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RESEARCH PAPERS

# Spreading Characteristics and Microscale Evaporative Heat Transfer in an Ultrathin Film Containing a Binary Mixture

[+] Author and Article Information
Sashidhar S. Panchamgam, Joel L. Plawsky

The Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180

Peter C. Wayner1

The Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180wayner@rpi.edu

1

Corresponding author.

J. Heat Transfer 128(12), 1266-1275 (Mar 26, 2006) (10 pages) doi:10.1115/1.2349506 History: Received August 23, 2005; Revised March 26, 2006

## Abstract

Using image-analyzing interferometry, the thickness profile, in the range of $δ0$ (adsorbed thickness) $<δ<3μm$, at the leading edge of a moving ultrathin film with phase change, was measured for a mixture of pentane-octane and compared to that of pure pentane. An improved data-analysis procedure was used to enhance the use of the measured thickness profile. There were significant differences between these two systems, demonstrating the presence of large Marangoni interfacial shear stresses with the mixture. A control volume model was developed to evaluate the differences between the pure fluid and the mixture. The disjoining pressure at the leading edge was found to control fluid flow in the evaporating pure system. However, due to Marangoni stresses, the effect of disjoining pressure on the mixture was found to be small at steady state for the fluxes studied. With an upstream bulk mixture of 2% octane and 98% pentane, a shear stress due to the gradient of the liquid-vapor interfacial surface tension resulting from distillation controlled fluid flow in the contact line region. The average curvature of the evaporating pseudo-steady state pure system was significantly larger (smaller length and larger apparent contact angle at $δ=0.1μm$) than the isothermal value, whereas the reverse occurred for the mixture. Using a continuum model, a comparison of numerically obtained Marangoni stresses and local evaporative heat flux profiles between the two systems was also made.

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## Figures

Figure 1

(a) Schematic diagram of the experimental setup, (b) cross-sectional view (line AB in (a)) of the quartz cuvette with inside dimensions 3mm×3mm. Gravity g is acting perpendicular to the cross section, and (c) cross-sectional view (line CD in (a)) of the quartz cuvette (inside dimensions 3mm×43mm).

Figure 2

Reflectivity images illustrating the movement of the binary mixture meniscus due to change in the heater power: (a) isothermal state (t=2.86s), (b) receding state (t=8.64s), (c) advancing state (t=20.54s), and (d) pseudo-steady state (t=336.1s). Reflectivity images were captured at an axial location of x≈0 (near the heater).

Figure 3

Illustration of the meniscus movement due to change in the heater power. I I′: Isothermal reference state, R-1: Receding cycle, and A-1: Advancing cycle, and a schematic of the control volume of an evaporating corner meniscus used for macroscopic interfacial force balance and continuum model.

Figure 4

Comparison of profiles of the distance traveled as a function of time of the pentane and the binary mixture menisci

Figure 5

Comparison of interfacial velocity profiles as a function of time of (a) the pentane meniscus and (b) the binary mixture meniscus

Figure 6

(a) Comparison of thickness profiles of the pentane meniscus at (1) isothermal state (t=0.07s), (2) advancing state (t=10.2s), and (3) pseudo-steady state (t=163.2s), and (b) expanded for contact line region (15)

Figure 7

(a) Comparison of thickness profiles of the binary mixture meniscus at (1) isothermal state (t=2.86s), (2) receding state (t=8.64s), and (3) pseudo-steady state (t=366.1s), and (b) expanded for contact line region

Figure 8

Comparison of curvature profiles of (a) the pentane meniscus and (b) the binary mixture meniscus

Figure 9

Comparison of adsorbed film-thickness profiles as a function of time of (a) the pentane meniscus and (b) the binary mixture meniscus. iso represents isothermal meniscus, min represents minimum, and avg represents an average value over the pseudo-steady-state regime

Figure 10

Comparison of profiles of the slope angle at δ=0.1μm as a function of time of (a) the pentane meniscus and (b) the binary mixture meniscus

Figure 11

Comparison of the maximum curvature profiles as a function of time of (a) the pentane meniscus and (b) the binary mixture meniscus

Figure 12

Comparison of various terms in Eq. 2 [A: 1.5δ2σ′∕3υ, D: 3βδσ′∕3υ, E: σδ3K′∕3υ, F: 3σδ2βK′∕3υ, and H: −12β(−Bavg)δ′∕3υδ3] for the mass flow rate equation for (a) the pentane and (b) the binary mixture menisci during nonisothermal (pseudo-steady) state for the adsorbed film region concentration, x1(L)=0.94

Figure 13

(a) dσ∕dy and (b) mole fraction of pentane (x1) as a function of meniscus length for the pentane (P) and the binary mixture (M) menisci during nonisothermal (pseudo-steady) state. x1 and σ′ profiles for the binary mixture meniscus in nonisothermal state were evaluated for the adsorbed film region concentration, x1(L)=0.94

Figure 14

Comparison of evaporative heat flux (q″) profiles of the pentane (P) and the binary mixture (M) menisci in isothermal and nonisothermal (pseudo-steady) states. The evaporative heat flux for the binary mixture meniscus in nonisothermal state was evaluated for the adsorbed film region concentration, x1(L)=0.94

Figure 15

Comparison of Π0,t∕Π0,0 between the pentane and the binary mixture menisci

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