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

Matar, Omar; Troian, Sandra M.

doi:10.1063/1.166385

Cited by 65 publications

(66 citation statements)

References 32 publications

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“…More studies of this system of equations using other parameter values 24,25,33 confirms that the transient growth observed in Fig. 4 can achieve even larger amplification ratios.…”

Section: Stability Of Time-dependent Base Statementioning

confidence: 78%

“…[22][23][24][25] An energy decomposition reveals that there is a switch in the destabilizing agent between large and small K disturbances. While the transverse Marangoni flux produces thickened arteries that grow into liquid channels for large K, the streamwise Marangoni flux produces similar channeling of the fluid for small K. In both cases, the destabilizing flow is resisted by streamwise capillary flow which is stabilizing at all times.…”

Section: Discussionmentioning

confidence: 99%

“…We suspect this mode represents the same neutrally stable mode which was identified by the quasisteady linear stability analysis as the mode with the largest growth rate. [22][23][24][25] As shown in Fig. 4͑b͒, the amplification ratio experienced by disturbances in the surfactant concentration, G ⌽ , is insignificant.…”

Section: Base State Profilesmentioning

confidence: 99%

“…We have investigated several parameter sets in an effort to determine the spectrum of spreading behavior and the source of digitation. 24,25,33 The choice discussed below reflects the common response of the system and demonstrates the most important features of the spreading process. We concentrate on the following set of initial conditions in analyzing the stability of the time dependent base states: 2 .…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…The inclusion of additional but weaker forces like capillarity and surface diffusion confirmed linearly stable flow. 24,25 These quasisteady calculations highlighted certain important features of the spreading process. First, the analyses underscored the importance of allowing variations in both the film thickness and surfactant concentration.…”

Section: Introductionmentioning

confidence: 99%

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The development of transient fingering patterns during the spreading of surfactant coated films

Matar

Troian

1999

Physics of Fluids

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The spontaneous spreading of an insoluble surfactant monolayer on a thin liquid film produces a complex waveform whose time variant shape is strongly influenced by the surface shear stress. This Marangoni stress produces a shocklike front at the leading edge of the spreading monolayer and significant film thinning near the source. For sufficiently thin films or large initial shear stress, digitated structures appear in the wake of the advancing monolayer. These structures funnel the oncoming flow into small arteries that continuously tip-split to produce spectacular dendritic shapes. A previous quasisteady modal analysis has predicted stable flow at asymptotically long times ͓Phys. Fluids A 9, 3645 ͑1997͔͒. A more recent transient analysis has revealed large amplification in the disturbance film thickness at early times ͓O. K. Matar and S. M. Troian, ''Growth of nonmodal transient structures during the spreading of surfactant coated films,'' Phys. Fluids A 10, 1234 ͑1998͔͒. In this paper, we report results of an extended sensitivity analysis which probes two aspects of the flow: the time variant character of the base state and the non-normal character of the disturbance operators. The analysis clearly identifies Marangoni forces as the main source of digitation for both small and large wave number disturbances. Furthermore, initial conditions which increase the initial shear stress or which steepen the shape of the advancing front produce a larger transient response and deeper corrugations in the film. Disturbances applied just ahead of the deposited monolayer rapidly fall behind the advancing front eventually settling in the upstream region where their mobility is hampered. Recent findings confirm that additional forces which promote film thinning can further intensify disturbances ͓O. K. Matar and S. M. Troian, ''Spreading of surfactant monolayer on a thin liquid film: Onset and evolution of digitated structures,'' Chaos 9, 141 ͑1999͒. The transient analysis presented here corroborates our previous results for asymptotic stability but reveals a source for digitation at early times. The energy decomposition lends useful insight into the actual mechanisms preventing efficacious distribution of surfactant.

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“…More studies of this system of equations using other parameter values 24,25,33 confirms that the transient growth observed in Fig. 4 can achieve even larger amplification ratios.…”

Section: Stability Of Time-dependent Base Statementioning

confidence: 78%

Section: Discussionmentioning

confidence: 99%

Section: Base State Profilesmentioning

confidence: 99%

Section: Numerical Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The development of transient fingering patterns during the spreading of surfactant coated films

Matar

Troian

1999

Physics of Fluids

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Lateral surface nonuniformities in drying latex films

Gundabala

Lei

Ouzineb³

et al. 2008

AIChE Journal

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The length scales of film thickness non-uniformities, commonly observed in polymer colloid (i.e. latex) films, are predicted. This prediction is achieved by investigating the stability behaviour of drying latex films. A linear stability analysis is performed on a base solution representing a uniformly drying latex film containing a surfactant. The analysis identifies film thickness non-uniformities over two length scales: long (millimetre) range (from lubrication theory) and short (micrometer) range (from nonlubrication theory). Evaporation and surfactant desorption into the bulk film are identified as the primary destabilizing mechanisms during drying. Experimental evidence through direct visualization and atomic force microscopy confirm the existence of non-uniformities over both length scales, which are shown to be functions of parameters such as initial particle volume fraction, surfactant amount and desorption strength, whilst being independent of drying rate.Published in JAIChE 54 (2008) 3092-3105

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On Marangoni effects in a heated thin fluid layer with a monolayer surfactant. Part I: model development and stability analysis

Wang

Carey

2005

Int. J. Numer. Meth. Fluids

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SUMMARYWe develop a model for surface tension driven ow induced by an insoluble surfactant monolayer on a heated thin uid layer. The mathematical model is based on a perturbation analysis for a thin uid layer. The resulting model involves coupling of ow and heat transfer to an additional transport equation for surfactant concentration on the surface. We develop the stability analysis of this coupled system. We characterize the stability behaviour and induced wave motion into four parametric regions based on linear stability analysis. A ÿnite element formulation and numerical studies of the behaviour in the various stability regimes are given in Part II.

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

Cited by 65 publications

References 32 publications

The development of transient fingering patterns during the spreading of surfactant coated films

The development of transient fingering patterns during the spreading of surfactant coated films

Lateral surface nonuniformities in drying latex films

On Marangoni effects in a heated thin fluid layer with a monolayer surfactant. Part I: model development and stability analysis

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