Origin of apparent viscosity in yield stress fluids below yielding

For more than 20 years it has been debated if yield stress fluids are solid below the yield stress or actually flow; whether true yield stress fluids exist or not. Advocates of the true yield stress picture have demonstrated that the effective viscosity increases very rapidly as the stress is decreased towards the yield stress. Opponents have shown that this viscosity increase levels off, and that the material behaves as a Newtonian fluid of very high viscosity below the yield stress. In this paper, we demonstrate experimentally (on four different materials, using three different rheometers, five different geometries, and two different measurement methods) that the low-stress Newtonian viscosity is an artifact that arises in non–steady-state experiments. For measurements as long as 10 seconds we find that the value of the “Newtonian viscosity” increases indefinitely. This proves that the yield stress exists and marks a sharp transition between flowing states and states where the steady-state viscosity is infinite —a solid! Copyright c © EPLA, 2009 Introduction. – Yield stress materials can be either “fluid” or “solid”; a typical example is toothpaste, that flows (i.e., is fluid) when pushed out of the tube but no longer flows (is solid) under the influence of gravity while posed on a toothbrush. Such materials are of paramount importance for a large number of applications; examples are concrete, oil drilling fluids, granular and building materials, cosmetic products, and foodstuffs. For all these yield stress fluids, it is important to understand their flow characteristics and notably the yield stress to correctly predict their flow behavior. The canonical yield stress picture assumes that the material is solid until a critical shear stress is exceeded. Above that stress the material yields and subsequently flows. The Bingham or the Herschel-Bulkley (H-B) models are widely used to describe such behavior; the latter reads: σ= σy +αγ̇ , where σ is the shear stress (the subscript y indicates the yield stress) and γ̇ the velocity gradient or shear rate; a and n are adjustable model parameters. This model can successfully describe the flow behavior of “simple” yield stress fluids such as carbopol, emulsions, foams, etc. over large ranges of shear rates. In thixotropic yield stress fluids, the viscosity and yield stress increase with time when the sample is at rest (called aging), (a)E-mail: [email protected] but decrease with time under shear (called rejuvenation). This leads to time-varying viscosity and yield stress, viscosity bifurcation, and other interesting phenomena. (For a recent mini-review see [1].) In this study we have examined only simple yield stress fluids, but we briefly compare our results to measurements on thixotropic yield stress fluids. For our discussion, the key prediction of the H-B and other simple yield stress models is that the viscosity (defined as the ratio of the stress and shear rate) diverges continuously when the yield stress is approached from above. Hence, below the yield stress, the viscosity is infinite, and the material behaves as a solid. Figure 1A), depicts a H-B fit to the viscosity of a carbopol sample, from which it appears that the viscosity indeed diverges as σ is decreased towards σy. However, for a number of years there has been a controversy as to whether or not the yield stress marks a transition between such a “solid” and a “liquid” state, or if it instead marks a transition between two liquid states with very different viscosities. That is, if true yield stress fluids actually exist. Probably the earliest work that seriously questions the solidity of yield stress fluids below σy is a 1985 paper by Barnes and Walters [2]. They show data on carbopol samples apparently demonstrating the existence of a finite viscosity plateau (i.e. Newtonian