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** G A Rigid Sphere in Axisymmetric, Extensional Flow **

** Sphere axisymmetric extensional flows **

** Sphere in Linear Flows Axisymmetric Extensional Flow and Simple Shear **

We first derive the kinematics of the deformation. The flow situation is shown in Fig. 14.14. Coordinate z is the vertical distance in the center of the axisymmetric bubble with the film emerging from the die at z = 0. The radius of the bubble R and its thickness 8 are a function of z. We chose a coordinate system C, embedded in the inner surface of the bubble. We discussed extensional flows in Section 3.1 where we defined the velocity field of extensional flows as... [Pg.838]

G. A RIGID SPHERE IN AXISYMMETRIC, EXTENSIONAL FLOW I. The Flow Field... [Pg.470]

Axisymmetric Flow. A gas bubble is immersed in a viscous Newtonian fluid that is undergoing an axisymmetric extensional flow. The fluid is viscous enough that the relevant Reynolds number is small so that the creeping-motion approximation can be applied. The capillary number based on the extension rate, E, and the surface tension, a, is small, i.e.,... [Pg.517]

Problem 7-13. The Viscosity of a Dilute Suspension of Spherical Bubbles. Consider again the Problem 7 12. This time, assume that the bubble remains spherical. If you have already solved 7 12, the solution for part (b) provides the velocity and pressure fields for a spherical bubble. If you have not previously solved 7 12, you will need to determine the solution for a spherical bubble in an axisymmetric extensional flow, using the boundary conditions... [Pg.518]

In the extensional flow, the principal axis of deformation is x and the shape is axisymmetric about this axis. The ratio of major to minor axis in this case is... [Pg.543]

Sphere in Linear Flows Axisymmetric Extensional Flow and Simple Shear... [Pg.555]

Mass Transfer From a Spherical Bubble in an Extensional Flow. Consider a spherical gas bubble that is suspended in a liquid that undergoes an axisymmetric extensional flow. The bubble contains a component A that is soluble in the exterior liquid... [Pg.690]

Another axisymmetric extensional flow is biaxial extension. In this deformation, there is a compression along the axis of symmetry that stretches in the radial direction, as shown in Fig. 9. The principal strain rate is defined as... [Pg.16]

Stone and Leal [70] applied the method to a droplet contaminated with an insoluble surfactant in an axisymmetric extensional flow. The effect of the... [Pg.227]

The sink flow analysis, which assumes a purely extensional flow (i.e., no shear component), was presented by Metzner and Metzner (1970) to evaluate the extensional viscosity from orifice Apen measurements. For an axisymmetric contraction, the flow into the orifice is analogous to a point sink for a planar contraction flow, the analogy is with a line sink (Batchelor, 1967). In the case of axisymmetric contraction (Figure 7.8.1), the use of spherical coordinates and continuity gives the velocity components... [Pg.327]

While we will not need the general tensorial form of the superposition principle for the purposes of this book, we will show the result of its use to describe the special case of axisymmetric, uniaxial (tensile) extensional flow ... [Pg.94]

extensional deformations can be created by impinging two liquid streams, creating a stagnation flow. Figure 7.7.1 illustrates both axisymmetric and planar stagnation flow. These flows are not homogeneous. A material element near the central part of the flow... [Pg.320]

** G A Rigid Sphere in Axisymmetric, Extensional Flow **

** Sphere axisymmetric extensional flows **

** Sphere in Linear Flows Axisymmetric Extensional Flow and Simple Shear **

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