9,383 research outputs found
Viscous Taylor droplets in axisymmetric and planar tubes: from Bretherton's theory to empirical models
The aim of this study is to derive accurate models for quantities
characterizing the dynamics of droplets of non-vanishing viscosity in
capillaries. In particular, we propose models for the uniform-film thickness
separating the droplet from the tube walls, for the droplet front and rear
curvatures and pressure jumps, and for the droplet velocity in a range of
capillary numbers, , from to and inner-to-outer viscosity
ratios, , from , i.e. a bubble, to high viscosity droplets.
Theoretical asymptotic results obtained in the limit of small capillary number
are combined with accurate numerical simulations at larger . With these
models at hand, we can compute the pressure drop induced by the droplet. The
film thickness at low capillary numbers () agrees well with
Bretherton's scaling for bubbles as long as . For larger viscosity
ratios, the film thickness increases monotonically, before saturating for
to a value times larger than the film thickness of a
bubble. At larger capillary numbers, the film thickness follows the rational
function proposed by Aussillous \& Qu\'er\'e (2000) for bubbles, with a fitting
coefficient which is viscosity-ratio dependent. This coefficient modifies the
value to which the film thickness saturates at large capillary numbers. The
velocity of the droplet is found to be strongly dependent on the capillary
number and viscosity ratio. We also show that the normal viscous stresses at
the front and rear caps of the droplets cannot be neglected when calculating
the pressure drop for
Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid
In this paper we examine some general features of the time-dependent dynamics of drop deformation and breakup at low Reynolds numbers. The first aspect of our study is a detailed numerical investigation of the ‘end-pinching’ behaviour reported in a previous experimental study. The numerics illustrate the effects of viscosity ratio and initial drop shape on the relaxation and/or breakup of highly elongated droplets in an otherwise quiescent fluid. In addition, the numerical procedure is used to study the simultaneous development of capillary-wave instabilities at the fluid-fluid interface of a very long, cylindrically shaped droplet with bulbous ends. Initially small disturbances evolve to finite amplitude and produce very regular drop breakup. The formation of satellite droplets, a nonlinear phenomenon, is also observed
Solid rocket booster internal flow analysis by highly accurate adaptive computational methods
The primary objective of this project was to develop an adaptive finite element flow solver for simulating internal flows in the solid rocket booster. Described here is a unique flow simulator code for analyzing highly complex flow phenomena in the solid rocket booster. New methodologies and features incorporated into this analysis tool are described
Geometric integration on spheres and some interesting applications
Geometric integration theory can be employed when numerically solving ODEs or
PDEs with constraints. In this paper, we present several one-step algorithms of
various orders for ODEs on a collection of spheres. To demonstrate the
versatility of these algorithms, we present representative calculations for
reduced free rigid body motion (a conservative ODE) and a discretization of
micromagnetics (a dissipative PDE). We emphasize the role of isotropy in
geometric integration and link numerical integration schemes to modern
differential geometry through the use of partial connection forms; this
theoretical framework generalizes moving frames and connections on principal
bundles to manifolds with nonfree actions.Comment: This paper appeared in prin
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