Shoichi Wakiya

Slow Motion in Shear Flow of a Doublet of Two Spheres in Contact

The exact solution of the Stokes equations for fluid motion around two spheres in contact is given in the most general flow situation. By use of this solution the behavior in shear flow of a doublet composed of two equal-sized spheres in contact is considered. Numerical calculation is carried out, and the motion of the doublet and the rate of energy dissipation are compared with the known case of spheroid.

Application of Bipolar Coordinates to the Two-Dimensional Creeping Motion of a Liquid. I. Flow over a Projection or a Depression on a Wall

The bipolar coordinate solution of the two-dimensional Stokes equations is applied to the flow along a plane wall with a projection or a depression. The resultant integral is evaluated by the calculus of residues to give an eigenvalue expansion and the eigenvalues are calculated for various values of the parameter. Special consideration is made for a cylinder inlaid in the wall.

Application of Bipolar Coordinates to the Two-dimensional Creeping Motion of a Liquid. : II. Some Problems for Two Circular Cylinders in Viscous Fluid

The bipolar coordinate solution of the two-dimensional Stokes equations is applied to flows around two circular cylinders. It is proved that there are three cases which this kind of solutions can describe. Solutions are presented for a cylinder revolving eccentrically in a cylindrical frame, a cylinder in the neighborhood of a plane wall and two cylinders in rotary motion as a pair.

On the Exact Solution of the Stokes Equations for a Torus

The field disturbed by a torus placed perpendicular to a slowly streaming uniform flow of a viscous fluid is considered by use of toroidal coordinates. The drag exerted on the torus and the flux passing through it undergo special consideration accompanied with numerical evaluations.

Mutual Interaction of Two Spheroids Sedimenting in a Viscous Fluid

A general solution of the Stokes equations of a viscous fluid with boundary conditions related to a spheroid is considered and the formulae for drag and moment are obtained to a certain order of approximation. The results are applied to the problem of sedimentation of two spheroids in which the spheroids have the same shape and velocity and their axes of symmetry are both in horizontal directions. The drag and torque acting on a spheroid are given in terms of mutual interaction of the spheroids. They are considered to a higher order for the special cases where the centers of the spheroids are both on a vertical line or in a horizontal plane.

Effect of a Plane Wall on the Impulsive Motion of a Sphere in a Viscous Fluid

The impulsive motion of a sphere along a plane wall in a viscous fluid is treated on the basis of the Stokes approximation. A solution to the equations for unsteady motion is obtained by applying the Laplace transformation with respect to time to the basic equations. Results obtained to a first approximation for the drag and the torque acting on the sphere show that: \renewcommand\labelenumi\arabicenumi.

Application of Bipolar Coordinates to the Two-Dimensional Creeping Motion of a Liquid.III.Separation in Stokes Flows

When there is a linear shear flow along a plane wall with a cylindrical depression, flow penetrating into the cavity separates from the wall, if the ratio of the depth of the cavity to the width of its mouth exceeds a critical value which is about 0.32. The pressure becomes infinite at the sharp edges of the cavity, while for the flow over a projection the pressure is a continuous function which on the boundary has two extremum values symmetrically about the cylindrical portion. As another example of separation in Stokes flows, the flow generated by the rotation of a circular cylinder which is eccentrically encircled with a larger cylinder or placed near a plane is considered.

Viscous Flow in a Bifurcate Channel

The technique presented by Dean is applied to find the solution for a slow two-dimensional steady motion of liquid in an infinite channel. The channel is composed of two parallel infinite plates and a semi-infinite partition plate which is in the middle of the infinite plates. The fluid velosity is assumed to have a parabolic distribution at infinity and the direction perpendicular to the edge line of the partition plate. The stream function is first assumed and two sets of constants contained in it are then adjusted so that slip of the velosity on the boundaries becomes sufficiently small. From the approximate solution obtained, the properties of the solution in the neighbourhood of the leading edge of the partition plate and the pressure drop along the channel due to the partition are discussed.

Fine Structure of the Stokes Flow near the Central Hole of a Torus

An alternative representation of Pell and Paynes solution for a torus in a uniform stream is given and using this the structure of flow near the hole of the torus is examined, particularly when the size of the hole is very small. When the hole radius is about 0.092 times the radius of a base circle making the torus by rotation, a vortex ring begins to grow on the axis of symmetry of the flow. As the hole size is decreased, such eddy regions form alternately on the torus and the symmetry axis.

Periodic Motions of a Viscous Fluid past a Sphere in a Cylindrical Tube

Slow periodic motions of a viscous incompressible fluid past a sphere in an infinitely long circular cylinder are considered. The basic equations are the Navier-Stokes equations of motion linearized by omitting convection terms. The primary parameters involved are a / R 0 , b / R 0 , a 2 ω/ν and R 0 2 ω/ν, where a and R 0 are the radii of the sphere and cylinder respectively, b is the distance of the particle from the cylinder axis, and ω/ν is the angular frequency divided by the kinematic viscosity. The drag and couple acting on the sphere and the translational and angular velocities of the sphere floating in the stream are finally given in the forms of power series with respect to these parameters.