On the shape of small sessile and pendant drops by singular perturbation techniques

1991 ◽  
Vol 233 ◽  
pp. 519-537 ◽  
Author(s):  
S. B. G. O'Brien
Keyword(s):  
Boundary Layer ◽  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Numerical Results ◽  
Matched Asymptotic Expansions ◽  
Perturbation Techniques ◽  
Pendant Drop ◽  
Asymptotic Expressions ◽  
Good Agreement ◽  
Pendant Drops

The problem of obtaining asymptotic expressions describing the shape of small sessile and pendant drops is revisited. Both cases display boundary-layer behaviour and the method of matched asymptotic expansions is used to obtain solutions. These give good agreement when compared with numerical results. The sessile solutions are relatively straightforward, while the pendant drop displays a behaviour which is both rich and interesting.

Asymptotic Methods for an Infinite Slider Bearing With a Discontinuity in Film Slope

1976 ◽  
Vol 98 (3) ◽  
pp. 446-452 ◽  
Author(s):  
J. A. Schmitt ◽  
R. C. DiPrima
Keyword(s):  
Boundary Layer ◽  
Film Thickness ◽  
Asymptotic Expansions ◽  
Asymptotic Expression ◽  
Asymptotic Methods ◽  
Matched Asymptotic Expansions ◽  
Slider Bearing ◽  
Trailing Edge ◽  
Slider Bearings ◽  
Special Cases

The method of matched asymptotic expansions is used to develop an asymptotic expression for the pressure for large bearing numbers for the case of an infinite slider bearing with a general film thickness that has a discontinuous slope at a point. It is shown that, in addition to the boundary layer of the pressure at the trailing edge, there is also a boundary layer in the derivative of the pressure at the point of discontinuity. The corresponding load formula is also derived. The special cases of the taper-flat and taper-taper slider bearings are discussed.

Nearly equilibrium dissociating boundary-layer flows by the method of matched asymptotic expansions

1966 ◽  
Vol 26 (4) ◽  
pp. 793-806 ◽  
Author(s):  
George R. Inger
Keyword(s):  
Boundary Layer ◽  
Asymptotic Expansions ◽  
High Speed ◽  
Numerical Solutions ◽  
The Body ◽  
Matched Asymptotic Expansions ◽  
Form Analysis ◽  
Perturbation Problem ◽  
Valid Solution ◽  
Non Equilibrium

The approach to equilibrium in a non-equilibrium-dissociating boundary-layer flow along a catalytic or non-catalytic surface is treated from the standpoint of a singular perturbation problem, using the method of matched asymptotic expansions. Based on a linearized reaction rate model for a diatomic gas which facilitates closed-form analysis, a uniformly valid solution for the near equilibrium behaviour is obtained as the composite of appropriate outer and inner solutions. It is shown that, under near equilibrium conditions, the primary non-equilibrium effects are buried in a thin sublayer near the body surface that is described by the inner solution. Applications of the theory are made to the calculation of heat transfer and atom concentrations for blunt body stagnation point and high-speed flat-plate flows; the results are in qualitative agreement with the near equilibrium behaviour predicted by numerical solutions.

Flow along a horizontal plate near a free surface

1993 ◽  
Vol 252 ◽  
pp. 399-418
Author(s):  
Milan Hofman
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Flat Plate ◽  
Viscous Liquid ◽  
Gravity Waves ◽  
Asymptotic Expansions ◽  
Small Amplitude ◽  
Surface Effect ◽  
Matched Asymptotic Expansions ◽  
Horizontal Plate

The problem of flow along a horizontal semi-infinite flat plate moving in its own plane through a viscous liquid just below the free surface is considered. The method of matched asymptotic expansions is used to analyse the interaction between the free surface and the boundary layer formed on the plate. It is found that, due to viscosity, small-amplitude gravity waves on the free surface can be formed. The formulae for the resistance of the plate containing the free-surface effect and for the lift, appearing as a new phenomenon, are derived.

scholarly journals SINGULAR PERTURBATIONS FOR THE FORCED VAN DER POL OSCILLATOR

1993 ◽  
Vol 24 (4) ◽  
pp. 417-430
Author(s):  
E. M. ELABBASY
Keyword(s):  
Singular Perturbation ◽  
Singular Perturbations ◽  
Numerical Results ◽  
Van Der Pol Oscillator ◽  
Perturbation Techniques ◽  
Van Der Pol ◽  
Forcing Term ◽  
Subharmonic Solutions ◽  
Analytical Results ◽  
Range Of Values

This paper deals with the Van der Pol oscillator with large si­ nusoidal forcing term. By using singular perturbation techniques a.symp­ totic solutions of such a system are constructed. We considered the case $b$ small and then we find the range of values of $b$ for which the Van der Pol oscillatore may have 3 stable subharmonic solutions for the same values of the parameters. We have integrated the equation numerically; then a comparison of the numerical results obtained with analytical results of this paper is given.

On the method of matched asymptotic expansions

1969 ◽  
Vol 65 (1) ◽  
pp. 209-231 ◽  
Author(s):  
L. E. Fraenkel
Keyword(s):  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Unknown Function ◽  
Singular Perturbation Problems ◽  
Matched Asymptotic Expansions ◽  
Uniform Approximations ◽  
Perturbation Problems ◽  
Asymptotic Matching

AbstractThe method of matched (or of ‘inner and outer’) asymptotic expansions is reviewed, with particular reference to two general techniques which have been proposed for ‘matching’; that is, for establishing a relationship between the inner and outer expansions, to finite numbers of terms, of an unknown function. It is shown that the first technique, which uses the idea of overlapping of the two expansions, can be difficult and laborious in some applications; while the second, which is the ‘asymptotic matching principle’ in the form stated by Van Dyke(13) can be incorrect. Two different sets of conditions sufficient for the validity of the asymptotic matching principle are then established, on the basis of assumptions about the structure of expressions which approximate to the desired function f(x,∈) for all relevant values of x. Finally, it is noted that in four classes of singular-perturbation problems for which complete and rigorous asymptotic theories exist, uniform approximations to the solutions have a structure which is a particular form of the general one assumed in this paper.

Free convection at low Prandtl numbers

1969 ◽  
Vol 37 (4) ◽  
pp. 785-798 ◽  
Author(s):  
H. K. Kuiken
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Prandtl Number ◽  
Asymptotic Expansions ◽  
Extreme Case ◽  
Matched Asymptotic Expansions ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Prandtl Numbers ◽  
Free Convection Boundary Layer

In this paper it is shown that the free convection boundary layer approaches a singular character if the Prandtl number tends to zero. The method of matched asymptotic expansions is used to integrate the equations for this extreme case. An expression is derived for the Nusselt—Grashof relation and the results are compared with those of previous investigations which attack the problem in a different way.

Singular Perturbation Techniques and Asymptotic Expansions for Some Complex Enzyme Reactions

2020 ◽  
pp. 43-53 ◽  
Author(s):  
Alberto Maria Bersani ◽  
Alessandro Borri ◽  
Alessandro Milanesi ◽  
Giovanna Tomassetti ◽  
Pierluigi Vellucci
Keyword(s):  
Singular Perturbation ◽  
Asymptotic Expansions ◽  
Perturbation Techniques ◽  
Enzyme Reactions

scholarly journals A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.

2019 ◽  
Vol 10 (1) ◽  
pp. 162-181
Author(s):  
A. M. Bersani ◽  
A. Borri ◽  
A. Milanesi ◽  
G. Tomassetti ◽  
P. Vellucci
Keyword(s):  
Singular Perturbation ◽  
Enzyme Kinetics ◽  
Chemical Reaction ◽  
Asymptotic Expansions ◽  
Competitive Inhibition ◽  
Perturbation Techniques ◽  
Inhibitory Mechanisms ◽  
Perturbation Order ◽  
Study Case ◽  
Uniform Expansions

Abstract In this paper we study the model of the chemical reaction of fully competitive inhibition and determine the appropriate parameter ∊ (related to the chemical constants of the model), for the application of singular perturbation techniques. We determine the inner and the outer solutions up to the first perturbation order and the uniform expansions. Some numerical results are discussed.

Trailing edge flows

1969 ◽  
Vol 39 (1) ◽  
pp. 193-207 ◽  
Author(s):  
N. Riley ◽  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Asymptotic Expansions ◽  
Pressure Field ◽  
Matched Asymptotic Expansions ◽  
Trailing Edge

The flow is examined in the neighbourhood of the trailing edge of slender aerodynamic shapes which terminate in either a cusp or a wedge. The manner in which the boundary layer reacts to the rapidly varying pressure field in such regions is analyzed using the method of matched asymptotic expansions. The case of a wedge is examined in greater detail and a criterion for separation to occur is established.

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