5 results
Local dynamics during thinning and rupture of liquid sheets of power-law fluids
- Vishrut Garg, Sumeet S. Thete, Christopher R. Anthony, Osman A. Basaran
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- Journal:
- Journal of Fluid Mechanics / Volume 942 / 10 July 2022
- Published online by Cambridge University Press:
- 17 May 2022, A15
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Rupture of liquid sheets of power-law fluids surrounded by a gas is analysed under the competing influences of pressure due to van der Waals attraction, inertia, viscous stress and capillary pressure due to surface tension. Results of a combined theoretical and computational study are presented over the entire range of parameters governing the thinning of a power-law fluid of power-law exponent $0 < n \le 1$ ($n=1$: Newtonian fluid) and Ohnesorge number $0 \le Oh < \infty$, where $Oh \equiv \mu _0/\sqrt {\rho h_0 \sigma }$, and $\mu _0, \rho, h_0$ and $\sigma$ stand for the zero-deformation-rate viscosity, density, the initial sheet half-thickness and surface tension, respectively. The dynamics in the vicinity of the space–time singularity where the sheet ruptures is asymptotically self-similar, and thus the variation with time remaining until rupture $\tau \equiv t_R - t$, where $t_R$ is the time instant $t$ at which the sheet ruptures, of sheet half-thickness, lateral length scale and lateral velocity is determined analytically and confirmed by simulations. For sheets for which inertia is negligible ($Oh^{-1}=0$), two distinct viscous scaling regimes are found, one for $0.58 < n \le 1$ and the other for $n \le 0.58$. The thinning dynamics of inviscid sheets ($Oh = 0$) is identical to that of Newtonian ones. For real fluids for which neither viscosity nor inertia is negligible, it is shown that the aforementioned creeping and inertial flow regimes are transitory and the thinning of power-law sheets exhibits a remarkably richer set of scaling transitions compared with Newtonian sheets.
Oscillations of a ring-constrained charged drop
- Brayden W. Wagoner, Vishrut Garg, Michael T. Harris, Doraiswami Ramkrishna, Osman A. Basaran
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- Journal:
- Journal of Fluid Mechanics / Volume 921 / 25 August 2021
- Published online by Cambridge University Press:
- 30 June 2021, A19
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Free drops of uncharged and charged inviscid, conducting fluids subjected to small-amplitude perturbations undergo linear oscillations (Rayleigh, Proc. R. Soc. London, vol. 29, no. 196–199, 1879, pp. 71–97; Rayleigh, Philos. Mag., vol. 14, no. 87, 1882, pp. 184–186). There exist a countably infinite number of oscillation modes, $n=2, 3, \ldots$, each of which has a characteristic frequency and mode shape. Presence of charge ($Q$) lowers modal frequencies and leads to instability when $Q>Q_R$ (Rayleigh limit). The $n=0$ and $n=1$ modes are disallowed because they violate volume conservation and cause centre of mass (COM) motion. Thus, the first mode to become unstable is the $n=2$ prolate–oblate mode. For free drops, there is a one-to-one correspondence between mode number and shape (Legendre polynomial $P_n$). Recent research has shifted to studying oscillations of spherical drops constrained by solid rings. Pinning the drop introduces a new low-frequency mode of oscillation ($n=1$), one associated primarily with COM translation of the constrained drop. We analyse theoretically the effect of charge on oscillations of constrained drops. Using normal modes and solving a linear operator eigenvalue problem, we determine the frequency of each oscillation mode. Results demonstrate that for ring-constrained charged drops (RCCDs), the association between mode number and shape is lost. For certain pinning locations, oscillations exhibit eigenvalue veering as $Q$ increases. While slightly charged RCCDs pinned at zeros of $P_2$ have a first mode that involves COM motion and a second mode that entails prolate–oblate oscillations, the modes flip as $Q$ increases. Thereafter, prolate–oblate oscillations of RCCDs adopt the role of being the first mode because they exhibit the lowest vibration frequency. At the Rayleigh limit, the first eigenmode – prolate–oblate oscillations – loses stability while the second – involving COM motion – remains stable.
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.
Inertial impedance of coalescence during collision of liquid drops
- Krishnaraj Sambath, Vishrut Garg, Sumeet S. Thete, Hariprasad J. Subramani, Osman A. Basaran
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- Journal:
- Journal of Fluid Mechanics / Volume 876 / 10 October 2019
- Published online by Cambridge University Press:
- 01 August 2019, pp. 449-480
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The fluid dynamics of the collision and coalescence of liquid drops has intrigued scientists and engineers for more than a century owing to its ubiquitousness in nature, e.g. raindrop coalescence, and industrial applications, e.g. breaking of emulsions in the oil and gas industry. The complexity of the underlying dynamics, which includes occurrence of hydrodynamic singularities, has required study of the problem at different scales – macroscopic, mesoscopic and molecular – using stochastic and deterministic methods. In this work, a multi-scale, deterministic method is adopted to simulate the approach, collision, and eventual coalescence of two drops where the drops as well as the ambient fluid are incompressible, Newtonian fluids. The free boundary problem governing the dynamics consists of the Navier–Stokes system and associated initial and boundary conditions that have been augmented to account for the effects of disjoining pressure as the separation between the drops becomes of the order of a few hundred nanometres. This free boundary problem is solved by a Galerkin finite element-based algorithm. The interplay of inertial, viscous, capillary and van der Waals forces on the coalescence dynamics is investigated. It is shown that, in certain situations, because of inertia two drops that are driven together can first bounce before ultimately coalescing. This bounce delays coalescence and can result in the computed value of the film drainage time departing significantly from that predicted from existing scaling theories.
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.