4 results
Pinch-off of a surfactant-covered jet
- Hansol Wee, Brayden W. Wagoner, Vishrut Garg, Pritish M. Kamat, Osman A. Basaran
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- Journal:
- Journal of Fluid Mechanics / Volume 908 / 10 February 2021
- Published online by Cambridge University Press:
- 11 December 2020, A38
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Surfactants at fluid interfaces not only lower and cause gradients in surface tension but can induce additional surface rheological effects in response to dilatational and shear deformations. Surface tension and surface viscosities are both functions of surfactant concentration. Measurement of surface tension and determination of its effects on interfacial flows are now well established. Measurement of surface viscosities, however, is notoriously difficult. Consequently, quantitative characterization of their effects in interfacial flows has proven challenging. One reason behind this difficulty is that, with most existing methods of measurement, it is often impossible to isolate the effects of surface viscous stresses from those due to Marangoni stresses. Here, a combined asymptotic and numerical analysis is presented of the pinch-off of a surfactant-covered Newtonian liquid jet. Similarity solutions obtained from slender-jet theory and numerical solutions are presented for jets with and without surface rheological effects. Near pinch-off, it is demonstrated that Marangoni stresses become negligible compared to other forces. The rate of jet thinning is shown to be significantly lowered by surface viscous effects. From analysis of the dynamics near the pinch-off singularity, a simple analytical formula is derived for inferring surface viscosities. Three-dimensional, axisymmetric simulations confirm the validity of the asymptotic analyses but also demonstrate that a thinning jet traverses a number of intermediate regimes before eventually entering the final asymptotic regime.
Bubble coalescence in low-viscosity power-law fluids
- Pritish M. Kamat, Christopher R. Anthony, Osman A. Basaran
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- Journal:
- Journal of Fluid Mechanics / Volume 902 / 10 November 2020
- Published online by Cambridge University Press:
- 04 September 2020, A8
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As two spherical gas bubbles of radii $\tilde {R}$ are brought together inside a liquid of density $\tilde {\rho }$, viscosity $\tilde {\mu }$ and surface tension $\tilde {\sigma }$, the liquid sheet separating them drains, thins and ultimately ruptures. The instant and location at which the bubbles make contact, and whereby a circular hole of vanishingly small radius is formed in the thin sheet, represent the occurrence of a finite-time singularity. The large curvature near the edge of the sheet where the hole has just formed, and where the two bubbles are now connected via a microscopic gas bridge, drives liquid to flow radially outward, causing the sheet to retract and the radius of the hole $\tilde {R}_{min}$ to increase with time. Recent work in this area has uncovered self-similarity and universal scaling regimes when two bubbles coalesce in a Newtonian fluid. Motivated by applications in which the exterior is a deformation-rate-thinning, power-law fluid, recent studies on bubble coalescence in Newtonian fluids are extended to coalescence in power-law fluids. In such fluids, viscosity decreases with deformation rate $\dot {\tilde {\gamma }}$ raised to the $n - 1$ power where $0 < n \le 1$ ($n = 1$ for a Newtonian fluid). Attention is focused here on power-law fluids that are slightly viscous at zero deformation rate, i.e. when the Ohnesorge number $Oh = \tilde {\mu }_{0}/(\tilde {\rho } \tilde {R} \tilde {\sigma })^{1/2}$ is small ($Oh \ll 1$) and where $\tilde {\mu }_0$ is the zero-deformation-rate viscosity. A combination of thin-film theory and three-dimensional, axisymmetric computations is used to probe the dynamics in the aftermath of the singularity. Heretofore unexplored regimes are uncovered, and criteria are developed for transitions between different regimes. The existence of a truly inviscid regime, predicted long ago by Keller (Phys. Fluids, vol. 26, 1983, pp. 3451–3453) and which comes into play as a purely geometrical limit of the free-surface shape, is also reported. New insights are presented on the much studied Newtonian limit beyond the initial regime reported by Munro et al. (J. Fluid Mech., vol. 773, 2015, R3). The paper concludes with a phase diagram in $(n, \tilde {R}_{min}/\tilde {R})$-space, where the index $n$ characterizes the fluid and $\tilde {R}_{min}/\tilde {R}$ the extent of coalescence, that highlights the various regimes and transitions between them.
Surfactant-driven escape from endpinching during contraction of nearly inviscid filaments
- Pritish M. Kamat, Brayden W. Wagoner, Alfonso A. Castrejón-Pita, José R. Castrejón-Pita, Christopher R. Anthony, Osman A. Basaran
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- Journal:
- Journal of Fluid Mechanics / Volume 899 / 25 September 2020
- Published online by Cambridge University Press:
- 24 July 2020, A28
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Highly stretched liquid drops, or filaments, surrounded by a gas are routinely encountered in nature and industry. Such filaments can exhibit complex and unexpected dynamics as they contract under the action of surface tension. Instead of simply retracting to a sphere of the same volume, low-viscosity filaments exceeding a critical aspect ratio undergo localized pinch-off at their two ends resulting in a sequence of daughter droplets – a phenomenon called endpinching – which is an archetype breakup mode that is distinct from the classical Rayleigh–Plateau instability seen in jet breakup. It has been shown that endpinching can be precluded in filaments of intermediate viscosity, with the so-called escape from endpinching being understood heretofore only qualitatively as being caused by a viscous mechanism. Here, we show that a similar escape can also occur in nearly inviscid filaments when surfactants are present at the free surface of a recoiling filament. The fluid dynamics of the escape phenomenon is probed by numerical simulations. The computational results are used to show that the escape is driven by the action of Marangoni stress. Despite the apparently distinct physical origins of escape in moderately viscous surfactant-free filaments and that in nearly inviscid but surfactant-covered filaments, it is demonstrated that the genesis of all escape events can be attributed to a single cause – the generation of vorticity at curved interfaces. By analysing vorticity dynamics and the balance of vorticity in recoiling filaments, the manner in which surface tension gradients and concomitant Marangoni stresses can lead to escape from endpinching is clarified.
Self-similar rupture of thin films of power-law fluids on a substrate
- Vishrut Garg, Pritish M. Kamat, Christopher R. Anthony, Sumeet S. Thete, Osman A. Basaran
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- Journal:
- Journal of Fluid Mechanics / Volume 826 / 10 September 2017
- Published online by Cambridge University Press:
- 04 August 2017, pp. 455-483
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Thinning and rupture of a thin film of a power-law fluid on a solid substrate under the balance between destabilizing van der Waals pressure and stabilizing capillary pressure is analysed. In a power-law fluid, viscosity is not constant but is proportional to the deformation rate raised to the $n-1$ power, where $0<n\leqslant 1$ is the power-law exponent ($n=1$ for a Newtonian fluid). In the first part of the paper, use is made of the slenderness of the film and the lubrication approximation is applied to the equations of motion to derive a spatially one-dimensional nonlinear evolution equation for film thickness. The variation with time remaining until rupture of the film thickness, the lateral length scale, fluid velocity and viscosity is determined analytically and confirmed by numerical simulations for both line rupture and point rupture. The self-similarity of the numerically computed film profiles in the vicinity of the location where the film thickness is a minimum is demonstrated by rescaling of the transient profiles with the scales deduced from theory. It is then shown that, in contrast to films of Newtonian fluids undergoing rupture for which inertia is always negligible, inertia can become important during thinning of films of power-law fluids in certain situations. The critical conditions for which inertia becomes important and the lubrication approximation is no longer valid are determined analytically. In the second part of the paper, thinning and rupture of thin films of power-law fluids in situations when inertia is important are simulated by solving numerically the spatially two-dimensional, transient Cauchy momentum and continuity equations. It is shown that as such films continue to thin, a change of scaling occurs from a regime in which van der Waals, capillary and viscous forces are important to one where the dominant balance of forces is between van der Waals, capillary and inertial forces while viscous force is negligible.