Abstract: The dispersion of soluble matter introduced into a slow stream of solvent in a capillary tube can be described by means of a virtual coefficient of diffusion (Taylor 1953a) which represents the combined action of variation of velocity over the cross-section of the tube and molecluar diffusion in a radial direction. The analogous problem of dispersion in turbulent flow can be solved in the same way. In that case the virtual coefficient of diffusion K is found to be 10⋅1av* or K = 7.14aU√γ. Here a is the radius of the pipe, U is the mean flow velocity, g is the resistance coefficient and v* 'friction velocity'. Experiments are described in which brine was injected into a straight 3/8 in. pipe and the conductivity recorded at a point downstream. The theoretical prediction was verified with both smooth and very rough pipes. A small amount of curvature was found to increase the dispersion greatly. When a fluid is forced into a pipe already full of another fluid with which it can mix, the interface spreads through a length S as it passes down the pipe. When the interface has moved through a distance X, theory leads to the formula S^2 = 437aX(v*/U). Good agreement is found when this prediction is compared with experiments made in long pipe lines in America.

Abstract: When a soluble substance is introduced into a fluid flowing slowly through a small-bore tube it spreads out under the combined action of molecular diffusion and the variation of velocity over the cross section. It is shown analytically that the distribution of concentration produced in this way in centered on a point which moves with the mean speed of flow and is symmetrical about it in spite of the asymmetry of the flow. The dispersion along the tube is governed by a virtual coefficient of diffusivity which can be calculated from observed distributions of concentration. Since the analysis relates the longitudinal diffusivity to the coefficient of molecular diffusion, observations of concentration along a tube provide a new method for measuring diffusion coefficients. The coefficient so obtained was found, with KMnO4, to agree with that measured in other ways. The dispersion in steady flow is due to the combined action of convection parallel to the axis and molecular diffusion in the radial direction. It is of interest to consider, first, dispersion by convection alone,and then to introduce the effect of molecular diffusion. The results may be useful to physiologists who may wish to know how a soluble salt is dispersed in a blood vessel, but they may also be useful to physicists who wish to measure molecular diffusion coefficients. The experimental technique used for KMnO4 is described in detail, and results are compared with earlier measurements.

Abstract: Measurements of the amount of fluid left behind when a viscous liquid is blown from an open-ended tube are described.