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Research Papers: Heat and Mass Transfer

One-Dimensional Analysis of Gas Diffusion-Induced Cassie to Wenzel State Transition

[+] Author and Article Information
Jonah Kadoko

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155
e-mail: jonah.kadoko@tufts.edu

Georgios Karamanis

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155
e-mail: georgios.karamanis@tufts.edu

Toby Kirk

Department of Mathematics,
Imperial College London,
London SW7 2AZ, UK
e-mail: toby.kirk12@imperial.ac.uk

Marc Hodes

Department of Mechanical Engineering,
Tufts University,
Medford, MA 02155
e-mail: marc.hodes@tufts.edu

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 20, 2016; final manuscript received April 21, 2017; published online July 6, 2017. Assoc. Editor: Ronggui Yang.

J. Heat Transfer 139(12), 122006 (Jul 06, 2017) (10 pages) Paper No: HT-16-1676; doi: 10.1115/1.4036600 History: Received October 20, 2016; Revised April 21, 2017

We develop a one-dimensional model for transient diffusion of gas between ridges into a quiescent liquid suspended in the Cassie state above them. In the first case study, we assume that the liquid and gas are initially at the same pressure and that the liquid column is sealed at the top. In the second one, we assume that the gas initially undergoes isothermal compression and that the liquid column is exposed to gas at the top. Our model provides a framework to compute the transient gas concentration field in the liquid, the time when the triple contact line begins to move down the ridges, and the time when menisci reach the bottom of the substrate compromising the Cassie state. At illustrative conditions, we show the effects of geometry, hydrostatic pressure, and initial gas concentration on the Cassie to Wenzel state transition.

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Figures

Grahic Jump Location
Fig. 1

Schematic showing the liquid domain supported over one period of parallel ridges at time t = 0 for case studies I and II. The thin dashed lines represent the meniscus curvature at the critical time tcr, intermediate time t, and final time tf. (a) case study I and (b) case study II.

Grahic Jump Location
Fig. 2

Time dependence of dissolved gas concentration along the meniscus at times τ1, τ2,…, τj−1, τj. The solid line shows it up to τj and the dashed line shows it at future times up to tcr.

Grahic Jump Location
Fig. 3

Semilog plot of gas pressure versus time for case study I where initial conditions are (a) ρg,0 = 0 and (b) ρg,0 = 0.018 kg/m3 and the geometric parameters are s0 = 10 μm, a = 5 μm, and h = 800 μm. The critical and final time for (a) are tcr = 1.82 s and tf = 176.7 s, respectively.

Grahic Jump Location
Fig. 4

Plot of dissolved gas concentration in the liquid versus y for the cases where gas pressure in the cavity is held constant at p at t = tf and gas pressure is allowed to decrease to pcr at times t = tcr and t = tf. The liquid is initially degassed and s0 = 10 μm, a = 5 μm, and h = 800 μm. In the first case, dissolved gas concentration in the liquid is equivalent to the product of the auxiliary solution, Eq. (31), and constant surface concentration of pH.

Grahic Jump Location
Fig. 5

Plot of dissolved gas concentration in the liquid versus y in the vicinity of the meniscus at times 0.001 s, 0.62 s, and 1.82 s (tcr) for case study I. The inset shows the variation of surface concentration with time during the interval 0 < t < tcr.

Grahic Jump Location
Fig. 6

Plot of mass of gas in the cavity per unit depth versus t for case study I where s0 = 10 μm, a = 5 μm, h = 800 μm, and ρg,0 = 0

Grahic Jump Location
Fig. 7

Plot of longevity versus h for case study I where s0 = 10 μm, a = 5 μm, and ρg,0 = 0. The dotted line shows the limiting case of h = hmin.

Grahic Jump Location
Fig. 8

Plot of tf and tcr versus ρg,0/(pH) for case study II where s0 = 85 μm, a = 73.5 μm, and h = 16.5 cm. The dimensions were adapted from Xu et al.

Grahic Jump Location
Fig. 9

Plot of tcr and tf versus s0 in initially degassed water (case study II) where a = 73.5 μm and h = 16.5 cm. s0 varies from 15 μm to 85 μm.

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