Uniaxial extensional flows in liquid bridges (original) (raw)
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Journal of Non-Newtonian Fluid Mechanics, 1992
Large liquid bridges of constant volume (initial length L,, = 50 mm and radius R, = 2.5 mm) placed between two equal plane circular disks have been stretched in Plateau simulations (neutral buoyancy tank) by moving one disk with a constant velocity. While interfacial tension forces minimize the surface area, leading to contraction and break-up of the liquid bridge, inertia and friction forces act against it. Increasing inertia, friction and flow resistance, due to elongational viscosity, tend to stabilize the liquid bridge and thus form more cylindrical bridges. It has been found that none of the forces, especially inertia and interfacial tension forces, can be neglected even at elongation rates as low as 0.1 s-l.
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Journal of Non-Newtonian Fluid Mechanics, 1998
Large extensional deformations of viscoelastic fluid columns in filament stretching rheometers are studied through numerical simulations up to Hencky strains of greater than m = 4. The time-dependent axisymmetric calculations incorporate the effects of viscoelasticity, surface tension, fluid inertia, plus a deformable free surface and provide quantitative descriptions of the evolution in the filament profile, the kinematics in the liquid column and the resulting dynamic evolution in the viscous and elastic contributions to the total stress. In addition to investigating the variation in the apparent Trouton ratio expected in experimental measurements using this new type of extensional rheometer, we also investigate the generic differences between the response of Newtonian and viscoelastic fluid filaments described by the Oldroyd-B model. For small strains, the fluid deformation is governed by the Newtonian solvent contribution to the stress and the filament evolution is very similar in both the Newtonian and viscoelastic cases. However, in the latter case at large strains and moderate Deborah numbers, elastic stresses dominate leading to strain-hardening in the axial mid-regions of the column and subsequent drainage of the quasi-static liquid reservoir that forms near both end-plates. These observations are in good qualitative agreement with experimental observations. For small initial aspect ratios and low strains, the non-homogeneous deformation predicted by numerical simulations is well described by a lubrication theory solution. At larger strains, the initial flow non-homogeneity leads to the growth of viscoelastic stress boundary layers near the free surface which can significantly affect the transient Trouton ratio measured in the device. Exploratory design calculations suggest that mechanical methods for modifying the boundary conditions at the rigid end-plates can reduce this non-homogeneity and lead to almost ideal uniaxial elongational flow kinematics.
Chemical Engineering Science, 2001
Deformation and breakup of bridges of Newtonian and non-Newtonian #uids held captive between two disks that are separated from one another at a constant speed are studied computationally. When the liquid bridge is at the incipience of breakup, a thin liquid thread connects two large volumes of #uid that are pendant from and sessile on the top and bottom disks. High viscosity and elasticity are known from experiments to lead to formation of long threads: these are precursors of satellite droplets which are usually unwanted in applications such as ink-jet printing. To investigate the role of shear-thinning in suppressing long threads and to separate the e!ect of elasticity from shear-thinning, the rheology of non-Newtonian #uids is described here by a Carreau model which simply accounts for shear-thinning behavior. When the dynamics is axially symmetric with respect to the common axis of the bridge and the disks, the physics is described by a spatially two-dimensional (2-D) theory. In addition to this fully 2-D theory, a one-dimensional (1-D) theory based on the slender-jet approximation is also developed here. Both the 2-D and 1-D problems are solved by a method of lines employing the "nite element method for spatial discretization and an adaptive "nite di!erence technique for time integration. The computational results show that the limiting bridge length¸B at breakup increases with increasing stretching speed ; for both Newtonian and shear-thinning #uids. However, in the case of high-viscosity bridges, as compared to a Newtonian #uid with viscosity equal to the zero shear-rate viscosity of a shear-thinning #uid, the rate at which¸B of a shear-thinning #uid varies with ; becomes less pronounced as ; increases. Furthermore, in the case of low-viscosity bridges, the axial location along the thread at which the bridge breaks switches from the vicinity of the bottom of the bridge to its top and then back to its bottom again as ; is increased. This switch in the breakup location has important implications in determining the fate of satellite droplets if any are formed. It is also shown that both the shape of the bridge and that of the liquid thread are profoundly a!ected by shear-thinning behavior. 1-D models have of course been previously used but often without direct comparison to experimental measurements or predictions made with exact 2-D models. It is shown here for the "rst time that 1-D models are remarkably accurate at low stretching speeds but fail at high stretching speeds. Furthermore, it is demonstrated that as the bridges thin, the dynamics in the vicinity of the location where the bridge radius is smallest follow scaling laws recently developed by others who have analyzed the local behavior of the governing equations close to pinch-o!.
Stability limits and dynamics of nonaxisymmetric liquid bridges
1993
This program of theoretical and experimental ground-based and low gravity research is focussed on the understanding of the dynamics and stability limits of nonaxisymmetric liquid bridges. There are three basic objectives to the proposed work: (1) to determine the stability limits of nonaxisymmetric liquid bridges held between non-coaxially aligned disks; (2) to examine the dynamics of nonaxisymmetric bridges and nonaxisymmetric
Dynamics and statics of nonaxisymmetric and symmetric liquid bridges
1994
This program of theoretical and experimental ground-based research focuses on the understanding of the dynamics and stability limits of nonaxisymmetric and symmetric liquid bridges. There are three basic objectives: First, to determine the stability limits of nonaxisymmetric liquid bridges held between non-coaxial parallel disks, Second, to examine the dynamics of nonaxisymmetric bridges and nonaxisymmetric oscillations of initially axisymmetric bridges. The
Colloids and Interfaces
The interest to monophasic liquid capillary bridges (CB) has a long history. These shapes are attractive not only because of their interesting surface properties but also because of the possibility of their behavior to be analytically predicted by the equations of differential geometry. In the current paper we extend our previous studies by implementation of an approach for prediction of liquid gravityless CB behavior during their quasi-static stretching. It was found, that a simple linear relation, h r m ~ ln R r m , is valid the case of good wetting, 0° ≤ θ ≤ 90°, where h is the height of CB, R is the radius at the contact surface, rm is the CB waist radius, and θ is the solid/liquid (static, receding) contact angle. We experimentally studied the geometrical properties evolution of monophasic cedar oil and water CBs between two glass plates during their quasi-static (stepwise with equilibration after each step for 1–2 min.) stretching. In addition, we investigated a binary CB of a...