Completely developed and entry region mass transfer rates in turbulent pipe flow of drag reducing polymer solutions were studied experimentally using electrochemical techniques. The percent change in the fully developed mass transfer rate at a given volumetric flow was found to be greater than the percent change in the pressure gradient. The data are interpreted by using the law of the wall, valid for Newtonian fluids at large Schmidt numbers, whereby K + is related to Sc-0.74. The proportionality constant is correlated with percent drag reduction and is found to decrease with increasing drag reduction. The use of an analogy between momentum and mass transfer predicts a somewhat greater mass transfer reduction than was observed. Smith et al., 1969) have established that drag reducing polymers can cause a reduction in the rate of turbulent heat transfer between a wall and aqueous solutions with Prandtl numbers in the range of 5 to 10. This paper describes a study of turbulent mass transfer in a pipeline with a diameter of 2.61 cm. Entry region and fully developed mass transfer coefficients are presented for dilute solutions of the high molecular weight polyacrylamide, Separan AP-30, at Reynolds numbers from 13 000 to 86 500. GEORGEThese measurements were made using an improved electrochemical technique applicable to drag reducing aqueous solutions. The results are of particular interest since they give information on scalar transport at high Schmidt numbers, from 950 to 1260. A form of the Reynolds analogy is examined to see if it can relate mass transfer to momentum transfer for drag reducing solutions. CONCLUSIONS A N D SIGNIFICANCEThe percent change in the fully developed mass transfer rate at a given volumetric flow is found to be greater than the percent change in pressure gradient. The decrease in the mass transfer rate caused by the addition of drag reducing polymers is associated with changes in both the turbulence close to the wall and the Schmidt number.The law of the wall relation developed by Shaw (1976) for Newtonian fluids has been used to take into account the influence of Schmidt number. The coefficient B is correlated with percent drag reduction in Figure 9. It is found that it decreases with increasing drag reduction, being about 20% lower than for a Newtonian fluid at 40% drag reduction. This is consistent with the finding that turbulent velocity fluctuations normalized with the friction velocity U" are smaller for drag reducing fluids than for Newtonian fluids in the region occupied by the concentration boundary layer. Hozever, since no theory exists which correctly relates turbulent mass transfer to the fluctuating velocity close to a wall, it is not possible to relate the change in B to observed changes in turbulence properties close to a wall. The analogy between momentum transfer and mass transfer agrees with the observation that the mass transfer rate is decreased more than the pressure gradient but overpredicts the amount by which mass transfer rate is decreased. RELATION TO PREVIOUS WOR...

Oscillatory convective instability is shown to occur in a rotating fluid layer when convection is caused by surface-tension gradients at a free surface. The asymptotic equations, valid when the Taylor number approaches infinity, are solved analytically, and the critical Marangoni number is evaluated numerically. Fluids with Prandtl numbers above 0·201 will exhibit only stationary instability. Fluids with smaller Prandtl numbers will exhibit oscillatory instability with the critical Marangoni number varying as M0T½ where M0 depends on the Prandtl number and T is the Taylor number.

Electrochemical techniques are used to show that drag-reducing polymers decrease the magnitude and the frequency of mass transfer fluctuations. Measurements of the frequency spectrum of the mass transfer fluctuations allow calculation of the normal component of velocity fluctuations in the immediate vicinity of the wall. This information is used to interpret the observed effect of drag-reducing polymers on the rate of mass transfer. Eleni Vassiliadou SCOPEA paper by McConaghy and Hanratty (1977) presents results of the effect of dilute polymer solutions of Separan AP-30 on measurements of average mass transfer coefficients between a turbulent fluid and a pipe wall for fully developed velocity and concentration fields. They found that the decrease in the mass transfer rate, caused by the addition of polymers, at a given volumetric flow rate, is greater than the percent change in the pressure gradient, and that the use of an analogy between momentum and mass transfer overpredicts the amount by which the mass transfer rate is decreased.This paper shows how drag-reducing polymers affect the fluctuations in the mass transfer coefficient. It is based on measurements presented in theses by McConaghy (1974) and Vassiliadou (1983). The motivation for this paper is the testing of ideas that have emerged from recent numerical experiments that simulated turbulent mass transfer at a wall (Campbell and Hanratty, 1983). CONCLUSIONS AND SIGNIFICANCEDrag-reducing polymers cause a large decrease in_the magnitude of the mass transfer fluctuations, (P)''*/K, and change the character of the function describing the fluctuating mass transfer coefficient, k(t). The function does not have the large pulses found for a Newtonian fluid, and is described reasonably well by a Gaussian distribution. Furthermore, the frequency characterizing k(t), made dimensionless with wall parameters, is less than for a Newtonian fluid.Campbell and Hanratty (1983) transfer is the zero frequency value of the dimensionless spectral density function, W,(O), characterizing the normal component of velocity fluctuations in the immediate vicinity of the wall. This quantity is calculated from the measurements of the spectral function of the mass transfer fluctuations that are presented. It is found to decrease with increasing drag-reduction.The dependence of the time-averaged mass transfer coefficient on W,(O) is found to be the same as predicted in the numerical experiments of Campbell and Hanratty. However (k2)"'/E is found to be more strongly dependent on WB(0). This suggests that other hydrodynamic variables than W,(O) need to be considered.