## Evaporative instabilities in climbing films

Venue: | J. Fluid Mech |

Citations: | 4 - 0 self |

### BibTeX

@ARTICLE{Hosoi_evaporativeinstabilities,

author = {A. E. Hosoi and John W. M. Bush},

title = {Evaporative instabilities in climbing films},

journal = {J. Fluid Mech},

year = {}

}

### OpenURL

### Abstract

We consider flow in a thin film generated by partially submerging an inclined rigid plate in a reservoir of ethanol – or methanol–water solution and wetting its surface. Evaporation leads to concentration and surface tension gradients that drive flow up the plate. An experimental study indicates that the climbing film is subject to two distinct instabilities. The first is a convective instability characterized by flattened convection rolls aligned in the direction of flow and accompanied by free-surface deformations; in the meniscus region, this instability gives rise to pronounced ridge structures aligned with the mean flow. The second instability, evident when the plate is nearly vertical, takes the form of transverse surface waves propagating up the plate. We demonstrate that the observed longitudinal rolls are driven by the combined influence of surface deformations and alcohol concentration gradients. Guided by the observation that the rolls are flattened, we develop a quasi-two-dimensional theoretical model for the instability of the film, based on lubrication theory, which includes the effects of gravity, capillarity and Marangoni stresses at the surface. We develop stability criteria for the film which are in qualitative agreement with our experimental observations. Our analysis yields an equation for the shape of the interface which is solved numerically and reproduces the salient features of the observed flows, including the slow lateral drift and merging of the ridges. 1.

### Citations

58 | Long-scale evolution of thin liquid films - Oron, Davis, et al. - 1997 |

43 | Thin films with high surface tension - Myers - 1998 |

30 |
On convection currents in a horizontal layers of fluid, when the higher temperature is on the under side
- Rayleigh
- 1916
(Show Context)
Citation Context ...d’s (1900) seminal experimental observations of cellular convection in a horizontal layer of spermaceti heated from below were originally erroneously attributed to buoyancy-driven thermal convection (=-=Rayleigh 1916-=-), but are now known to have been due to Marangoni effects (Block 1956; Koschmieder 1967). Pearson (1958) examined the stability of a horizontal layer of depth H of fluid of viscosity µ, density ρ and... |

24 | On convection cells induced by surface tension - Pearson - 1958 |

20 |
Liquid-vapor phase-change phenomena: an introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment
- Carey
(Show Context)
Citation Context ...he free surface − ∂c ∂z ∣ = Q (4.7) z=h where Q is a parameter that depends on the temperature and on the microscopic properties of the mixture such as heat of vaporization and chemical conductivity (=-=Carey 1992-=-). Following our experimental data, we choose Q to be constant (see figure 7), thus neglecting the higher-order influences of vapour pressure, curvature and concentration on the evaporation rate. Inte... |

19 | Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463–494. Caginalp,G. An analysis of a phase field model of a free boundary - Burelbach, Bankoff, et al. - 1988 |

11 | On cellular convection driven by surface-tension gradients: Effects of mean surface tension and surface viscosity - Scriven, Sternling - 1964 |

10 |
Surface tension at the cause of Bénard cells and surface deformation in a liquid film
- Block
- 1956
(Show Context)
Citation Context ...horizontal layer of spermaceti heated from below were originally erroneously attributed to buoyancy-driven thermal convection (Rayleigh 1916), but are now known to have been due to Marangoni effects (=-=Block 1956-=-; Koschmieder 1967). Pearson (1958) examined the stability of a horizontal layer of depth H of fluid of viscosity µ, density ρ and thermal diffusivity κ, driven by a vertical temperature gradient, Θ ≡... |

9 | Surface tension and buoyancy effects in cellular convection - Nield - 1964 |

9 |
On the interaction of two scales of convection in the mantle
- Richter, Parsons
- 1975
(Show Context)
Citation Context ...of background shear and surface deformation. The tendency of shear to align convection rolls in the direction of the mean flow has been established both theoretically and experimentally (Bénard 1927; =-=Richter & Parsons 1975-=-; Gumerman & Homsy 1974). In our system the shear236 A. E. Hosoi and J. W. M. Bush Figure 13. A time series showing the generation of total vorticity, |ω| = √ v 2 z + v 2 x +(wx − uz) 2 where white r... |

9 | On convective instability induced by surface-tension gradients - Smith - 1966 |

5 | Nonlinear Stability of Evaporating/ Condensing Liquid Films - Bankoff |

5 |
Thermocapillary instabilities
- Davis
- 1987
(Show Context)
Citation Context ...ce may be mitigated by the influence of gravity, and his stability criterion may be expressed as γΘ < 2ρgH; consequently, long-wave 3 instabilities always become important in sufficiently thin films (=-=Davis 1987-=-). These previous analyses are summarized in table 1. An exploratory experimental study of evaporatively forced convection within layers of both homogeneous and binary fluids was presented by Berg, Bo... |

4 | On the expansion of a drop of liquid floating on the surface of another liquid. Tipographia dei fratelli Fusi - Marangoni - 1865 |

4 | Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities - Smith, Davis - 1983 |

3 | Evaporative convection - Berg, Acrivos, et al. - 1966 |

3 | Natural convection in pools of evaporating liquids - Berg, Boudart, et al. - 1966 |

3 |
CRC Handbook of Chemistry and Physics, 72 nd edition
- Lide
- 1991
(Show Context)
Citation Context ...rface tension due to temperature ∂σ/∂T ∼ 0.2 dyn cm−1 ◦C−1‡ Table 3. Estimated values for parameters in experiments. † from Vuilleumier et al. (1995), ∗ from experiments by the authors, ‡ CRC values (=-=Lide 1974-=-). Concentration is measured by volume fraction. h lower c(h) c(h) Figure 8. The mechanism driving the longitudinal rolls. The base concentration profile is set by evaporation from the free surface, d... |

2 | On a nonlinear thermocapillary effect in thin liquid layers - Oron, Rosenau - 1994 |

2 | Effect of nonlinear temperature profiles on onset of convection driven by surface tension gradients, Ind. Engng Chem. Fundam. 7 - Vidal, Acrivos - 1968 |

2 |
Tears of wine: the stationary state
- Vuilleumier, Ego, et al.
- 1995
(Show Context)
Citation Context ...m parameters (see table 3) yields Ms = τH2 µD ∼ 0.5 × (2 × 10−3 ) 2 10−2 ∼ 10. (3.1) × 10−5 Note that in our system, the surface stress is associated with compositional rather than thermal gradients (=-=Vuilleumier et al. 1995-=-). Since τ and H are measured experimentally and the ratio of molecular diffusivity, D, to thermal diffusivity, κ, isD/κ =(1.26 × 10 −5 cm 2 s −1 )/(1.5 × 10 −3 cm 2 s −1 ) ∼ 10 −2 , the thermal Maran... |

2 | Spreading and instabilities induced by a soluted Marangoni effect - Fanton, Cazabat - 1998 |

2 | Tears of wine. Europhys - Fournier, Cazabat - 1992 |

2 | 1855 On certain curious motions observable at the surfaces of wine and other alcoholic liquors - Thomson |

1 | Sur les tourbillons cellulaires et la th'eorie de rayleigh - enard, H - 1927 |

1 | 2000 Tear ducts of wine - Bush |

1 | Experimental study of marangoni-b'enard convection in a liquid layer induced by evaporation. Experimental Heat Transfer - Chai - 1998 |

1 | Tears of wine. Europhys. Lett. 20, 517. Evaporative instabilities in climbing films 17 - Fournier - 1992 |

1 |
Ridges in a liquid surface due to the temperature dependence of surface tension
- Hershey
- 1939
(Show Context)
Citation Context ...actant or temperature gradients; for example, the fine convection rolls apparent in thin layers of coffee (Walker 1983), the ridges evident in the boundary of a film of water flowing down an incline (=-=Hershey 1939-=-), and the ridge structures evident in the meniscus region in a pan of hot cooking oil. When a candle is burning, a radial surface tension gradient is generated in the liquid wax owing to the temperat... |

1 |
On convection under an air surface
- Koschmieder
- 1967
(Show Context)
Citation Context ...ayer of spermaceti heated from below were originally erroneously attributed to buoyancy-driven thermal convection (Rayleigh 1916), but are now known to have been due to Marangoni effects (Block 1956; =-=Koschmieder 1967-=-). Pearson (1958) examined the stability of a horizontal layer of depth H of fluid of viscosity µ, density ρ and thermal diffusivity κ, driven by a vertical temperature gradient, Θ ≡ dT/dz, with a non... |

1 | The history of the spreading coefficient - Ross - 1992 |

1 | Instability of a meniscus due to surface tension gradient-driven flow - Ryck - 1999 |

1 |
The Marangoni effects
- Scriven, Sternling
- 1960
(Show Context)
Citation Context ...nferred that convection could be driven by surface tension gradients due to variations in either composition or temperature and today this mode of convection bears his name (see historical reviews by =-=Scriven & Sternling 1960-=-; Ross & Becher 1992). Evaporative convection arises in a variety of natural and industrial settings, and an extensive review of its manifestations may be found in Berg, Acrivos & Boudart (1966). Evap... |

1 | Sur les tourbillons en festons - Volkoviski - 1935 |

1 |
What causes the 'tears' that form on the inside of a glass of wine? Sci
- Walker
- 1983
(Show Context)
Citation Context ...ituations involving surface tension gradients generated by either concentration, soluble surfactant or temperature gradients; for example, the fine convection rolls apparent in thin layers of coffee (=-=Walker 1983-=-), the ridges evident in the boundary of a film of water flowing down an incline (Hershey 1939), and the ridge structures evident in the meniscus region in a pan of hot cooking oil. When a candle is b... |

1 |
Sur les tourbillons cellulaires et la théorie de Rayleigh. Compt. Rendue 185
- Bénard
- 1927
(Show Context)
Citation Context ...ed influence of background shear and surface deformation. The tendency of shear to align convection rolls in the direction of the mean flow has been established both theoretically and experimentally (=-=Bénard 1927-=-; Richter & Parsons 1975; Gumerman & Homsy 1974). In our system the shear236 A. E. Hosoi and J. W. M. Bush Figure 13. A time series showing the generation of total vorticity, |ω| = √ v 2 z + v 2 x +(... |

1 | Evaporative convection. Adv. Chem. Engng 6, 61–123. instabilities in climbing films 239 - Berg, Acrivos, et al. - 1966 |

1 |
Convective instabilities in concurrent two phase flow: Part i. Linear stability
- Gumerman, Homsy
- 1974
(Show Context)
Citation Context ...surface deformation. The tendency of shear to align convection rolls in the direction of the mean flow has been established both theoretically and experimentally (Bénard 1927; Richter & Parsons 1975; =-=Gumerman & Homsy 1974-=-). In our system the shear236 A. E. Hosoi and J. W. M. Bush Figure 13. A time series showing the generation of total vorticity, |ω| = √ v 2 z + v 2 x +(wx − uz) 2 where white represents high vorticit... |