John C. Slattery

Correlation for dynamic contact angle

Abstract A correlation is suggested for available experimental measurements of the advancing dynamic contact angle measured through the liquid phase during the displacement of a liquid—gas interface through a glass capillary tube. This same correlation is shown to describe the advancing contact angle as a wire enters a liquid from a gas, so long as the effects of inertia and gravity appear to be negligible. This suggests that experimental measurements of the dynamic contact angle may be independent of the macroscopic geometry.

Surfaces—I: Momentum and moment-of-momentum balances for moving surfaces

Abstract The moment-of-momentum balance for moving surfaces with simultaneous mass transfer to the adjacent phases is developed to show that the surface stress tensor is symmetric. The momentum balance previously presented by S criven is extende dto account for the effects of mass transfer between the surface and the adjacent phases. The tangential component of the momentum balance given by S criven is shown to be valid either when the surface has no normal component of velocity or when the surface mass density is vanishingly small.

Disk and biconical interfacial viscometers

Abstract An exact solution is obtained for the zero-thickness disk interfacial viscometer shown in Fig. 1. From a measurement of the torque required to hold the disk stationary when the dish rotates at a given angular velocity, the surface shear viscosity can be determined. With a small correction, this solution can be applied to the thin biconical bob interracial viscometer shown in Fig. 2.

Non-newtonian boundary-layer flow

The approximate boundary-layer treatment originally due to Pohlhausen has been extended both for two-dimensional and for axially symmetric bodies to fluids whose behaviours may be described by the Ostwald-de Waele model. The form of the velocity profile chosen (a fourth-order polynomial) limits the development to 0·7356 ⩽ n ⩽ 1·0 for axially symmetric, blunt bodies and to n ⩽ 1·0 for two-dimensional flows. The results are presented in a parallel of a form standard for Newtonian fluids and in a form more suitable for machine computation. A simple quadrature based upon a linear approximation is given as well. As an example, the boundary layer on a sphere is analysed; the calculated point of separation increases with n in qualitative agreement with previously reported experimental data.

Balance equations and structural models for phase interfaces

Abstract The general balance equations are developed for an interface represented by a dividing surface and for a moving common line represented as an intersection of dividing surfaces. The surface excess variables associated with a dividing surface are expressed both in terms of those variables describing the three-dimensional interfacial region of finite thickness and in terms of those variables describing bulk phases that extend up to the dividing surface. A structural model for the interface is suggested in which a suspension of solid bodies representing surfactant molecules is distributed about a singular surface separating two adjacent bulk solvent phases. The suspension is required to have the same average behavior as the interfacial region. This is interpreted as meaning that the general jump balance for a continuum dividing surface represented by an interfacial suspension is a local area average. Specific results are derived for two structural models, each in the same simple shear field. One consists of a dilute suspension of neutrally buoyant spheres floating with their centers restricted to the dividing surface. The other is a dilute suspension of chains of neutrally buoyant spheres with the sphere at one end of the chain floating in the dividing surface.

Non-Newtonian flow past a sphere

Abstract Drag coefficients for spheres moving through five aqueous solutions of carboxymethylcellulose (CMC) were measured. With the assumption that the behaviour of these fluids could be approximated by the Ellis model, two dimensionless correlations for the drag coefficient in terms of a modified Reynolds number and two other dimensionless groups were prepared. The Ellis model is easy to use and provides a much better description of non-Newtonian behaviour than the more commonly used Ostwald-de Waele model. The correlation is of value for the prediction of the settling time of a sphere in a non-Newtonian fluid. The results seem to indicate that the behaviours of the CMC solutions studied are independent of the third invariant of the rate of deformation tensor.

Alternative solution for spinning drop interfacial tensiometer

Abstract An alternative solution for the spinning drop surface tensiometer is presented which is more convenient for an experimentalist to use.

A linear stability analysis for immiscible displacements

A linear stability analysis has been performed for a miscible displacement in a semi-infinite system of finite thickness and unbounded width. A more general description of dispersion has been adopted than those used by previous workers. It is shown that, when there is a step change in concentration and the mobility ratio is unfavorable, the displacement can be unstable at the injection boundary. But, if the concentration is changed sufficiently slowly with time at the entrance to the system, the displacement is stable to infinitesimal perturbations, no matter how unfavorable the mobility ratio. When the mobility ratio is favorable, the displacement is unconditionally stable.

Nonlinear interfacial stress-deformation behavior measured with several interfacial viscometers

Abstract Two techniques for measuring nonlinear interfacial stress-deformation behavior using rotational interfacial viscometers are proposed. Either a single bob can be used or two bobs of slightly different radii can be employed. A series of experiments with the interface between air and an aqueous solution of 0.1 wt% dodecyl sodium sulfate have been carried out using the disk, knife-edge, and thin biconical bob interfacial viscometers. Four sets of data have been analyzed using the single-bob technique. Data for two disks also have been analyzed by the double-bob technique. Agreement among the results supports the validity of the proposed methods. The same system has been studied in a deep-channel interfacial viscometer. For the first time, consistent measurements of interfacial stress-deformation behavior have been obtained from two different interfacial viscometers.

Blunt knife-edge and disk surface viscometers

Abstract Previously developed bounding principles are applied to the blunt knife-edge and disk surface viscometers for the case of a gas—liquid interface that is described by the Boussinesq surface fluid model. The results are in the form of approximate relationships with error bounds for the torque exerted upon the knife-edge or disk as a function of the surface shear viscosity.