Shear-banding fluid(s) under time-dependent shear flows. Part II: A test of the Moorcroft-Fielding criteria

Abstract

Complex systems often exhibit shear banding-the coexistence of two different states characterized by their internal structuring and local shear rates. For some of them, the heterogeneous flow corresponds to the final steady state response while for others, shear banding can only be transient, the banding structure healing back to homogeneous flow in the ultimate steady state after long-lived periods. In order to explain the diversity of observations, Moorcroft and Fielding have established general criteria for the onset of banding in time-dependent flows of complex systems, ranging from polymeric fluids to soft glassy materials [Moorcroft et al., Phys. Rev. Lett., 2013, 110, 086001]. The proposed criteria are based on the time evolution of the bulk rheological response function of the system to a given time-dependent flow protocol and are associated with a specific signature in the mechanical response. In this contribution, we test the validity of these criteria in the case of two common time-dependent flow protocols: a step stress and a shear startup. Two types of fluids are examined. On the one hand, a wormlike micelles system exhibiting steady shear banding is studied experimentally, using rheometry coupled with direct visualisations and particle image velocimetry. On the other hand, we analyse previous literature on yield stress fluids exhibiting transient shear banding. Under creep flow, for both types of fluids the onset of banding arises in a time window compatible with the Moorcroft-Fielding criterion. However, the mechanical signature, i.e. the shape of the bulk mechanical signal as a function of time is not the one expected within some of the specific models with which the general Moorcroft-Fielding criteria were tested numerically. Under shear startup, both types of fluids behave differently. The criterion holds for yield stress fluids, the onset of banding arising just after the stress overshoot, as expected. On the contrary, for wormlike micelles the window of instability is delayed, even if the overshoot clearly plays a crucial role in the nucleation of the shear-induced structures. Regardless of the flow protocol or the system, wall slip seems to go hand in hand with banding indicating that it is a key ingredient to take into account.

I. Sommaire

Shear banding is an ubiquitous phenomenon in complex fluids flows where it is usually associated with the concentration of the shear in some regions of the flow¹,103. In most common situations, shear banding results in a heterogeneous flow, in which the fluid splits into two macroscopic coexisting bands of diﬀering local shear rates and internal mesostructures for the same shear stress. The spatial organisation of the flow corresponds to two shear bands stacked along the flow gradient direction with the interface between the bands lying in the velocity-vorticity plane.

Over the past fifteen years, shear banding has been observed in various classes of complex fluids having very diﬀerent mesoscopic architectures, including polymeric fluids and soft glassy materials (SGM). Shear banding has been first reported in surfactant wormlike micelles21,77,100, and has since been observed in lyotropic lamellar surfactant phases101,102, micellar systems of block copolymers solutions79, polymer solutions15,61 (even if still controversial73), biological fluids18,66, star polymers98,99, emulsions6,91, suspensions49,82, colloidal gels25,50 and microgels32,34. For exhaustive bibliogra phy regarding experimental evidence of shear banding the reader can refer to various reviews that encompass the diﬀerent classes of complex fluids9,13,33,43,69,78,103.

K_\gamma \equiv \frac{d\sigma}{d\gamma} < 0

Among these systems, not all display shear banding as ultimate steady state. Indeed shear banding has been reported to be only transient in polymer solutions55 and in various SGM including simple yield stress fluids such as soft repulsive glasses32,34,35 and some thixotropic and aging materials such as attractive colloidal gels and suspensions49,52,82. In these cases, a homogeneous flow was ultimately observed after long-lived induction periods, during which shear bands persisted.

Divoux, T., Fardin, M. A., Manneville, S., and Lerouge, S., “Shear banding of complex fluids,” Annual Review of Fluid Mechanics 48, 81–103 (2016), https://doi.org/10.1146/annurev-fluid-122414-034416. ↩︎