Macromolecules drag reduction

A review on drag-reducing polymers is given in the literature [1359]. It has been suggested that drag reduction occurs by the interactions between elastic macromolecules and turbulent-flow macrostructures. In turbulent pipe flow, the region near the wall, composed of a viscous sublayer and a buffer layer, plays a major role in drag reduction. 

C.L. McCormick, RD. Hester, S.E. Morgan, and A.M. Safieddine, Water-soluble copolymers. 30. Effects of molecular structure on drag reduction efficiency, Macromolecules, 23(8) 2124-2131, April 1990. 

In order to obtain a higher effectiveness of drag reduction, it was therefore more convenient to produce the actual experimental solution from the more diluted stock solution. This is already an indication that the state of solution of macromolecules plays an important role in the interpretation of the results. However, a molecular weight of 10.1 106 g/mol and a concentration of 1000 ppm is just below the critical concentration c (this c is based on viscometric measurements) (Kulicke 1982). Above this critical concentration, mechanical entanglements ensure between the macromolecules. Beneath this limit, interactions between the molecules come into... 

Works published by Brostow (1984) as well as by Kim (1986) seem to indicate that the chemical structure correlates with the stability of a macromolecule in turbulent flow. As mentioned above, the drag reduction of polymeric fluids seems to be linked... 

In turbulent flow, the macromolecules are also believed to experience burst-induced elongation. However, it has to date not been possible to formulate structure-property relationships which allow an ad hoc prediction of the onset of mechanical degradation and its influence on drag reduction. 

Hlavacek B, Rollin LA, Schreiber HP (1976) Drag reduction effectiveness of macromolecules Polymer 17 81... 

Savins JG (1964) Drag reduction characteristics of solution of macromolecules in turbulent pipe flow Soc Petrol Eng J 4 203... 

McCormick, C. L., Hester, R. D., Morgan, S. E., and Safleddine, A. M., Water-soluble copolymers 31. Effects of molecular parameters, solvation, and polymer associations on drag reduction performance. Macromolecules, 23, 2132-2139 (1990). 

Virk, P. S., Elastic sublayer model for drag reduction by dilute solutions of hnear macromolecules, J. FluidMech., 45, 417-440 (1971). 

The drag reduction and drag increase appear to be related properties of polymer macromolecules with the following similarities. 

The polymers which give drag reduction and drag increase have all large unbranched or moderately branched macromolecules with extremely high molecular weights. 

The initial drag reduction is the same in water and water-isopropanol mixture and the loss of effectiveness is due to the degradation of the macromolecules. The final properties are similar in the 2 solvents, but, the rate of degradation is greater in distilled water. 

On this basis one can obtain additional information about the dependence of the friction drag reduction effect on the size of macromolecules. Let us, to this effect, use the results of ref. C4]. 

In turbulent flow conditions, both rigid and flexible macromolecules diluted solutions exhibit drag reduction, which was described for the first time by Toms (25) and often reviewed since [Hoyt (26), Berman (27), Virk (28)]. Many practical applications have been proposed for this effect increase of the range of water-hose nozzles, better efficiency of fluidized beds and central heating, increase of the flow rate in pipe lines, increase of the speed of torpedos etc... But the fundamental origin(s) of drag reduction is still debated. 

Virk, P.S., An Elastic Sublayer Model for Drag Reduction by Dilute Polyme Solutions of Linear Macromolecules , J. Fluid Mech., Part 3, 417 (1971... 

A widely accepted hypothesis of the mechanism responsible for drag reduction is that the microscale eddies in the bufferzone of the turbulent boundary layer are suppressed. It is thought that the macromolecules (injected or pre-mixed) affect the sublayer instability which produces jet-like vortices, the so-called "bursts", which erupt into the boundary layer and lead to the production of much turbulent energy. Recent experiments have shown [l] that the polymer molecules seem to act as a "barrier" restricting communication across the boundary layer so that the fluid near the wall flows in a more laminar manner [2]. 

The drastic reduction in wall shear stress caused by the addition of small amounts of linear macromolecules to a flowing solvent, was first reported by Toms, some 36 years ago, and later supported by numerous experiments. A similar effect had been observed earlier, during the second world war, in study of gasoline flow following addition of aluminum soaps. The report of those findings, however, was not published at that time and only a patent appeared much later [1]. This case was probably the first industrial application of drag reductions. ... 

Hydrodynamic drag reduction is an unusual effect involving macromolecules in a turbulent flow for very dilute solutions, the resistance to flow can be reduced compared to that of the pure solvent. Indeed, the presence of high-molecular-weight polymer chains can produce large levels of drag... 

Therefore, in the case of turbulent flow, the drag reduction effect depends by the individual macromolecules stretching degree [1086]. By photographing J.W. Hoyt succeeded to visualise the elongated particles [1087]. The possible extrapolations and the limits of this effect have been defined by Hoyt starting from the friction velocity, u, caused by the friction to the pipe wall, which is expressed as ... 

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