Michael E. Ryan

Velocities of extended bubbles in inclined tubes

Abstract The velocities of extended bubbles (slug flow bubbles) have been measured in inclined circular tubes. Eotvos numbers ranged from 4.9 to 490 and Morton numbers from 2.2 × 10 −11 to 1.5 × 10 4 . The Froude number for any angle of inclination was correlated as a function of angle and the values of the Froude numbers for the horizontal and vertical orientations.

Perturbation method in gas-assisted power-law fluid displacement in a circular tube and a rectangular channel

In this paper the two dimensional flow of a power-law fluid is studied analytically using a singular perturbation method in order to determine the residual liquid film thickness of power-law fluids on the wall of a circular tube or a rectangular channel when displaced by another immiscible fluid. Inner and outer expansions are developed in terms of a small parameter CA1/3 (modified capillary number). A differential equation for the shape of gas bubble is solved numerically in order to determine the inner solution. The method of matched asymptotic expansions is used to match the inner and outer solutions. This approach indicated that the residual liquid film thickness of non-Newtonian fluids increases with decreasing power-law index.

Gas-assisted non-newtonian fluid displacement in circular tubes and noncircular channels

The motion of long bubbles into Newtonian and non-Newtonian fluids confined in horizontal circular tubes, rectangular channels, and square cross-sectional channels has been studied both theoretically and experimentally. Of particular interest is the determination of residual liquid film thickness on the walls. Isothermal experiments have been conducted to measure the displacement of the gas–liquid interface as a function of the applied pressure differential. The velocity of the interface and residual liquid film thickness have been determined for both Newtonian and non-Newtonian (shear thinning and viscoelastic) fluids. These experimental results are in good agreement with similar experimental studies conducted by other investigators. The experimental results indicate that the liquid film thickness of constant viscosity viscoelastic fluids (Boger fluids) deposited on the tube wall is thicker than that of comparable Newtonian fluids. A simple mathematical analysis was developed using a power-law model. The mathematical model successfully captures the gas–liquid dynamics for Newtonian and non-Newtonian fluid displacement in a tube and rectangular channel. The prediction of the liquid fraction deposited on the walls is in qualitative agreement with the experimental observations of previous investigators (Chem. Eng. Sci. 24 (1969) 471; A.I.Ch.E. 16 (1970) 925; Chem. Eng. Sci. 30 (1975) 379). The model gives similar results to a numerical solution (Polm. Eng. Sci. 35 (1995) 877) in which a constitutive equation containing a yield stress is used to model the non-Newtonian behavior. The model is used to determine the location and velocity of the advancing bubble front for the case of a power-law fluid. The results indicate that the gas–liquid interface advances more rapidly with decreasing values of the power-law index above a certain value of dimensionless time (t/tb≈0.75).

An experimental study of the motion of long bubbles in inclined tubes

Abstract The rise velocity of tube-draining bubbles in Newtonian and non-Newtonian fluids has been studied for vertical and inclined tubes. The experimental data are described in terms of the Froude ( Fr ), Eotvos ( Eo ), and Morton ( M ) numbers. The Froude number is given as a function of the angle of inclination ( θ ) and Eo in order to represent the effect of tube size, inclination angle, and fluid properties on the rise velocity of the bubble. As the angle of inclination from the horizontal increases, Fr increases, reaches a maximum, and then decreases for all fluids. The maximum Fr value occurs at larger angles of inclination when the fluid is non-Newtonian. For Newtonian and non-Newtonian fluids possessing similar values of surface tension and zero-shear rate viscosity, the Fr values are similar for vertical tubes. However, the Fr values are generally lower for non-Newtonian fluids in inclined tubes under these same conditions.

Analysis of extrudate swell from an annular die

Abstract An isothermal annular jet swell problem has been analyzed using a control volume based finite difference scheme. This numerical scheme has been previously used for the analysis of the jet swell problem in capillary and slit dies, and is also shown to be applicable to annular geometries as well. In the absence of gravity and surface tension, the thickness swell ratio reaches 15.88%, which is in reasonable agreement with values reported in the literature. A relatively long jet was employed in this study and the effect of gravity on the jet shape appeared to be significant. In accordance with other calculations in the literature, the surface tension was found to have a more pronounced effect on the inner free surface compared with the outer free surface. The effects of the power-law index and die gap size were also investigated, and a suggestion for improvement of the numerical approach is briefly described.

Gas-assisted displacement of a Newtonian fluid confined in a Hele-Shaw cell

Abstract The two-dimensional flow in a rectangular channel containing a Newtonian fluid was solved analytically in terms of eigenfunctions as θ→π/2, where θ is the angle between the normal to the interface and the axial direction. From this analysis, the relationship between the parameters Ca, λ, and kd were obtained. These parameters are related to the amount of liquid deposited on the walls of the rectangular channel. This analysis provides a satisfactory relationship between m and Ca for values of kd between 1.8 and 2.0. It is expected that the coating thickness obtained from this analysis for a rectangular channel is close to the experimental data for a value of kd taken to be 1.95 since the perturbation solution at low capillary number is close to this value of kd. The solution is valid for an interface is almost parallel to the walls of the Hele-Shaw cell.

Analysis of nonisothermal extrudate swell

Abstract Nonisothermal extrudate swell through capillary and annular dies was studied numerically using a control volume finite difference method. In order to examine the effect of the relevant dimensionless parameters on the swelling behavior of the extrudate, Newtonian liquids having a temperature dependent viscosity have been chosen and computations have been performed for various process conditions. Four dimensionless groups, i.e., the Peclet number (Pe), the Brinkman number (Br), the Biot number (Bi), and an exponential parameter β expressing the temperature dependence of viscosity, were examined respectively, and the sensitivity of each group on the swelling ratio was determined. The parameter β was found to be the most sensitive factor.