Raymond W. Flumerfelt

Effects of dynamic interfacial properties on drop deformation and orientation in shear and extensional flow fields

Abstract A first-order perturbation analysis of the deformation and orientation of drops in shear and extensional flow fields is presented. The solution parallels that of Cox except that a more general stress boundary condition is used at the drop interface. This condition accounts for possible interfacial tension variations on the drop surface as well as surface shear and dilatational viscosity effects. In addition to providing a quantitative basis for understanding observed deviations between experimental observations and previous theoretical predictions, the analysis provides the theoretical foundation for dynamic interfacial property measurements from relatively simple deformation and orientation tests.

Experimental studies of drop dynamics in shear fields: Role of dynamic interfacial effects

Abstract The behavior of drops in shear fields is experimentally studied and the roles of interfacial viscous effects and interfacial tension gradients are investigated. Specifically, drop deformation, orientation, and internal and external circulation tests are reported and these are compared with various theoretical predictions. Only in the case of systems with very high bulk viscosities were dynamic interfacial effects found to be negligible. In lower viscosity systems, even those with only contaminant amounts of surface active agents, significant interfacial shear viscosities and apparent dilatational viscosities were obtained. The experimental results are consistent with the previous theoretical predictions of Flumerfelt, and the latter theory provides a basis for interfacial viscous property measurements.

Instability of stationary and uniformly moving cylindrical fluid bodies—I. Newtonian systems

Abstract The early work of Tomotika provides a basis for analyzing the instability of stationary and uniformly moving cylindrical fluid bodies. The classical results of Rayleigh, Christiansen and Weber for critical growth rates and wavenumbers are obtained as zero order limits of Tomotikas general solution expanded in terms of the key characteristic parameters: the viscosity ratio, the density ratio and the dispersed and continuous phase Ohnesorge numbers. By employing more than one characteristic time, these limits, as well as others, are obtained in a general solution framework. Numerical results provide insights into the effects of the physical forces, as well as criteria and bounds for the application of the limiting cases.

Mechanics of the displacement process of drilling muds by cement slurries using an accurate rheological model

This study deals with the development of a mathematical model to describe the miscible displacement of drilling muds by cement slurries under laminar flow conditions. The model accounts for the effects of differing properties, geometry, and displacement rates. The model assumes that mixing in the displacement zone by molecular diffusion is minimal, and uses the Robertson-Stiff model to describe the rheological properties of both the drilling fluid and the cement slurry. The application of the model to a range of displacement conditions (densities, viscosities, yield stresses, displacement rates, etc.) indicates the conditions under which optimal or near optimal displacements are possible, and hence, provides a basis for designing efficient cementing operations from simple material property characterizations. Of special interest is the effect of the yield stress. These parameters are found to strongly affect the displacement efficiency, particularly the formation of cement channels. Such results are described quantitatively in the study. The effects of the other rheological properties, the densities, and the displacement rates are also described. 17 references.

Transient dilation of bubbles and drops: theoretical basis for dynamic interfacial measurements

Abstract An oscillating bubble (or drop) method for studying surface rheology and mass transfer at interfaces is analyzed. A general solution is obtained under conditions of small amplitude oscillations, soluble surfactant in both phases, general adsorption kinetics, and linear viscoelastic surface behavior. In addition, various limiting cases are identified, and criteria for determining such behavior are presented. Using data on a specific gas-liquid-surfactant system, it is shown that such proposed tests are sufficiently sensitive to be of experimental value. Characteristic parameters which include the effects of compositional and intrinsic surface viscoelasticity can be determined from frequency response tests. In the cases of insoluble monolayers and bulk phase limited mass transfer, it is possible to determine the intrinsic surface viscoelastic parameters explicitly. In adsorption/desorption limited cases, independent mass transfer tests are required. This method shows particular promise for gas-liquid systems.

Instability of stationary and uniformly moving cylindrical fluid bodies—II. Viscoelastic threads and experimental observations

Abstract The instability analysis of Part I is extended to the breakup of viscoelastic threads in fluid media (also possibly viscoelastic). Critical Growth rates and wave-numbers are calculated in terms of the viscosity ratio, the Ohnesorge numbers (continuous and dispersed phases), and elasticity numbers for each of the respective phases. Comparisons with results for Newtonian systems indicate viscoelastic threads to be less stable than Newtonian threads under similar conditions. Also, the critical wave-numbers observed with viscoelastic threads can differ significantly from those observed with Newtonian systems, particularly if the relative magnitudes of elasticity of the dispersed and continuous phases are quite different. Systems with similar magnitudes of elasticity in each phase exhibit wave-numbers similar to Newtonian systems of similar viscosities. Experimental results obtained from observations of fluid thread breakup in a Taylor four-roller device provide a basis for checking the predictions of the lineararized theory for both Newtonian and viscoelastic systems. In general, the agreement is good and the theoretical predictions of Parts I and II seem to be reasonable representations of experimental fact.

A new method for surface shear viscosity measurements: Decay of surface motions at a rotated gas—liquid interface

Abstract The theoretical basis for a new method for the measurement of the surface shear viscosity of a Newtonian liquid—gas interface is presented. The method involves the observation of decaying surface motions of a cup of liquid following cessation of steady rigid body rotation. Its basis stems from the sensitivity of the resulting angular displacements of surface elements to the shear properties of the interface. The method is most sensitive when the ratio of liquid height to cup radius is approximately 1 and when the observed surface elements are at radial positions somewhat removed from the cup walls. Series and graphical solutions are provided for determining the surface shear viscosity from measurements of original cup angular speed, cup geometry, surface particle angular displacement, and bulk fluid properties. Finally, experimental results are reported on water/air and oil/air systems with negligibly small surface shear viscosity effects. Angular displacement measurements show good agreement with those predicted theoretically.

Interfacial viscoelastic response to oscillatory shear deformations

Abstract The theoretical basis for a new frequency response method of determining the material properties of a viscoelastic liquid/gas interface is presented. The method involves measurement, at the surface, of the amplitude change and phase shift of oscillations imposed on a cup of liquid. It is based upon the effect that shear properties of a viscoelastic interface can have on velocities at a liquid/gas surface. The method is most sensitive for geometries where cup radius-to-liquid height ratios are about 0.5. Also, the sensitivity increases with frequency with the upper limit being constrained by the first appearance of secondary motions. A general series solution and computational algorithm are provided. The method is sufficiently sensitive to measure a viscosity ratio, defined as surface shear viscosity bulk shear viscosity cup radius, between 0.1 and 1.0.

Interfacial surfactant concentrations on an oscillating droplet: Solution of a singular boundary-initial value problem

Abstract Using singular spectral theory, a boundary-initial value problem is solved for the interfacial concentration of a surfactant on a liquid droplet oscillating in a surrounding second immiscible liquid phase. Besides being of value to the specific application the methodology of this paper is useful for a variety of boundary-initial value problems of interest to chemical engineers in which material domains have infinite or semi-infinite extents.

Transient response of muscle and nonbrain tissue to adjustments in O2 and CO2 balance.

The development of a valid description of respiratory system dynamics constitutes an essential first step in studies dealing with the closed-loop feedback character of the regulation of ventilation. In this paper, the essential framework of such a description is discussed. Body tissues are divided into muscle, brain, and all other tissues. Each of these subsystems is further divided into a blood pool, an interstitial space, and an intracellular fluid compartment. Considerable attention is paid to the description of the reaction and transport processes within blood and tissue fluids. The general equations developed for these are presented and then applied specifically to the muscle and tissue subsystems. The poor capacity of muscle tissue to store CO2 during the initial phase of a disturbance in CO2 balance is examined using two types of model systems. The first assumes muscle to be homogeneous with respect to perfusion and metabolism, and seeks to explain the behavior of muscle tissue regarding CO2 storage on the basis of limitations to CO2 diffusion across the cellular membrane and the capillary wall. The second group of model systems considers muscle tissue to be inhomogeneous with respect to metabolism and/or perfusion. For these, muscle is represented as two parallel compartments which differ in their volumes, metabolic rates, and in the level of perfusion. The computed results from both groups of model systems are compared with experimental data on the time variations in muscle venous blood PO2, PCO2, and pH for different physiological experiments involving disturbances in O2 and CO2 balances. In general, such studies provide a basis for appraising the role and relative importance of different transport and reaction processes in internal respiration as well as the adequacy and sensitivity of different types and levels of analytical description.