Fingering instability of thin spreading films driven by temperature gradients

Cazabat, A. M.; Heslot, F.; Troian, Sandra M.; Carles, Philippe

doi:10.1038/346824a0

Cited by 412 publications

(338 citation statements)

References 5 publications

Supporting

Mentioning

327

Contrasting

Order By: Relevance

“…when additional pressure forcibly ruptures the film or (to a lesser extent) when capillary pressure-driven water movement occurs in the absence of gravity). This agrees with our results (Tables 1 and 2) and is also supported by the bulk of published experimental and theoretical evidence (Huppert, 1982 ;Melo et al, 1989 ;Troian et al, 1989Troian et al, , 1990Cazabat et al, 1990Cazabat et al, , 1992. These authors have shown that in forced spreading the liquid front undergoes a fingering instability.…”

Section: Why Do Capillary Forces Fail ?supporting

confidence: 93%

Water rise kinetics in refilling xylem after desiccation in a resurrection plant

et al. 2000

View full text Add to dashboard Cite

The acropetal water refilling kinetics of the dry xylem of branches (up to 80 cm tall) of the resurrection plant Myrothamnus flabellifolia were determined with high temporal resolution by observation of light refraction at the advancing water front and the associated recurving of the folded leaves. To study the effect of gravity on water rise, data were acquired for cut upright, horizontal and inverted branches. Water rise kinetics were also determined with hydrostatic and osmotic pressure as well as at elevated temperatures (up to 100mC) under laboratory conditions and compared with those obtained with intact (rooted) and cut branches under field conditions. Experiments in which water climbed under its capillary pressure alone, showed that the axial flow occurred only in a very few conducting elements at a much higher rate than in many of the other ones. The onset of transpiration of the unfolded and green leaves did not affect the rise kinetics in the ' prominent ' conducting elements. Application of pressure apparently increased the number of elements making a major contribution to axial xylem flow. Analysis of these data in terms of capillary-pressure-driven water ascent in leaky capillaries demonstrated that root pressure, not capillary pressure, is the dominant force for rehydration of rooted, dry plants. The main reasons for the failure of capillary forces in xylem refilling were the small, rate-limiting effective radii of the conducting elements for axial water ascent (c. 1 µm compared with radii of the vessels and tracheids of c. 18 µm and 3 µm, respectively) and the very poor wetting of the dry walls. The contact (wetting) angles were of the order of 80m and decreased on root or externally applied hydrostatic pressure. This supported our previous assumption that the inner walls of the dry conducting elements are covered with a lipid layer that is removed or disintegrates upon wetting. Consistent with this, potassium chloride and, particularly, sugars exerted an osmotic pressure effect on axial water climbing (reflection coefficients zero, but small). Although the osmotically active solutes apparently suppressed radial water spread through the tissue to the leaf cells, they reduced the axial water ascent rather than accelerating it as predicted by the theory of capillary-driven water rise in leaky capillaries. Killing cells by heat treatment and removal of the bark, phelloderm, cortex and phloem also resulted in a reduction of the axial rise rate and final height. These observations demonstrated that radial water movement driven by the developing osmotic and turgor pressure in the living cells was important for the removal of the lipid layer from the walls of those conducting elements that were primarily not involved in water rise. There is some evidence from field measurements of the axial temperature gradients along rooted branches that interfacial (Marangoni) streaming facilitated lipid removal (under formation of vesicle-like structures and lipid bodies) upon wetting.

show abstract

Section: Why Do Capillary Forces Fail ?supporting

confidence: 93%

Water rise kinetics in refilling xylem after desiccation in a resurrection plant

et al. 2000

View full text Add to dashboard Cite

show abstract

“…The value ofτ is prescribed as indicated; surface tension gradients of similar magnitude have been achieved in an experimental setting using heated substrates [4]. Comparing the top and middle set of colour maps reveals the effect of the surface tension gradient,τ , see equation (1), acting in the streamwise direction.…”

Section: Marangoni Effectsmentioning

confidence: 99%

“…There have been many subsequent investigations, mainly numerical, of the phenomenon; for example Diez and Kondic [3] explored gravity-driven flow on inclined planar and patterned substrates, discovering that the inclination angle affects the shape and length of the rivulet patterns formed. Cazabat et al [4] investigated experimentally the case of a film driven, in opposition to gravity, by thermal gradients and found that, in a similar way to gravity-driven films, rivulets form at the advancing front -the surface tension gradients present having a large influence on the associated dynamics. Eres et al [5] developed a model to replicate their experimental set up and predicted the break up of the associated rivulets at low velocities.…”

Section: Introductionmentioning

confidence: 99%

“…It consists of a thin fluid film of thickness H, flowing down a substrate (width, W p , length, L p ) inclined at angle θ to the horizontal; the volumetric flow rate is Q 0 per unit width. The fluid is considered to be incompressible with constant density, ρ, and viscosity, µ, and variable surface tension, σ, given by σ = σ 0σ = σ 0 + τ X with σ 0 the value of surface tension at X = 0 and τ (= ∂σ/∂X) a constant surface tension gradient [4]. The film is considered to be fully wetting; a precursor film of thickness, H * , located ahead of the advancing front, alleviates the singularity associated with the attendant contact line [6,8,9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Gravity-driven thin film flow: The influence of topography and surface tension gradient on rivulet formation

Slade¹,

Veremieiev²,

Lee³

et al. 2013

Chemical Engineering and Processing: Process Intensification

View full text Add to dashboard Cite

. (2013) 'Gravity-driven thin lm ow : the in uence of topography and surface tension gradient on rivulet formation.', Chemical engineering and processing : process intensi cation., 68 . pp. 7-12. Further information on publisher's website:http://dx.doi.org/10.1016/j.cep.2012.07.003Publisher's copyright statement: NOTICE: this is the author's version of a work that was accepted for publication in Chemical Engineering and Processing: Process Intensi cation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be re ected in this document. Changes may have been made to this work since it was submitted for publication. A de nitive version was subsequently published in Chemical Engineering and Processing: Process Intensi cation, 68, June 2013, 10.1016/j.cep.2012.07.003. Additional information:Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThe evolution of an advancing fluid front formed by a gravity-driven thin film flowing down a planar substrate is considered, with particular reference to the presence of Marangoni stresses and/or surface topography. The system is modelled using lubrication theory and solved via an efficient, adaptive multigrid method that incorporates automatic, errorcontrolled grid refinement/derefinement and time stepping. The detailed three dimensional numerical results obtained reveal that, for the problems investigated, while both of the above features affect the merger of rivulets by either delaying or promoting the same, topography influences the direction of growth.

show abstract

“…We assume the rate of heat transfer from the interface to be negligible and set the thermal flux to zero at z = h(x,t); this is supported by the fact that, for typical experimental conditions, the Biot number is small. 5,6,38 We also impose continuity of temperature at z = 0. In addition, at the liquid−solid interface, we apply the nopenetration condition on w, and a Navier slip condition on u 39 to relieve the stress singularity which would otherwise arise at the moving contact line: u = βu z ; here, β is a slip length.…”

Section: ■ Problem Formulationmentioning

confidence: 99%

Thermocapillary-Driven Motion of a Sessile Drop: Effect of Non-Monotonic Dependence of Surface Tension on Temperature

et al. 2014

View full text Add to dashboard Cite

ABSTRACT:We study the thermocapillary-driven spreading of a droplet on a nonuniformly heated substrate for fluids associated with a non-monotonic dependence of the surface tension on temperature. We use lubrication theory to derive an evolution equation for the interface that accounts for capillarity and thermocapillarity. The contact line singularity is relieved by using a slip model and a Cox-Voinov relation; the latter features equilibrium contact angles that vary depending on the substrate wettability, which, in turn, is linked to the local temperature. We simulate the spreading of droplets of fluids whose surface tension−temperature curves exhibit a turning point. For cases wherein these turning points correspond to minima, and when these minima are located within the droplet, then thermocapillary stresses drive rapid spreading away from the minima. This gives rise to a significant acceleration of the spreading whose characteristics resemble those associated with the "superspreading" of droplets on hydrophobic substrates. No such behavior is observed for cases in which the turning point corresponds to a surface tension maximum. ■ INTRODUCTIONThe motion of sessile droplets over liquids and solids is of central importance to a number of industrial applications such as coating flow technology, inkjet printing, microfluidics and microelectronics, and medical diagnostics. Despite the apparent simplicity of the physical setup involved, this motion is rather complex and some of its aspects remain poorly understood; in particular, the mechanisms underlying the dynamics of the threephase contact line are still the subject of debate. In view of its complexity 1 and its practical importance, droplet motion has received considerable attention in the literature and has been the subject of two major reviews. 2,3 In this work, we consider the motion of sessile droplets on non-isothermal solid walls, driven by thermocapillarity. The walls underlying the droplets are subjected to a temperature gradient which induces surface tension gradient-driven droplet deformation and migration from low to high surface tension regions. Thermocapillary-driven droplet motion was studied by Bouasse 4 who demonstrated the possibility of inducing droplet-climbing on a heated wire, against the action of gravity, by heating its lower end. Studies involving horizontal substrates have shown that, unless the magnitude of the imposed temperature gradient is sufficiently large, no droplet motion is possible due to contact angle hysteresis, while under certain conditions, steady migration of droplets has been shown. 5,6 A number of studies have examined the thermocapillary motion of droplets theoretically. Brochard 7 determined the spreading characteristics of a wedge-shaped drop in the presence of chemical or thermal gradients via local force and energy balances. This work was generalized by Ford and Nadim 8 to arbitrary, two-dimensional droplet shapes and different contact angles at the two contact lines. Lubrication theory was used to describe the...

show abstract

Fingering instability of thin spreading films driven by temperature gradients

Cited by 412 publications

References 5 publications

Water rise kinetics in refilling xylem after desiccation in a resurrection plant

Water rise kinetics in refilling xylem after desiccation in a resurrection plant

Gravity-driven thin film flow: The influence of topography and surface tension gradient on rivulet formation

Thermocapillary-Driven Motion of a Sessile Drop: Effect of Non-Monotonic Dependence of Surface Tension on Temperature

Contact Info

Product

Resources

About