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 1953
a
) 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∙1
av
*
or
K
= 7∙14
aU
√
γ
. Here
a
is the radius of the pipe,
U
is the mean flow velocity,
γ
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
= 437
aX
(
v
*
/
U
). Good agreement is found when this prediction is compared with experiments made in long pipe lines in America.
This study aims to display the retention of the thermo-responsive
properties of the copolymer poly(N-isopropyl acrylamide-methyl methacrylate)
[P(NIPAM/MMA)] when coated on the inner diameter of a glass capillary tube,
and to prove the stability of the copolymer coating when subjected to
pressure driven fluid flow. The study shows that the fluid flow through such
a capillary tube follows Hagen-Poiseuille flow. Furthermore, this study
examines methods of improving polymer adhesion to glass by hydrofluoric acid
etching. Such a coated tube system is applicable in drug delivery, self
cleaning tubes, and microelectromechanical systems (MEMS).
The absolute viscosity calculated from the formula(where p = the pressure, t the time, r the radius, l the length of capillary, and v the volume of liquid), which connects the viscosity of a liquid with the rate of flow through a long capillary tube, is not often made use of, mainly on account of the difficulty of accurately determining some of the constants (r in particular).
The general formulae given in the previous paper are investigated in detail using a simple relaxation-time approximation for the collision operator, and numerical results are obtained for the total gas flow through a capillary tube at various values of the ratio of tube radius to collision mean free path. For all values of this ratio, the results obtained agree with experiment to within about 2%.
The morphology of liquid-gas interfaces in adiabatic two-phase microchannel flow through a transparent acrylic microchannel of 500 μm × 500 μm square cross section is investigated. Water seeded with 0.5 μm-diameter fluorescent polystyrene particles is pumped through the channel, and the desired adiabatic two-phase flow regime is achieved through controlled air injection. The diagnostic technique relies on obtaining particle position data through epifluorescent imaging of the flow at excitation and emission wavelengths of 532 and 620 nm, respectively. The particle positions are then used to resolve interface locations to within ±2 μm in the viewing plane. This technique was previously demonstrated by the authors for a static meniscus in a capillary tube. The complete interface geometry between liquid and gas phases is obtained for operation in the annular flow regime by mapping the interface within individual focal planes at various depths within the channel. The diagnostic technique is shown to successfully locate and measure interfaces between transparent, immiscible fluids in a dynamic microchannel flow environment.
Note on the Standard of Relative Viscosity, and on “Negative Viscosity.”