非ニュートン液体に対する円すい平板粘度計の理論

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In a cone and plate viscometer a cone with a wide vertical angle is placed on a horizontal flat plate. The generator of the cone makes a very small angle α with the plate which is of the order of one degree to two degrees. The wedge-like space between the cone and the plate is filled with liquid to be investigated. Let the cone be fixed; the plate rotates with a constant angular velocity Ω for a non-Newtonian liquid specified by an arbitrary flow curve. The relationship between M and Ω for a Newtonian steady flow has already been presented by several authors. Thus the formula M=(2πa^3/3)・(ηΩ/α) has been derived, where a is the radius of the plate and η is the coefficient of viscosity. One of the most important characteristics of a cone and plate viscometer lies in the fact that the rate of shear is practically constant throughout one sample. Thus this type of viscometer is quit suitable for the measurement of non-Newtonian liquids. With regard to the motion of the liquid, the following assumptions are made the liquid is incompressible the motion of the liquid is laminar the motion is steady no body force acts on the liquid the motion has an axial symmetry each liquid particle moves on a circle on the horizontal plane perpendicular to the axis of rotation there is no relative motion between the walls and the liquid in immediate contact with the walls the end-effect is neglected. The assumption means utter disregard of centrifugal forces, and as well as the assumption is allowable for small values of Ω. We take a spherical coordinate system r, θand φ whose origin is at the vertex of the cone. If we assume that the angular velocity ω of a liquid particle around the axis of the cone is a function of θalone, then the shear stress τ_<θφ> is given by τ<θφ> =c/sin^2θ, where c is a constant. For a non-Newtonian liquid specified by an arbitrary flow curve f(τ), we get [numerical formula] The constant c is related with the torque M on the plate by the relationship M=c・2πa^3/3. For a special case of a non-Newtonian liquid obeying power law flow curve f(τ)=k_<τ^n> the following formula has been obtained: [numerical formula] We have also studied another special case of a Bingham body specified by a plastic viscosity and a yield value. For non-Newtonian liquid specified by a flow curve [numerical formula] can be determined from the experimental relationship between Ωand M.
社団法人日本材料学会の論文
1966-05-15

非ニュートン液体に対する円すい平板粘度計の理論

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