Fingering instability in thin wetting films

Troian, Sandra M.; Wu, X. L.; Safran, S. A.

doi:10.1103/physrevlett.62.1496

Cited by 205 publications

(174 citation statements)

References 8 publications

Supporting

Mentioning

158

Contrasting

Order By: Relevance

“…Moreover, the swarming process is accompanied by spatial gradients of surfactin concentration. Since surfactin is a surfactant, concentration gradients give rise to Marangoni forces, which have been shown to create branching patterns in the spreading of liquid droplets [25]. Moreover, many models to explain swarming assume that the surface of the agar is covered by a thin liquid film [6,2].…”

Section: Critical Review Of the Correspondence Between Experiments Anmentioning

confidence: 99%

Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

Marrocco

Henry

Holland

et al. 2010

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

Abstract.Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and non-growing) and nutrient concentration. We test the numerical behavior of such models and compare them to relevant experimental data together with a critical analysis of the validity of the models based on recent observations of the swarming bacteria which show that nutrients are not limitating but distinct subpopulations growing at different rates are likely present.

show abstract

Section: Critical Review Of the Correspondence Between Experiments Anmentioning

confidence: 99%

Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

Marrocco

Henry

Holland

et al. 2010

Math. Model. Nat. Phenom.

View full text Add to dashboard Cite

show abstract

“…Various experimental studies [2][3][4][5][6] have shown that once the spreading of surfactant commences, the film thickness near the source region begins to thin and develops a digitated appearance as shown in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

“…1 also undergo lateral spreading, shielding, and tip-splitting, features characteristic of viscous fingering patterns. The surfactant patterns are known to occur quite easily and have been found under many different experimental conditions including spreading in rectilinear 4,5 or axisymmetric geometry, 2,3,6 spreading from a source held at constant concentration 4,5 or from a finite reservoir, 2,3,6 spreading on films ranging in thickness from microns [2][3][4][5][6] to millimeters, 10 with soluble 2,4,10 or insoluble 3,5,10 surfactants of various head group charge, and with a surfactant source either above 2,3,10 or below 3,10 the critical micelle concentration. This latter concentration defines the point at which the air-liquid interface can no longer accommodate surfactant thereby forcing excess surface molecules into the bulk liquid to form micellar clusters.…”

Section: Introductionmentioning

confidence: 99%

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Matar

Troian

1999

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We describe the response of an insoluble surfactant monolayer spreading on the surface of a thin liquid film to small disturbances in the film thickness and surfactant concentration. The surface shear stress, which derives from variations in surfactant concentration at the air-liquid interface, rapidly drives liquid and surfactant from the source toward the distal region of higher surface tension. A previous linear stability analysis of a quasi-steady state solution describing the spreading of a finite strip of surfactant on a thin Newtonian film has predicted only stable modes. ͓Dynamics in Small Confining Systems III, Materials Research Society Symposium Proceedings, edited by J. M. Drake, J. Klafter, and E. R. Kopelman ͑Materials Research Society, Boston, 1996͒, Vol. 464, p. 237; Phys. Fluids A 9, 3645 ͑1997͒; O. K. Matar Ph.D. thesis, Princeton University, Princeton, NJ, 1998͔. A perturbation analysis of the transient behavior, however, has revealed the possibility of significant amplification of disturbances in the film thickness within an order one shear time after the onset of flow ͓Phys. Fluids A 10, 1234 ͑1998͒; ''Transient response of a surfactant monolayer spreading on a thin liquid film: Mechanism for amplification of disturbances,'' submitted to Phys. Fluids͔. In this paper we describe the linearized transient behavior and interpret which physical parameters most strongly affect the disturbance amplification ratio. We show how the disturbances localize behind the moving front and how the inclusion of van der Waals forces further enhances their growth and lifetime. We also present numerical solutions to the fully nonlinear 2D governing equations. As time evolves, the nonlinear system sustains disturbances of longer and longer wavelength, consistent with the quasi-steady state and transient linearized descriptions. In addition, for the parameter set investigated, disturbances consisting of several harmonics of a fundamental wavenumber do not couple significantly. The system eventually singles out the smallest wavenumber disturbance in the chosen set. The summary of results to date seems to suggest that the fingering process may be a transient response which nonetheless has a dramatic influence on the spreading process since the digitated structures redirect the flux of liquid and surfactant to produce nonuniform surface coverage. © 1999 American Institute of Physics. ͓S1054-1500͑99͒02001-7͔ Surfactant molecules play a vital role in many biological and industrial processes because of their native ability to lower surface tension in proportion to their concentration. Their presence greatly improves the wetting and spreading capability of commonplace substances like inks, paints, and herbicides. Lung surfactants produced in the alveoli are critical in maintaining lung compliance. A deficiency in lung surfactant production, for example, is known to cause pulmonary edema and other respiratory difficulties. When surfactant molecules contact a liquid surface of higher surface tension, a shear stress develops...

show abstract

“…We explore a range of gel strengths and droplet surface tensions and find that the onset of the instability and the number of arms depend on the ratio of surface tension to gel strength. However, the arm length grows with an apparently universal law L ∝ t 3/4 .PACS numbers: 47.55.nd, 62.20.Mk, 47.20.Dr, 47.20.Gv The surface-tension driven spreading of liquids is industrially and biologically important, and has been studied in detail on both solid and liquid substrates [1,2,3]. Less is known about how droplet spreading is modified in the presence of a compliant substrate, a situation especially relevant to biological applications [4,5].…”

mentioning

confidence: 99%

Instabilities in Droplets Spreading on Gels

et al. 2007

View full text Add to dashboard Cite

We report a novel surface-tension driven instability observed for droplets spreading on a compliant substrate. When a droplet is released on the surface of an agar gel, it forms arms/cracks when the ratio of surface tension gradient to gel strength is sufficiently large. We explore a range of gel strengths and droplet surface tensions and find that the onset of the instability and the number of arms depend on the ratio of surface tension to gel strength. However, the arm length grows with an apparently universal law L ∝ t 3/4 .PACS numbers: 47.55.nd, 62.20.Mk, 47.20.Dr, 47.20.Gv The surface-tension driven spreading of liquids is industrially and biologically important, and has been studied in detail on both solid and liquid substrates [1,2,3]. Less is known about how droplet spreading is modified in the presence of a compliant substrate, a situation especially relevant to biological applications [4,5]. We perform droplet-spreading experiments on gel agar, a viscoelastic material, to explore the influence of substrate on the spreading dynamics of the droplet. We find a novel branching instability with an onset that is controlled by the ratio of surface tension difference to the shear strength of the gel. The existence of a spreading morphology in which a spreading droplet becomes spatially localized has important implications for the industrial and medical application of surfactants.Droplets spread differently on liquids, which are mobile, than on solids, which are essentially rigid [3,6,7]. The present experiments on spreading on a viscoelastic substrate (gel agar) are intended as a way to span these two limits: by increasing the agar concentration, one can tune the substrate from liquid-like to solid-like behavior. The difference in surface tension between the droplet (PDMS, a silicone oil; or Triton X-305, a surfactant solution) and the substrate drives the spreading process.Previous work on the spreading of droplets on gel substrates [8,9] showed circular spreading with rates intermediate between those observed on solid and liquid substrates, contrary to what we find. In addition, prior studies of viscoelastic substrates have focused on substrate breakup or fracture when subjected to stresses [10,11,12,13]. Here, we observe a failure of the gel driven by surface tension. After the initial failure, there are two morphologically different manifestations of the instability, influenced by both the substrate elasticity and the surface tensions, which we call starbursts and wispy drops. For weak gels (shear modulus G 30 Pa), the drop breaks into distinct crack-like spreading arms in a starburst formation, as shown in Fig. 1a. Morphologically, this is similar to cracking patterns observed in [10,12]. We observe that the arms have steep sides ex- tending into the gel and are filled with material from the spreading droplet. Above the onset of the starburst instability, the rate of spreading is found to be controlled only by the width of the arms, with collapse in the data across substrate modulus, surface tension, ...

show abstract

Fingering instability in thin wetting films

Cited by 205 publications

References 8 publications

Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

Spreading of a surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures

Instabilities in Droplets Spreading on Gels

Contact Info

Product

Resources

About