investigation of an Evaporating Thin Film on a Heated Surface

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