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147
An accurate adaptive solver for surfacetensiondriven interfacial flows
 Journal of Computational Physics
, 2009
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VolumeofFluid Interface Tracking with Smoothed Surface Stress Methods for ThreeDimensional Flows
, 1997
"... This article is devoted to the description and assessment of a numerical procedure for the simulation of flows with interfaces between viscous Newtonian fluids. The interfaces are modeled as discontinuities with constant surface tension. This physical model is relevant for many applications. Of part ..."
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Cited by 45 (0 self)
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This article is devoted to the description and assessment of a numerical procedure for the simulation of flows with interfaces between viscous Newtonian fluids. The interfaces are modeled as discontinuities with constant surface tension. This physical model is relevant for many applications. Of particular interest to us are phenomena such as droplet formation and breakup where interface topology may change through the reconnection of the interface. The method may also be useful to study complex multiphase flows, when for instance the fluid particles undergo threedimensional perturbations.
Coalescence of liquid drops
 J. Fluid Mech
, 1999
"... When two drops of radius R touch, surface tension drives an initially singular motion which joins them into a bigger drop with smaller surface area. This motion is always viscously dominated at early times. We focus on the earlytime behavior of the radius rm of the small bridge between the two drop ..."
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Cited by 35 (1 self)
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When two drops of radius R touch, surface tension drives an initially singular motion which joins them into a bigger drop with smaller surface area. This motion is always viscously dominated at early times. We focus on the earlytime behavior of the radius rm of the small bridge between the two drops. The flow is driven by a highly curved meniscus of length 2πrm and width ∆ ≪ rm around the bridge, from which we conclude that the leadingorder problem is asymptotically equivalent to its twodimensional counterpart. An exact twodimensional solution for the case of inviscid surroundings [Hopper, J. Fluid Mech. 213, 349 (1990)] shows that ∆ ∝ r 3 m and rm ∼ (tγ/πη)ln[tγ/(ηR)]; and thus the same is true in three dimensions. The case of coalescence with an external viscous fluid is also studied in detail both analytically and numerically. A significantly different structure is found in which the outer fluid forms a toroidal bubble of radius ∆ ∝ r 3/2 m at the meniscus and rm ∼ (tγ/4πη)ln[tγ/(ηR)]. This basic difference is due to the presence of the outer fluid viscosity, however small. With lengths scaled by R a full description of the asymptotic flow for rm(t) ≪ 1 involves matching 1 of lengthscales of order r 2 m,r 3/2 m, rm, 1 and probably r 7/4 m.
Elastocapillary thinning and breakup of model elastic liquids
 J. Rheol
, 2001
"... We study the elastocapillary selfthinning and ultimate breakup of three polystyrenebased ideal elastic fluids by measuring the evolution in the filament diameter as slender viscoelastic threads neck and eventually break. We examine the dependence of the transient diameter profile and the time to ..."
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Cited by 33 (4 self)
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We study the elastocapillary selfthinning and ultimate breakup of three polystyrenebased ideal elastic fluids by measuring the evolution in the filament diameter as slender viscoelastic threads neck and eventually break. We examine the dependence of the transient diameter profile and the time to breakup on the molecular weight, and compare the observations with simple theories for breakup of slender viscoelastic filaments. The evolution of the transient diameter profile predicted by a multimode FENEP model quantitatively matches the data provided the initial stresses in the filament are taken into account. Finally, we show how the transient uniaxial extensional viscosity of a dilute polymer solution can be estimated from the evolution in the diameter of the necking filament. The resulting ‘‘apparent extensional viscosity’ ’ profiles are compared with similar results obtained from a filament stretching rheometer. Both transient profiles approach the same value for the steady state extensional viscosity, which increases with molecular weight in agreement with the Rouse–Zimm theory. The apparent discrepancy in the growth rate of the two transient curves can be quantitatively explained by examining the effective stretch rate in each configuration. Filament thinning studies and filament stretching experiments thus form complementary experiments that lead to consistent measures of the transient extensional viscosity of a given test fluid. © 2001 The Society of Rheology.
Wetting and spreading
, 2009
"... Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact wi ..."
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Cited by 26 (0 self)
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Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the threephase contact line separating “wet ” regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of
How to extract the Newtonian viscosity from capillary breakup measurements in a filament rheometer
 J. RHEOL
, 2000
"... The liquid filament microrheometer originally described by Bazilevsky et al. (1990) provides a simple way of extracting material parameters for Newtonian and viscoelastic fluids from measurements of the capillary breakup of a thin fluid thread. However, there is an unresolved discrepancy in the valu ..."
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Cited by 25 (3 self)
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The liquid filament microrheometer originally described by Bazilevsky et al. (1990) provides a simple way of extracting material parameters for Newtonian and viscoelastic fluids from measurements of the capillary breakup of a thin fluid thread. However, there is an unresolved discrepancy in the value of the Newtonian viscosity obtained from the experimental data when using the existing theoretical analysis. We demonstrate how to correctly analyze measurements of the midpoint radius and present a simple formula that enables one to obtain quantitative values for the Newtonian viscosity for a range of viscous fluids. The validity of this correction is supported by numerical simulations and experiments with a number of viscous Newtonian fluids. In addition we analyze the role of gravitational body forces on modifying the dynamics of capillary thinning of a Newtonian liquid filament. Finally, we show how such capillary breakup devices may be used to make quantitative timeresolved measurements of changes in the viscosity of hygroscopic materials or fluids with a volatile solvent component that are exposed to an ambient atmosphere.
Inviscid coalescence of drops
 Subb. to J. Fluid Mech
, 2002
"... We study the coalescence of two drops of an ideal fluid driven by surface tension. The velocity of approach is taken to be zero and the dynamical effect of the outer fluid (usually air) is neglected. Our approximation is expected to be valid on scales larger than ℓν = ρν 2 /σ, which is 10nm for wate ..."
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Cited by 18 (1 self)
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We study the coalescence of two drops of an ideal fluid driven by surface tension. The velocity of approach is taken to be zero and the dynamical effect of the outer fluid (usually air) is neglected. Our approximation is expected to be valid on scales larger than ℓν = ρν 2 /σ, which is 10nm for water. Using a highprecision boundary integral method, we show that the walls of the thin retracting sheet of air between the drops reconnect in finite time to form a toroidal enclosure. After the initial reconnection, retraction starts again, leading to a rapid sequence of enclosures. Averaging over the discrete events, we find the minimum radius of the liquid bridge connecting the two drops to scale like rb ∝ t 1/2.
Using filament stretching rheometry to predict strand formation and “processability” in adhesives and other nonNewtonian fluids
 Rheologica Acta
, 2000
"... The spinning of polymeric fibers, the processing of numerous foodstuffs and the peel & tack characteristics of adhesives is associated with the formation, stability and, ultimately, the longevity of thin fluid ‘strands’. This tendency to form strands is usually described in terms of the tackines ..."
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Cited by 18 (3 self)
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The spinning of polymeric fibers, the processing of numerous foodstuffs and the peel & tack characteristics of adhesives is associated with the formation, stability and, ultimately, the longevity of thin fluid ‘strands’. This tendency to form strands is usually described in terms of the tackiness of the fluid or by heuristic concepts such as ‘stringiness ’ [Lakrout et al., J. Adhesion 69, 307 (1999)]. The dynamics of such processes are complicated due to spatially and temporally nonhomogeneous growth of extensional stresses, the action of capillary forces and the evaporation of volatile solvents. We describe the development and application of a simple instrument referred to as a microfilament rheometer (MFR) that can be used to readily differentiate between the dynamical response of different pressuresensitive adhesive fluid formulations. The device relies on a quantitative observation of the rate of extensional thinning or ‘necking’ of a thin viscous or viscoelastic fluid filament in which the solvent is free to evaporate across the free surface. This highresolution measurement of the radial profile provides a direct indication of the ultimate time to breakup of the fluid filament. This critical time
Capillary Breakup Rheometry of LowViscosity Elastic Fluids
 SUBMITTED TO APPLIED RHEOLOGY
, 2004
"... We investigate the dynamics of the capillary thinning and breakup process for low viscosity elastic fluids such as dilute polymer solutions. Standard measurements of the evolution of the midpoint diameter of the necking fluid filament are augmented by high speed digital video images of the break up ..."
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Cited by 17 (6 self)
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We investigate the dynamics of the capillary thinning and breakup process for low viscosity elastic fluids such as dilute polymer solutions. Standard measurements of the evolution of the midpoint diameter of the necking fluid filament are augmented by high speed digital video images of the break up dynamics. We show that the successful operation of a capillary thinning device is governed by three important time scales (which characterize the relative importance of inertial, viscous and elastic processes), and also by two important length scales (which specify the initial sample size and the total stretch imposed on the sample). By optimizing the ranges of these geometric parameters, we are able to measure characteristic time scales for tensile stress growth as small as 1 millisecond for a number of model dilute and semidilute solutions of polyethylene oxide (PEO) in water and glycerin. If the aspect ratio of the sample is too small, or the total axial stretch is too great, measurements are limited, respectively, by inertial oscillations of the liquid bridge or by the development of the wellknown beadsonastring morphology which disrupt the formation of a uniform necking filament. By considering the magnitudes of the natural time scales associated with viscous flow, elastic stress growth and inertial oscillations it is possible to construct an “operability diagram ” characterizing successful operation of a capillary breakup extensional rheometer. For Newtonian fluids, viscosities greater than approximately 70 mPa.s are required; however for dilute solutions of high molecular weight polymer the minimum viscosity is substantially lower due to the additional elastic stresses arising from molecular extension. For PEO of molecular weight 106 g/mol, it is possible to measure relaxation times of order 1 ms in dilute polymer solutions of viscosity 2 – 10 mPa.s.