The Oldroyd-B fluid in elastic instabilities, turbulence and particle suspensions

The Oldroyd-B fluid has become the starting point for almost all complex flow calculations and analysis involving behavior of dilute polymer solutions. reasons this are clear: based on kinetic theory high molecular weight “phantom” chains near equilibrium, resulting model, in its simplest form, produces a single mode description solution constitutive equation terms symmetric dyad order parameter. physical connection to individual is therefore unambiguous through end-to-end configuration tensor. from mathematical coupled Cauchy’s motion continuity been examined decades strengths weaknesses predicting features non-linear viscometric non-viscometric flows well known. Moreover, “simple” extensions (e.g. FENE-P model) can ameliorate most serious these shortcomings. For example, multi-mode model provide quantitative predictions linear viscoelasticity wide range Remarkably, even with shortcomings, invaluable at least qualitatively, as purely elastic instabilities, turbulent drag modification, effective rheology particles suspended While remaining mindful model’s any student diverse fields may find an important point.