| A turbulent Newtonian fluid in many aspects behaves like a non-Newtonian fluid, exhibiting visco-elastic and memory effects as shown by Rivlin [1], Crow [2], Liepmann [3], Lumley [4], Builtjes [5], and Huang [6], among others. Thixotropy is a flowinduced phenomenon, which occurs in gels, emulsions, foods, coatings, and many other materials. Specific examples include milk, ink, paints, blood, and mayonnaise. The defining characteristic of a thixotropic fluid is the change in its material properties, such as viscosity and elasticity, with time under shear; see, for example, Mewis [7] and Barnes [8]. In this work, we shall focus on the thixotropic effect of a turbulent Newtonian fluid from the perspective of the natural viscosity of turbulence, in order to separate the natural viscosity of turbulence from the elastic effect of turbulence, noting that a study on the latter would be an interesting work on the normal-stress effect, i.e., the Weissenberg effect of turbulence [9, 10]. The natural viscosity is an intrinsic property of a fluid, as ¹ shown by Truesdell [11, 12] in 1964 and 1974. For instance, Lumley [13] mentioned that for a dilute polymer solution its viscosity is usually characterized by the zero-shear intrinsic viscosity for simple shear flow, namely, the natural viscosity in the sense of Truesdell [11]. Therefore, to investigate the thixotropic effect of a turbulent Newtonian fluid, we can compare the natural viscosity of turbulence with the natural viscosities of the typical thixotropic fluids to show whether or not a turbulent Newtonian fluid behaves like a thixotropic fluid. To this end and for illustration, we shall seek an explicit expression for the natural viscosity of a turbulent Newtonian fluid based on the Reynolds stress transport equation. However, the Reynolds stress transport equation is not closed unless is modelled, and its closure equation, such as a second-order closure model, must be provided before any calculations to be performed. |
