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  • 1
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    Experimental characterization of viscoelastic effects on two- and three-dimensional shear instabilities (2000)
    Cambridge University Press
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    Publication Date: 2000-08-10
    Description: Instabilities of a wake produced by a circular cylinder in a uniform water flow are studied experimentally when viscoelastic solutions are injected through holes pierced in the cylinder. It is shown that the viscoelastic solutions fill the shear regions and drastically modify the instabilities. The two-dimensional instability giving rise to the Karman street is found to be inhibited: The roll-up process appears to be delayed and the wavelength of the street increase. The wavelength increase obeys an exponential law and depends on the elasticity number, which provides a ratio of elastic forces to inertial forces. The three-dimensional instability leading to the A mode is generally found to be suppressed. In the rare case where the A mode is observed, its wavelength is shown to be proportional to the wavelength of the Karman street and the streamwise stretching appears to be inhibited. Injection of viscoelastic solutions also decreases the aspect ratio of the two-dimensional wake, and this is correlated with stabilization of the A mode and with changes in the shape of the Karman vortices. The observations of this work are consistent with recent numerical simulations of viscoelastic mixing layers. The results suggest mechanisms through which polymers inhibit the formation of high-vorticity coherent structures and reduce drag in turbulent flows.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 2
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    Surfactant- and elasticity-induced inertialess instabilities in vertically vibrated liquids (2008)
    Cambridge University Press
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    Publication Date: 2008-08-08
    Description: We investigate instabilities that arise when the free surface of a liquid covered with an insoluble surfactant is vertically vibrated and inertial effects are negligible. In the absence of surfactants, the inertialess Newtonian system is found to be stable, in contrast to the case where inertia is present. Linear stability analysis and Floquet theory are applied to calculate the critical vibration amplitude needed to excite the instability and the corresponding wavenumber. A previously reported long-wavelength instability is found to persist to finite wavelengths, and the connection between the long-wavelength and finite-wavelength theories is explored in detail. The instability mechanism is also probed and requires the Marangoni flows to be sufficiently strong and in the appropriate phase with respect to the gravity modulation. For viscoelastic liquids, we find that instability can arise even in the absence of surfactants and inertia. Mathieu equations describing this are derived and these show that elasticity introduces an effective inertia into the system. © 2008 Cambridge University Press.
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    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 3
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    Instability of long-wavelength disturbances on gravity-modulated surfactant-covered thin liquid layers (2002)
    Cambridge University Press
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    Publication Date: 2002-09-10
    Description: The effect of gravity modulation on long-wavelength disturbances at the free surface of a surfactant-covered thin liquid layer is analysed. The surfactants are assumed to be insoluble so that variations in their concentration along the free surface produce Marangoni flows in the underlying liquid. Lubrication theory is applied to obtain nonlinear partial differential equations that describe the behaviour of the free surface height and surfactant concentration, and the stability of these equations to small-amplitude disturbances is examined by applying Floquet theory. It is found that long-wavelength disturbances are destabilized by gravity modulation when surfactants are present, whereas such disturbances are stable when surfactants are absent. Results from additional calculations indicate that the instability becomes more difficult to excite as the Marangoni forces, body forces, capillary forces and surfactant diffusivity increase, and becomes easier to excite as the van der Waals forces increase.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    Stability of pressure-driven creeping flows in channels lined with a nonlinear elastic solid (2005)
    Cambridge University Press
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    Publication Date: 2005-02-10
    Description: The effect of pressure gradients on the stability of creeping flows of Newtonian fluids in channels lined with an incompressible and impermeable neo-Hookean material is examined in this work. Three different configurations are considered: (i) pressure-driven flow between a rigid wall and a wall lined with a neo-Hookean material; (ii) pressure-driven flow between neo-Hookean-lined walls; and (iii) combined Couette-Poiseuille flow between a rigid wall and a neo-Hookean-lined wall. In each case, a first normal stress difference whose magnitude depends on depth arises in the base state for the solid, and linear stability analysis reveals that this leads to a shortwave instability which is removed by the presence of interfacial tension. For sufficiently thick solids, low-wavenumber modes become unstable first as the applied strain increases above a critical value, whereas for sufficiently thin solids, high-wavenumber modes becomes unstable first. Comparison of the dimensionless critical strains shows that configurations (i) and (ii) are more difficult to destabilize than Couette flow past a neo-Hookean solid. For configuration (iii), the nonlinear elasticity of the solid leads to two physically distinct critical conditions, in contrast to what happens when a linear elastic material is used. The mechanisms underlying the behaviour of the critical strains are explained through an analysis of the interfacial boundary conditions. © 2005 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    Competitive displacement of thin liquid films on chemically patterned substrates (2007)
    Cambridge University Press
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    Publication Date: 2007-01-04
    Description: The behaviour of the interface between stratified thin liquid films bounded by parallel solid surfaces and subject to van der Waals forces which drive dewetting is studied in this work. Chemically homogeneous surfaces are considered first; this is followed by an investigation of chemically heterogeneous surfaces. The lubrication approximation is applied to obtain a single nonlinear evolution equation which describes the interfacial behaviour, and both the linear stability and nonlinear development of the interface are examined. The sensitivity of the interfacial rupture time to problem parameters such as the viscosity ratio, initial interfacial height, interfacial tension, and magnitude of the van der Waals forces is characterized in detail for the homogeneous case. This serves as a basis for a study of the heterogeneous case, where the strong dependence of the rupture time on the length scale of the heterogeneity is found to be relatively independent of changes in the remaining problem parameters. The mechanisms underlying the rupture-time behaviour are also explored in detail. The results suggest a route by which one liquid can become emulsified in the other, and may be beneficial to industrial processes such as lithographic printing which are based on wettability phenomena. © 2007 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
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    Energy amplification in channel flows of viscoelastic fluids (2008)
    Cambridge University Press
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    Publication Date: 2008-04-25
    Description: Energy amplification in channel flows of Oldroyd-B fluids is studied from an input - output point of view by analysing the ensemble-average energy density associated with the velocity field of the linearized governing equations. The inputs consist of spatially distributed and temporally varying body forces that are harmonic in the streamwise and spanwise directions and stochastic in the wall-normal direction and in time. Such inputs enable the use of powerful tools from linear systems theory that have recently been applied to analyse Newtonian fluid flows. It is found that the energy density increases with a decrease in viscosity ratio (ratio of solvent viscosity to total viscosity) and an increase in Reynolds number and elasticity number. In most of the cases, streamwise-constant perturbations are most amplified and the location of maximum energy density shifts to higher spanwise wavenumbers with an increase in Reynolds number and elasticity number and a decrease in viscosity ratio. For similar parameter values, the maximum in the energy density occurs at a higher spanwise wavenumber for Poiseuille flow, whereas the maximum energy density achieves larger maxima for Couette flow. At low Reynolds numbers, the energy density decreases monotonically when the elasticity number is sufficiently small, but shows a maximum when the elasticity number becomes sufficiently large, suggesting that elasticity can amplify disturbances even when inertial effects are weak. © 2008 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
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    Forced spreading of films and droplets of colloidal suspensions (2014)
    Cambridge University Press
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    Publication Date: 2014-02-21
    Description: When a thin film of a colloidal suspension flows over a substrate, uneven distribution of the suspended particles can lead to an uneven coating. Motivated by this phenomenon, we analyse the flow of perfectly wetting films and droplets of colloidal suspensions down an inclined plane. Lubrication theory and the rapid-vertical-diffusion approximation are used to derive a coupled pair of one-dimensional partial differential equations describing the evolution of the interface height and particle concentration. Precursor films are assumed to be present, the colloidal particles are taken to be hard spheres, and particle and liquid dynamics are coupled through a concentration-dependent viscosity and diffusivity. We find that for sufficiently high Péclet numbers, even small initial concentration inhomogeneities produce viscosity gradients that cause the film or droplet front to evolve continuously in time instead of travelling without changing shape as happens in the absence of colloidal particles. At high enough particle concentrations, particle diffusion can lead to the formation of long-lived secondary flow fronts in films. Our results suggest that particle concentration gradients can have a dramatic influence on interface evolution in flowing films and droplets, a finding which may be relevant for understanding the onset of patterns that are observed experimentally. © 2014 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
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    Droplet spreading and absorption on rough, permeable substrates (2015)
    Cambridge University Press
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    Publication Date: 2015-11-06
    Description: Wetting of permeable substrates by liquids is an important phenomenon in many natural and industrial processes. Substrate heterogeneities may significantly alter liquid spreading and interface shapes, which in turn may alter liquid imbibition. A new lubrication-theory-based model for droplet spreading on permeable substrates that incorporates surface roughness is developed in this work. The substrate is assumed to be saturated with liquid, and the contact-line region is described by including a precursor film and disjoining pressure. A novel boundary condition for liquid imbibition is applied that eliminates the need for a droplet-thickness-dependent substrate permeability that has been employed in previous models. A nonlinear evolution equation describing droplet height as a function of time and the radial coordinate is derived and then numerically solved to characterize the influence of substrate permeability and roughness on axisymmetric droplet spreading. Because it incorporates surface roughness, the new model is able to describe the contact-line pinning that has been observed in experiments but not captured by previous models. © 2015 Cambridge University Press.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 9
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    The dynamics of three-dimensional liquid bridges with pinned and moving contact lines (2012)
    Cambridge University Press
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    Publication Date: 2012-08-02
    Description: Liquid bridges with moving contact lines are relevant in a variety of natural and industrial settings, ranging from printing processes to the feeding of birds. While it is often assumed that the liquid bridge is two-dimensional in nature, there are many applications where either the stretching motion or the presence of a feature on a bounding surface lead to three-dimensional effects. To investigate this we solve Stokes equations using the finite-element method for the stretching of a three-dimensional liquid bridge between two flat surfaces, one stationary and one moving. We first consider an initially cylindrical liquid bridge that is stretched using either a combination of extension and shear or extension and rotation, while keeping the contact lines pinned in place. We find that whereas a shearing motion does not alter the distribution of liquid between the two plates, rotation leads to an increase in the amount of liquid resting on the stationary plate as breakup is approached. This suggests that a relative rotation of one surface can be used to improve liquid transfer to the other surface. We then consider the extension of non-cylindrical bridges with moving contact lines. We find that dynamic wetting, characterized through a contact line friction parameter, plays a key role in preventing the contact line from deviating significantly from its original shape as breakup is approached. By adjusting the friction on both plates it is possible to drastically improve the amount of liquid transferred to one surface while maintaining the fidelity of the liquid pattern. © Copyright 2012 Cambridge University Press.
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    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 10
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    Delaying the onset of dynamic wetting failure through meniscus confinement (2012)
    Cambridge University Press
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    Publication Date: 2012-07-30
    Description: Dynamic wetting is crucial to processes where liquid displaces another fluid along a solid surface, such as the deposition of a coating liquid onto a moving substrate. Numerous studies report the failure of dynamic wetting past some critical process speed. However, the hydrodynamic factors that influence the transition to wetting failure remain poorly understood from an empirical and theoretical perspective. The objective of this investigation is to determine the effect of meniscus confinement on the onset of dynamic wetting failure. A novel experimental system is designed to simultaneously view confined and unconfined wetting systems as they approach wetting failure. The experimental apparatus consists of a scraped steel roll that rotates into a bath of glycerol. Confinement is imposed via a gap formed between a coating die and the roll surface. Flow visualization is used to record the critical roll speed at which wetting failure occurs. Comparison of the confined and unconfined data shows a clear increase in the relative critical speed as the meniscus becomes more confined. A hydrodynamic model for wetting failure is developed and analysed with (i) lubrication theory and (ii) a two-dimensional finite-element method (FEM). Both approaches do a remarkable job of matching the observed confinement trend, but only the two-dimensional model yields accurate estimates of the absolute values of the critical speeds due to the highly two-dimensional nature of the stress field in the displacing liquid. The overall success of the hydrodynamic model suggests a wetting failure mechanism primarily related to viscous bending of the meniscus. © Copyright 2012 Cambridge University Press.
    Print ISSN: 0022-1120
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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