The Sherwood number and drag coefficient for a single gas bubble moving in a power law fluid and a Bingham plastic fluid are obtained using perturbation methods. The perturbation parameters for power law and Bingham plastic fluids are m (= n – 1/2) and E (=  τ oR/U μ o), respectively. It is found that in the case of power law fluid, mass transfer and drag increase with increasing pseudoplasticity. These theoretical results are found to be in good agreement with the available experimental data and the data obtained in the present study. In the case of Bingham plastic fluid, mass transfer and drag are found to increase with increase in the Bingham number NB (= 2ε). Contours of plug flow regions, where local stresses are less than the yield stress, are obtained as a function of the Bingham number NB. These results qualitatively predict the zero terminal velocity observed for bubble motion in liquids with very high yield stress. They are also in good agreement with the trends of the results obtained previously for solid sphere motion in Bingham plastic fluids.

We use Brownian dynamics simulation to study coil-stretch transition of macromolecules in solution. Into a simple elongational flow field, we introduce freely jointed bead-rod chain model molecules in their coiled and stretched states, and follow the conformational changes. We find good agreement of our simulation results with the available theoretical predictions for low and high strain rates (⑀ ). At the intermediate elongation rates ͑near the onset of coil-stretch transition͒ of the flow field, we find that the residence time required for stretching of an initially coiled chain can be extremely large as compared to predicted (1ϩln(ͱN))⑀ Ϫ1, especially for the non-free-draining case. Hence, the chain conformation is dependent on the initial state of the chain molecule for residence time as long as 100⑀Ϫ1 . Thus, hysteresis is predicted when chain residence time in such an elongational flow field is limited, as in practical situations. Further, at such intermediate ⑀ , the chain molecule is seen to undergo Brownian fluctuation induced jumps between a randomly coiled state and another partially stretched state. This suggests the existence of more than one equilibrium conformation that is unstable to Brownian fluctuations.

The presence of ionic interactions in polymers has been utilized to stabilize macromolecular assemblies in dilute solutions. The ionic aggregates display unique solution properties. Molecular associations in such polymers lead to higher viscoelasticity compared to that in the nonionic polymeric precursor. Such ionic aggregates are shown to lead to oil-soluble drag reducers with improved shear stability. In this study, we found that the drag reduction levels in the ionomer can be about twice as much as those in the nonionic polymeric precursor. On the other hand, a study of the shear stability indicates that the decay of the drag reduction activity for the nonionic polymer is more than twice that of its derived ionic polymer. Interestingly, the solution characteristics of ionic aggregates improve with increasing temperature, as manifested by enhanced drag reduction levels due to such a polymer, whereas for the nonionic polymer the reverse trend is observed.The findings of this work may have a significant bearing on the design of new generation drag reducers.

Enhanced shear stability of associating polymers during drag reduction observed recently has been attributed to the breakage of reversible associations (e.g., hydrogen bonds) in preference to covalent bonds in the polymer backbone. A simple mechanistic analysis of a perfectly "zipped" assembly of fully extended bead rod chain model of two macromolecules in steady elongational flow is presented. It explains the enhanced stability as a result of (i) distribution (near the vulnerable chain center) of the drag tension into the two parallel "zipped" chains, and (ii) reduction of the drag force due to the enhanced hydrodynamic shielding. Some guidelines for optimum design of shear stable and effective drag reducing macromolecules have been deduced.

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