The Bursting of Pointed Drops in Slow Viscous Flow

1973 ◽  
Vol 40 (1) ◽  
pp. 18-24 ◽  
Author(s):  
J. Buckmaster
Keyword(s):  
Surface Tension ◽  
Viscous Fluid ◽  
Viscous Flow ◽  
Small Drop ◽  
Shape Preserving ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Viscous Drops ◽  
Steady Solutions ◽  
Body Theory

Viscous drops, confined by the slow axisymmetric straining motion of a viscous fluid, are considered when the surface tension is weak. The shape of the drops is determined using slender-body theory, and it is found that steady solutions only exist for sufficiently small drop viscosities. Nonuniqueness exists, with bifurcation from a simple quadratic solution. At high drop viscosities, when there are no steady solutions, a description of the unsteady elongation of shape-preserving drops is obtained. This is the bursting phenomenon described experimentally by Taylor [1].

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

Rods falling near a vertical wall

1977 ◽  
Vol 83 (2) ◽  
pp. 273-287 ◽  
Author(s):  
W. B. Russel ◽  
E. J. Hinch ◽  
L. G. Leal ◽  
G. Tieffenbruck
Keyword(s):  
Integral Equation ◽  
Viscous Fluid ◽  
Numerical Solution ◽  
Vertical Wall ◽  
Numerical Results ◽  
Slender Body ◽  
Asymptotic Results ◽  
Slender Body Theory ◽  
Friction Coefficients ◽  
Body Theory

As an inclined rod sediments in an unbounded viscous fluid it will drift horizontally but will not rotate. When it approaches a vertical wall, the rod rotates and so turns away from the wall. Illustrative experiments and a slender-body theory of this phenomenon are presented. In an incidental study the friction coefficients for an isolated rod are found by numerical solution of the slender-body integral equation. These friction coefficients are compared with the asymptotic results of Batchelor (1970) and the numerical results of Youngren ' Acrivos (1975), who did not make a slender-body approximation.

Slender-body theory for steady sheared plumes in very viscous fluid

2008 ◽  
Vol 612 ◽  
pp. 21-44 ◽  
Author(s):  
ROBERT J. WHITTAKER ◽  
JOHN R. LISTER
Keyword(s):  
Simple Model ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Experimental Studies ◽  
Slender Body ◽  
Slender Body Theory ◽  
Dimensionless Parameters ◽  
Dynamical Regimes ◽  
Body Theory ◽  
Good Agreement

A simple model based on slender-body theory is developed to describe the deflection of a steady plume by shear flow in very viscous fluid of the same viscosity. The key dimensionless parameters measuring the relative strengths of the shear, diffusion and source flux are identified, which allows a number of different dynamical regimes to be distinguished. The predictions of the model show good agreement with many, but not all, observations from previous experimental studies. Possible reasons for the discrepancies are discussed.

Separated Flow About a Slender Body in Forward and Lateral Motion

2008 ◽  
Author(s):  
Ronald W. Yeung ◽  
Robert K. M. Seah ◽  
John T. Imamura
Keyword(s):  
Viscous Flow ◽  
Cross Flow ◽  
Separated Flow ◽  
Vortex Method ◽  
Slender Body ◽  
Order Effects ◽  
Forward Motion ◽  
Slender Body Theory ◽  
Flow Equations ◽  
Body Theory

This paper presents a solution method for obtaining the hydrodynamic forces and moments on a submerged body translating at a yaw angle. The method is based on the infinite-fluid formulation of the Free Surface Random Vortex Method (FSRVM), which is re-formulated to include the use of slender-body theory. The resulting methodology is given the name: Slender-Body FSRVM (SB-FSRVM). It utilizes the viscous-flow capabilities of FSRVM with a slender-body theory assumption. The three-dimensional viscous-flow equations are first shown to be reducible to a sequence of two-dimensional viscous-fluid problems in the cross-flow planes with the lowest-order effects from the forward velocity included. The theory enables one to analyze effectively the lateral forces and yaw moments on a body undergoing prescribed forward motion with the possible occurrence of flow separation. Applications are made to several cases of body geometry that are in steady forward motion, but at a yawed orientation. These include the case of a long “cone-tail” body. Comparisons are made with existing data where possible.

Asymptotic model for the dynamics of curved viscous fibres with surface tension

2009 ◽  
Vol 622 ◽  
pp. 345-369 ◽  
Author(s):  
NICOLE MARHEINEKE ◽  
RAIMUND WEGENER
Keyword(s):  
Surface Tension ◽  
Boundary Conditions ◽  
Capillary Number ◽  
Temporal Evolution ◽  
Slender Body ◽  
Explicit Description ◽  
Asymptotic Model ◽  
Slender Body Theory ◽  
Viscous Transport ◽  
Body Theory

In this paper, we derive and investigate an asymptotic model for the dynamics of curved viscous inertial Newtonian fibres subjected to surface tension, as they occur in rotational spinning processes. Accordingly, we extend the slender body theory of Panda, Marheineke & Wegener (Math. Meth. Appl. Sci., vol. 31, 2008, p. 1153) by including surface tension and deducing boundary conditions for the free end of the fibre. The asymptotic model accounts for the inner viscous transport and places no restrictions on either the motion or the shape of the fibre centreline. Depending on the capillary number, the boundary conditions yield an explicit description for the temporal evolution of the fibre end. We study numerically the behaviour of the fibre as a function of the effects of viscosity, gravity, rotation and surface tension.

On asymmetrical slow viscous flows caused by the motion of two equal spheres almost in contact

1969 ◽  
Vol 65 (2) ◽  
pp. 543-556 ◽  
Author(s):  
M. E. O'Neill
Keyword(s):  
Exact Solution ◽  
Viscous Fluid ◽  
Viscous Flow ◽  
Asymptotic Theory ◽  
Viscous Flows ◽  
Slow Viscous Flow ◽  
Angular Velocities ◽  
Well Posed

An exact solution is given for the slow viscous flow caused by the translation of two equal spheres in contact with equal velocities perpendicular to their line of centres. An asymptotic theory is presented for solving the problem when two equal spheres of radius a almost in contact rotate with equal and opposite angular velocities. The problem when the spheres touch is shown not to be well posed; the forces acting on the spheres are shown to be O(1) and the couples of the form α log∈ + β where α and β are independent of the minimum clearance 2∈α between the spheres and have been determined explicitly. The relevance of the results to the free settling of two spheres in a viscous fluid under the influence of gravity is discussed.

Lateral Force and Yaw Moment on a Slender Body in Forward Motion at a Yaw Angle

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Ronald W. Yeung ◽  
Robert K. M. Seah ◽  
John T. Imamura
Keyword(s):  
Viscous Flow ◽  
Cross Flow ◽  
Slender Body ◽  
Order Effects ◽  
Forward Motion ◽  
Slender Body Theory ◽  
Flow Equations ◽  
The Cross ◽  
Yaw Angle ◽  
Body Theory

This paper presents a solution method for obtaining the lateral hydrodynamic forces and moments on a submerged body translating at a yaw angle. The method is based on the infinite-fluid formulation of the free-surface random-vortex method (FSRVM), which is reformulated to include the use of slender-body theory. The resulting methodology is given the name: slender-body FSRVM (SB-FSRVM). It utilizes the viscous-flow capabilities of FSRVM with a slender-body theory assumption. The three-dimensional viscous-flow equations are first shown to be reducible to a sequence of two-dimensional viscous-fluid problems in the cross-flow planes with the lowest-order effects from the forward velocity included in the cross-flow plane. The theory enables one to effectively analyze the lateral forces and yaw moments on a body undergoing prescribed forward motion with the possible occurrence of cross-flow separation. Applications are made to several cases of body geometry that are in steady forward motion, but at a yawed orientation. These include the case of a long “cone-tail” body. Comparisons are made with existing data where possible.

Tip streaming from slender drops in a nonlinear extensional flow

1984 ◽  
Vol 144 ◽  
pp. 281-295 ◽  
Author(s):  
J. D. Sherwood
Keyword(s):  
Steady State ◽  
Extensional Flow ◽  
Axisymmetric Flow ◽  
Rayleigh Instability ◽  
Slender Body Theory ◽  
Viscous Drops ◽  
Roll Mill ◽  
Viscous Drop ◽  
Axis Of Symmetry ◽  
Body Theory

The deformation of inviscid and slightly viscous drops is studied using slender-body theory. The imposed axisymmetric flow is a combination of a linear extensional flow, with velocity uz = G1 z along the axis of symmetry, together with a cubic flow uz = G3z3. When G3/G1 is sufficiently small the viscous drop breaks in a manner similar to that described by Acrivos & Lo (1978). For larger G3 > 0 the drop breaks by a rapid growth at its end. Steady-state experiments in a 4-roll mill show the ejection of a column of liquid from the tip of the drop, though this is probably caused by a change in the pressure gradient rather than the mechanism described above. The ejected column then breaks into droplets via the Rayleigh instability. It is hypothesized that one or other of these mechanisms corresponds to tip streaming as observed by Taylor (1934).

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