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  • 1
    Electronic Resource
    Electronic Resource
    An experimental study of rivulet instabilities in centrifugal spin coating of viscous Newtonian and non-Newtonian fluids (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 1491-1504 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: An experimental study on the onset and evolution of centrifugally driven rivulets is presented, which aims to investigate the influence on the instability of various experimental conditions (drop volume and rotational frequency), the wetting properties of the liquid (surface tension and contact angle), and fluid viscoelasticity. The apparatus allows continuous observation of the drop shapes following an impulsive spin-up of the substrate, and these are analyzed by digital image analysis. The flows exhibit an onset time, or, equivalently, a critical radius, before which the drop spreads axisymmetrically. Data on drop spreading are compared with simple predictions of lubrication theory. The measured azimuthal wave number and growth rate of the instability are in good agreement with the linear stability analysis of Troian et al. [Europhys. Lett. 10, 25 (1989)], as long as the critical radius is taken from the experiment itself. The most unstable wavelength is found to be independent of both drop size and rotation speed in the range of parameters investigated, as observed previously by Melo et al. [Phys. Rev. Lett. 63, 1958 (1989)]. On the other hand, a change in the wetting properties of the liquid significantly modifies the critical radius, which, in turn, affects the number of fingers, with the nonwetting fluid exhibiting a smaller critical radius. This trend is in agreement with the mechanism of instability that is linked to the presence of a capillary ridge near the edge of the drop. No qualitative nor quantitative difference in behavior has been observed between a Boger fluid having a relaxation time of about 1 s, and its Newtonian solvent, in the experimental conditions considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868263
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  • 2
    Electronic Resource
    Electronic Resource
    Linear stability of lid-driven cavity flow (1994)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 6 (1994), S. 2690-2701 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Previous experimental studies indicate that the steady two-dimensional flow in a lid-driven cavity becomes unstable and goes through a sequence of transitions before becoming turbulent. In this study, an analysis of this instability is undertaken. The two-dimensional base flow is computed numerically over a range of Reynolds numbers and is perturbed with three-dimensional disturbances. The partial differential equations governing the evolution of these perturbations are then obtained using linear stability analysis and normal mode analysis. Using a finite difference discretization, a generalized eigenvalue problem is formulated from these equations whose solution gives the dispersion relation between complex growth rate and wave number. An eigenvalue solver using simultaneous iteration is employed to identify the dominant eigenvalue which is indicative of the growth rate of these perturbations and the associated eigenfunction which characterizes the secondary state. This paper presents stability curves to identify the critical Reynolds number and the critical wavelength of the neutral mode and discusses the mechanism of instability through energy calculations. This paper finds that the loss of stability of the base flow is due to a long wavelength mode at a critical Reynolds number (Re) of 594. The mechanism is analyzed through a novel application of the Reynolds–Orr equations and shown to be due to a Goertler type instability. The stability curves are relatively flat indicating that this state will be challenged by many shorter wavelength modes at a slightly higher Reynolds number. In fact, a second competing mode with a wavelength close to the cavity width was found to be unstable at Re=730. The present results of the reconstructed flow based on these eigenfunctions at the neutral state, show striking similarities to the experimental observations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.868158
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  • 3
    Electronic Resource
    Electronic Resource
    A Theoretical Study of Pressure Drop and Transport in Packed Beds at Intermediate Reynolds Numbers (1973)
    s.l. : American Chemical Society
    Industrial and engineering chemistry 12 (1973), S. 82-90 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/i160045a014
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  • 4
    Electronic Resource
    Electronic Resource
    Convective instabilities in concurrent two phase flow: Part I. Linear stability (1974)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 20 (1974), S. 981-988 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The linear stability of thermally stratified horizontal two-phase Couette flow is analyzed for the case of a constant vertical temperature gradient. Instabilities driven by buoyancy, surface tension gradients, or shear are allowed for. It is shown that the instability can take three possible forms: streamwise oriented roll vortices, long interfacial waves, and short Tollmien-Schlichting waves. It is shown that the stability limits for rolls are identical to those for plane, stagnant layers. A long wave expansion is presented and the stability limits for this mode are given algebraically. The nonexistence of a Squire's Theorem is demonstrated and some numerical experiments at moderate Reynolds numbers are described. Detailed comparisons with previous work are possible for only one fluid pair, but it is shown that reasonably accurate statements may be made to determine which mode may manifest itself in any given experimental situation.
    Additional Material: 1 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690200520
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  • 5
    Electronic Resource
    Electronic Resource
    Convective instabilities in porous media with through flow (1976)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 22 (1976), S. 168-174 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The stability of a thermally stratified, saturated porous media through which mass is being ejected is considered theoretically. The stability parameter is a flow modified D'Arcy-Rayleigh number and is a function of a single scalar variable, the dimensionless through-flow strength. Results of both linear and energy theory are given, and it is seen that the fluid can lose stability by either a buoyantly driven mode or by a continuous analogue of the Saffman-Taylor mode.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690220121
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  • 6
    Electronic Resource
    Electronic Resource
    Convective instabilities in concurrent two-phase flow: Part II. Global stability (1974)
    Hoboken, NJ : Wiley-Blackwell
    AIChE Journal 20 (1974), S. 1161-1167 
    Details
    ISSN: 0001-1541
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The method of energy is used to determine global stability limits for thermally stratified two-phase plane Couette flow. Instabilities due to surface tension variations, buoyancy effects, and shear are allowed for, but surface waves are specifically excluded from consideration. Under these assumptions, the Marangoni, Rayleigh, and Reynolds numbers completely describe the system. Stability plots, valid for disturbances of any magnitude, are presented for both streamwise oriented roll vortices and two-dimensional transversely oriented disturbances. It is shown that rolls are the most dangerous disturbances in the sense that they cannot be shown to be stable relative to transverse disturbances at any nonzero Reynolds numbers. Comparisons are made with existing linear limits, and these are seen to be close only for moderate Reynolds numbers.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/aic.690200615
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