Colloquium: Theory of drag reduction by polymers in wall-bounded turbulence

Abstract

The flow of fluids in channels, pipes or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases many-folds when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered in the mid-twentieth century that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a "skin" or a "bulk" effect. In this colloquium review we first summarize the phenomenology of drag reduction by polymers, stressing both its universal and non-universal aspects, and then proceed to review a recent theory that provides a quantitative explanation of all the known phenomenology. We treat both flexible and rod-like polymers, explaining the existence of universal properties like the Maximum Drag Reduction (MDR) asymptote, as well as non-universal cross-over phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally we also discuss other agents for drag reduction with a stress on the important example of bubbles.

Statistical properties of turbulence: An overview

“…For a recent discussion of drag reduction in pipe or channel flows we refer the reader to Ref. [41]. Here we concentrate on other phenomena that are associated with the addition of polymers to turbulent flows that are homogeneous and isotropic.…”

“…There are two dimensionless control parameters in this case: Re and the Weissenberg number W e, which is a ratio of the polymer-relaxation time and a typical shearing time in the flow (some studies [41] use a similar dimensionless parameter called the Deborah number De). Dramatically different behaviours arise depending on the values of these parameters.…”

“…If, instead, the flow is turbulent in the absence of polymers, i.e., we consider large-Re flows, then the addition of polymers leads to the dramatic phenomenon of drag reduction that has been known since 1949 [92]; it has obvious and important industrial applications [40,41,[93][94][95]. Normally drag reduction is discussed in the context of pipe or channel flows: on the addition of polymers to turbulent flow in a pipe, the pressure difference required to maintain a given volumetric flow rate decreases, i.e., the drag is reduced and a percentage drag reduction can be obtained from the percentage reduction in the pressure difference.…”

“…Turbulence also provides a variety of challenges for fluid dynamicists [5,[11][12][13], astrophysicists [14][15][16][17], geophysicists [18,19], climate scientists [20], plasma physicists [15][16][17]21,22], and statistical physicists [23][24][25][26][27][28][29][30][31][32]. In this brief overview, written primarily for physicists who are not experts in turbulence, we concentrate on some recent advances in the statistical characterisation of fluid turbulence [33] in three dimensions, the turbulence of passive scalars such as pollutants [34], two-dimensional turbulence in thin films or soap films [35,36], turbulence in the Burgers equation [37][38][39], and fluid turbulence with polymer additives [40][41][42]; in most of this paper we restrict ourselves to homogeneous, isotropic turbulence [33,43,44]; and we highlight some similarities between the statistical properties of systems at a critical point and those of turbulent fluids [31,45,46]. Several important problems that we do not attempt to cover include Rayleigh-Bénard tur...…”

Effect of a Polymer Additive on Heat Transport in Turbulent Rayleigh-Bénard Convection

“…It has been known for about six decades that minute quantities of a polymer dissolved in a fluid can reduce significantly the drag experienced by turbulent flows near solid surfaces (see, for instance, [1,2]). During this time literally thousands of papers have been written about this technologically important problem.…”