Particle Suspensions in Viscoelastic Fluids: Freely Suspended, Passive, and Active Matter
Authors: Jain Anika , Zhang Anni , Binagia Jeremy , Shaqfeh Eric S. G. 
Published: July 2022

The rheology of suspensions of rigid particles in polymeric fluids is a particularly important field of study as these materials find applications in a variety of industries, such as consumer product applications (e.g., foods, pharmaceuticals, personal care products), materials design applications (e.g., injected composite materials, adhesives and coatings, paints), energy applications (e.g., fracking fluids), and biomedical devices. Understanding how these multi-phase materials respond to processing flow conditions helps in process optimization, such as designing more efficient processes that save time and energy and preserve the desired final properties. The rheology of these materials can be complex when compared to suspensions in a Newtonian fluid. In this context and as discussed in previous chapters, non-colloidal suspensions of rigid particles in Newtonian fluids exhibit no shear rate dependence in steady shear flow for particle volume fractions less than 30% (Chan and Powell, 1984; and Gadala-Maria and Acrivos, 1980), but this is not the case when the suspending fluid is polymeric. While the mechanics of suspended particles in Newtonian fluids enjoys a long and detailed history as discussed in previous chapters, the mechanics of suspended particles in non-Newtonian fluids is not nearly as complete or organized. The particle-fluid interactions in an elastic fluid, even in the dilute particle limit, are difficult to tackle analytically due to non-linearities in the governing equations that increase the system complexity. While this statement is true for almost all non-Newtonian fluids far fromthe “weak flow” or “nearlyNewtonian” limit, there has been rapid progress in understanding particle suspensions in polymeric solutions in the last few years. Note the difficulty here, succinctly put, is that the polymers in solution act as “other particles” in a very similar sense to the “other particles” in a non-dilute particle suspension. Thus, for example, the correction to the Einstein viscosity (i.e., the first correction to the effective viscosity for an infinitely dilute suspension of spherical particles) when the suspending fluid is viscoelastic was only very recently calculated (Einarsson et al., 2018), and most of the work in achieving this resultwas focussed on calculating the average response of the nonlinear fluid to the particle rather than the particle response to the nonlinear fluid. Moreover, many of the simple rheological quantities of these suspensions, as measured experimentally for relatively concentrated suspensions with different particle sizes or shapes (Ohl and Gleissle, 1992, 1993; Aral and Kalyon, 1997; Zarraga et al., 2001; Mall-Gleissle et al., 2002; Scirocco et al., 2005; Haleem and Nott, 2009; Tanner et al., 2013; and Dai et al., 2014), are largely different from either similar suspensions in Newtonian fluids or the elastic suspending fluid without particles as can be observed in Fig. 8.1. This points to a scientific research area where real impact can be envisaged.