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  • 1
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    Continuation in a parameter - Experience with viscous and free surface flows (1983)
    In:  Other Sources
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    Publication Date: 2011-08-18
    Description: The results of modifications in continuation methods applied to obtain solutions to the Navier-Stokes systems of equations for incompressible, two-dimensional, steady flows are reported. It is shown that parameter continuation permits prediction of accurate, initial estimates for iterative processing of nonlinear finite difference and finite element equations of motions. The new parameter steps are derived from values of the preceding parameter steps. The accuracy of the estimates is ensured with appropriate choices of the step size. The continuation predictor/iterative corrector is demonstrated to trace the branches of parameter space along which steady flow states are found, and techniques are available for tracing multiply branching paths. The techniques are applied to solving the Navier-Stokes equations for flow through a rotating square channel, the formation of a falling liquid curtain, and gyrostatic equilibria of rotating cylindrical drops.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 2
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    New class of asymmetric shapes of rotating liquid drops (1980)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: Shapes and stability of surface-tension-endowed drops rotating rigidly at fixed angular momentum are calculated by finite-element analysis. A new family of asymmetric two-lobed drop shapes is discovered that branches from, and rejoins, the Pik-Pichak family of symmetric two-lobed shapes. The computations are verified for axisymmetric and symmetric two-lobed drop shape by comparison with previous approximations.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physical Review Letters; 45; July 21
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  • 3
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    The shape and stability of rotating liquid drops (1980)
    In:  Other Sources
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    Publication Date: 2011-08-17
    Description: Equilibrium shapes and stability of rotating drops held together by surface tension are found by computer-aided analysis that uses expansions in finite-element basis functions. Shapes are calculated as extrema of appropriate energies. Stability and relative stability are determined from curvatures of the energy surface in the neighborhood of the extremum. Families of axisymmetric, two-, three-, and four-lobed drop shapes are traced systematically. Bifurcation and turning points are located and the principle of exchange of stabilities is tested. The axisymmetric shapes are stable at low rotation rates but lose stability at the bifurcation to two-lobed shapes. Two-lobed drops isolated with constant angular momentum are stable. The results bear on experiments designed to further those of Plateau (1863).
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
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  • 4
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    Axisymmetric shapes and stability of charged drops in an external electric field (1989)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: A highly conducting charged drop that is surrounded by a fluid insulator of another density can be levitated by suitably applying a uniform electric field. Axisymmetric equilibrium shapes and stability of the levitated drop are found by solving simultaneously the augmented Young-Laplace equation for surface shape and the Laplace equation for the elecric field, together with constraints of fixed drop volume, charge, and center of mass. The means are a method of subdomains, finite element basis functions, and Galerkin's method of weighted residuals, all facilitated by a large-scale computer. Shape families of fixed charge are treated systematically by first-order continuation. Previous analyses by Abbas et al. in 1967 and Abbas and Latham in 1969, in which the shapes of levitated drops are approximated as spheroids, are corrected. The new analysis shows that drops charged to less than the Rayleigh limit lose shape stability at turning points, with respect to external field strength, and that the instability seen in experiments of Doyle et al. in 1964 and others is not a bifurcation to a family of two-lobed shapes, but rather is a related imperfect bifurcation.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids A (ISSN 0899-8213); 1; 799-809
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  • 5
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    Axisymmetric shapes and stability of isolated charged drops (1989)
    In:  Other Sources
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    Publication Date: 2011-08-19
    Description: Axisymmetric equilibrium shapes and stability of isolated charged drops are found by solving simultaneously the Young-Laplace equation for surface shape and the Laplace equation for the electric field. Families of two-, three-, and four-lobed shapes that branch from the trunk family of spheres are treated systematically by means of the Galerkin/finite element method and a tessellation that deforms with the free surface. The results show that at the limit found by Rayleigh in 1882 the spherical family exchanges stability with a family of two-lobed shapes, a transcritically bifurcating family, one arm of which proves to consist of stable shapes. The results are reinforced by those of approximating the stable drop shapes as oblate spheroids. Thus oblate drops carrying charge in excess of the Rayleigh limit ought to be seen in experiments, though none have yet been reported.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Physics of Fluids A (ISSN 0899-8213); 1; 795-798
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  • 6
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    Profiles of electrified drops and bubbles (1982)
    In:  CASI
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    Publication Date: 2016-06-07
    Description: Axisymmetric equilibrium shapes of conducting drops and bubbles, (1) pendant or sessile on one face of a circular parallel-plate capacitor or (2) free and surface-charged, are found by solving simultaneously the free boundary problem consisting of the augmented Young-Laplace equation for surface shape and the Laplace equation for electrostatic field, given the surface potential. The problem is nonlinear and the method is a finite element algorithm employing Newton iteration, a modified frontal solver, and triangular as well as quadrilateral tessellations of the domain exterior to the drop in order to facilitate refined analysis of sharply curved drop tips seen in experiments. The stability limit predicted by this computer-aided theoretical analysis agrees well with experiments.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: JPL Proc. of the 2d Intern. Colloq. on Drops and Bubbles; p 322-329
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  • 7
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    Capillary forces exerted by liquid drops caught between crossed cylinders. A 3-D meniscus problem with free contact line (1982)
    In:  CASI
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    Publication Date: 2016-06-07
    Description: The Young-Laplace equation is solved for three-dimensional menisci between crossed cylinders, with either the contact line fixed or the contact angle prescribed, by means of the Galerkin/finite element method. Shapes are computed, and with them the practically important quantities: drop volume, wetted area, capillary pressure force, surface tension force, and the total force exerted by the drop on each cylinder. The results show that total capillary force between cylinders increases with decreasing contact angle, i.e. with better wetting. Capillary force is also increases with decreasing drop volume, approaching an asymptotic limit. However, the wetted area on each cylinder decreases with decreasing drop volume, which raises the question of the optimum drop volume to strive for, when permanent bonding is sought from solidified liquid. For then the strength of the bond is likely to depend upon the area of contact, which is the wetted area when the bonding agent was introduced in liquid form.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: JPL Proc. of the 2d Intern. Colloq. on Drops and Bubbles; p 308-314
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  • 8
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    Nonlinear oscillations of inviscid free drops (1991)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: The present analysis of free liquid drops' inviscid oscillations proceeds through solution of Bernoulli's equation to obtain the free surface shape and of Laplace's equation for the velocity potential field. Results thus obtained encompass drop-shape sequences, pressure distributions, particle paths, and the temporal evolution of kinetic and surface energies; accuracy is verified by the near-constant drop volume and total energy, as well as the diminutiveness of mass and momentum fluxes across drop surfaces. Further insight into the nature of oscillations is provided by Fourier power spectrum analyses of mode interactions and frequency shifts.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Journal of Computational Physics (ISSN 0021-9991); 97; 489-515
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  • 9
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    Equilibria, stability and bifurcations of rotating columns of fluid subjected to planar disturbances (1991)
    In:  Other Sources
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    Publication Date: 2019-07-12
    Description: Long gyrostatically rotating drops bonded by surface tension are amenable to conventional bifurcation analysis and newer, computer-aided analytical methods, and therefore are useful prototypes of three-dimensional drops. A study is conducted by setting aside instability to Rayleigh's axisymmetric mode and investigating the effects of translationally symmetric (planar) disturbances. The disadvantage of employing single-coordinate representation of drop shapes close to break-up is brought out. It is shown that a family of symmetric two-lobed shapes bifurcates from the main family of perfectly cylindrical shapes when the rotation rate reaches a critical value, in accord with the linearized hydrodynamic analysis of Hocking.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: Proceedings, Series A - Mathematical and Physical Sciences (ISSN 0080-4630); 433; 1887; 81-99
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  • 10
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    Computer-aided analysis of nonlinear problems in transport phenomena (1980)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: The paper describes algorithms for equilibrium and steady-state problems with coefficients in the expansions derived by the Galerkin weighted residual method and calculated from the resulting sets of nonlinear algebraic equations by the Newton-Raphson method. Initial approximations are obtained from nearby solutions by continuation techniques as parameters are varied. The Newton-Raphson technique is preferred because the Jacobian of the solution is useful for continuation, for analyzing the stability of solutions, for detecting bifurcation of solution families, and for computing asymptotic estimates of the effects on any solution of small changes in parameters, boundary conditions, and boundary shape.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: New approaches to nonlinear problems in dynamics; Dec 09, 1979 - Dec 14, 1979; Pacific Grove, CA
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