Akira Takami

The Steady Slow Motion of a Non-Newtonian Liquid through a Tapered Tube

A theory of the steady slow motion of a time-independent non-Newtonian liquid through a tapered tube is presented. The coefficient of viscosity µ which appears in the relationship between the stress and the rate of strain of a Newtonian liquid is assumed to be a function of the velocity gradient. Thus µ is a function of the coordinates of the liquid particles. The equations of motion of a non-Newtonian liquid through a tapered tube have been obtained under the following assumptions: i) the liquid is incompressible; ii) the motion of the liquid is laminar; iii) the motion is steady; iv) no body-force acts on the liquid; v) the motion has an axial symmetry; vi) there is no slip at the wall; vii) the stream-lines are straight lines passing through the vertex of the cone; viii) the motion is so slow that the inertia term can be neglected. The differential equation for the velocity distribution of a non-Newtonian liquid obeying power law has been derived.

Mathematical analysis of the pressure distribution in powder in equilibrium in a conical vessel

Abstract A mathematical analysis of the distribution of pressure (vertical stress) in powder mass filled in a conical vessel is presented, taking into account the variation of pressure with the distance from the axis of the cone. The free surface of the powder mass is assumed to be heaped. It is assumed that vertical stress and horizontal stress are interrelated by Rankines law. From the equilibrium condition of powder mass a fundamental equation has been derived to determine the pressure as a function of both the depth and the distance from the axis of the cone. A solution satisfying the boundary condition at the free surface has been obtained. It is shown that the analysis fits the experimental curves of the distribution of vertical stress

A theory of the pressure distribution in powder in equilibrium in a cylindrical vessel

Abstract A mathematical analysis of the distribution of pressure (vertical stress) in a powder mass filled in a cylindrical vessel is presented, taking into account the variation of pressure with the distance from the axis of the cylinder. The free surface of the powder mass is assumed to be even. It is assumed that vertical stress and horizontal stress are interrelated by Rankines law. From the equilibrium condition of the powder mass a fundamental equation has been derived to determine the pressure as a function of both the depth and the distance from the axis of the cylinder. A solution satisfying the boundary condition at the free surface has been obtained. It contains a number of indeterminate constants and is reduced to Janssens formula, provided that the pressure is independent of the distance from the axis of the cylinder. It is shown that our theory agrees fairly well with the experimental data of Yoshioka .

Theory of a Cone-Plate Viscometer for Non-Newtonian Liquids

A general relationship between the torque M and the angular velocity \varOmega of a plate is obtained for a time-independent non-Newtonian liquid specified by an arbitrary flow curve. It is assumed that the motion of the liquid is steady and that each liquid particle moves with a constant angular velocity on a circle on a horizontal plane perpendicular to the axis of rotation. The edge effects are neglected. It is shown how to determine the flow curve from the experimental relationship between M and \varOmega for some special cases. Following special cases are considered: i) non-Newtonian liquid obeying power law flow curve, ii) non-Newtonian liquid obeying flow curve expanded into power series, iii) Bingham body. It is shown that the relationship between M and \varOmega for a non-Newtonian liquid obeying power law flow curve is reduced to the well-known formula for a Newtonian liquid when the exponent tends to unity.

Theory of a Double Cone Viscometer for Non-Newtonian Liquids

A general relationship between the torque M and the angular velocity Ω is derived theoretically for a time-independent non-Newtonian liquid specified by an arbitrary flow curve. It is assumed that the motion of the liquid is laminar and steady and that each liquid particle moves with a constant angular velocity on a circle on a horizontal plane perpendicular to the axis of rotation. The edge-effect is neglected. It is shown how to determine the flow curve from the experimental relationship between M and Ω for some special cases: i) non-Newtonian liquid obeying power law flow curve, ii) non-Newtonian liquid whose flow curve is expanded into a power series, iii) Bingham body, and iv) non-Newtonian liquid obeying Cassons equation.