Engineering topics

Hong, D. C.

Publications and source records attributed to Hong, D. C..

4 records

NASA NTRS1988

Wire perturbations in the Staffman-Taylor problem

Zocchi et al. (1987) discovered that when two wires are symmetrically placed along the center of a Hele-Shaw cell, symmetric but narrow fingers of dimensionless width lambda less than 0.5 develop. The value of lambda decreases as the pushing velocity increases, but at a certain critical finger width the finger suddenly undergoes a transition to the asymmetrical state. A simple theory to predict this critical finger width as a function of D, the dimensionless distance between two wires is developed by assuming that the finger opens up a negative angle at the contact point.

Hong, D. C.↗

NASA NTRS1987

Pattern selection and tip perturbations in the Saffman-Taylor problem

An analytic approach to the Saffman-Taylor problem of predicting the width of a viscous finger in a Hele-Shaw cell is presented. The first purpose is to provide a systematic description of the way in which the singular perturbation introduced by capillary forces leads to a solvability mechanism for pattern selection. It is then shown how recent experimental observations by Couder et al. (1986) may be interpreted in terms suggested by this mechanism.

Hong, D. C.↗

NASA NTRS1986

Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy

This paper is concerned primarily with the development of an analytic approach to the theory of steady-state velocity selection in the boundary-layer model of dendritic solidification. The two-dimensional version of this model with a fourfold crystalline anisotropy alpha in the surface tension is considered. By extending a WKB method introduced in an earlier paper, the alpha dependence of the selected growth rate is determined in the limit of small alpha; and this rate is studied for large alphas in the limit in which the dimensionless undercooling approaches unity. Portions of the paper are devoted to a reinterpretation of the mathematical structure of the solvability condition in problems of this kind.

Langer, J. S.↗

NASA NTRS1986

Analytic theory of the selection mechanism in the Saffman-Taylor problem

An analytic approach to the problem of predicting the widths of fingers in a Hele-Shaw cell is presented. The analysis is based on the WKB technique developed recently for dealing with the effects of surface tension in the problem of dendritic solidification. It is found that the relation between the dimensionless width lambda and the dimensionless group of parameters containing the surface tension, nu, has the form lambda - 1/2 = nu exp 2/3 in the limit of small nu.

Hong, D. C.↗