(141j) From Microstructure to Macro-Rheology in Complex Fluids: Towards Targeted Rheology-Assisted Structural Assembly of Attractive Systems

The field of complex fluids encompasses a wide class of materials, which exhibit unusual mechanical responses to an applied stress or strain. In virtually all complex fluids, this rich and unusual mechanical response originates from a microstructure that responds to different applied stress or strain in specific and varied ways. Thus understanding the microstructure â?? macroscopic behavior relationship is a crucial step for systematically designing complex fluid materials for novel applications. The complex fluid landscape can be subdivided based on the particle-level interactions that govern their underlying microstructure and the resulting macro rheology. Attractive particulate-based systems are one such general class, with ever-growing applications in a wide range of consumer-product, food and other industries. These are, in their simplest form, liquid-liquid (emulsions) or solid-liquid (suspensions) binary mixtures in which the nature of interaction between the dispersed species is primarily attractive. As a result, nearest-neighbor pairs of particles are able to establish local stable energy minima. At the same time, the random nature of thermal fluctuations in a system, also referred to as Brownian motion, provides the particles with sufficient energy to experience other states and slowly build larger structures with other particles within their attraction range. However, any applied stress or strain effectively drives rearrangement and changes the energy landscape of every particle and thus the rheological behavior of these systems becomes complex under imposed flow conditions.

Another way to categorize complex fluids is based on their mechanical response. A sub-class of complex and structured fluids including (but not limited to) colloidal gels, nano emulsions, micellar solutions and crude oils can be identified as Thixotropic Elasto-Visco-Plastic (TEVP) materials. TEVPs, as suggested by their name, show a rich and complex set of rheological responses to imposed deformations in different regimes: below the yield stress, the microstructural network formed by individual particles remains intact and resists large deformations by external loading and the material acts as a viscoelastic solid. By increasing the applied stresses above the yielding point, the material starts to flow and undergoes plastic deformation and microstructural rearrangement over a wide range of length scales. Plastic flow results in a viscous-like response; however, due to constant formation and breakage of interparticle bonds that form the network, thixotropic behavior also begins to emerge. These time- and rate-dependent responses lead to other secondary effects including micro-phase separation, vorticity-aligned structure formation, shear banding, rigid plug development as well as shear-induced rejuvenation of the particle network. Continuum-level descriptions of TEVP fluids resort to describing such responses using ad hoc evolution equations for one or more scalar measures of this microstructural complexity. Although essential for defining the rheological response of any thixotropic fluid, these internal model parameters do not commonly correlate to specific physical processes in the test fluid. In this work we employ a mesoscale numerical simulation method that captures a canonical anisotropic and weakly attractive material microstructure at a sufficiently coarse-grained level that we can firstly reproduce characteristic rheological features of a TEVP fluid under flow, and secondly identify the sequence of microstructural changes that give rise to these macroscopic features.

In order to precisely understand the significance of microstructural rearrangements of an attractive system under flow on its rheology, accurate control over the initial configuration of particulate structure, as well as descriptive methods of visualizing the microstructure is required. This, in addition to difficulties in accurately controlling & quantifying the interaction between the particles, makes experimental study of the subject very challenging. Hence, computational methods have developed over the last few decades in order to mimic experimental conditions, with the advantage of being able to control the interaction types/strengths between the constituents as well as providing a detailed view of the microstructure under different conditions. As a result of the particle-level bond formation, and collective motion of attractive particles, multi-body and hydrodynamic interactions are essential in reproducing a realistic description of these systems. Thus, only during the past few years and after recent advances in computational capabilities, have these types of studies become possible on the dynamics of weakly-attractive systems.

In the first part of this work, we present a mesoscale simulation study of a model TEVP fluid. We perform Dissipative Particle Dynamics (DPD) simulations on model TEVP fluids consisting of 10 vol% 2D weakly attractive hexagonal solid particles reminiscent of the waxy crystalline particles observed in a waxy crude oil, which is known to exhibit many complex TEVP rheological signatures [1]. We substitute the traditional conservative force in DPD with a Morse potential in order to mimic the attractive nature of inter-particle interactions in these fluids.

Fij^C=-(â??U(r_ij)/2â??r_ij)e_ij with U(r_ij)=-Î?(2e^-κrij-e^-2κr_ij) (1)

Steady state flow curves for different values of the attraction strengths between the hexagonal disks are presented in Figure 1(a), confirming that the yielding behavior of TEVPs is captured in our DPD simulations. In order to correlate the microstructural changes of a TEVP fluid to its rheological response, we define a fabric tensor [2] formed by an ensemble average of the spatial configuration of particle-particle bonds:

Z=(ΣZ^p)/N with Z^p=Σn_i�n_i (2)

where n_i represents the unit vector along the center-center line of two bonded neighboring particles. The trace of this tensor gives the average number of bonds/links or the coordination number of the microstructure. The off-diagonal components of Z correspond to the average preferred orientation of particle bonds with respect to different directions, and the deviatoric normal components give insight with regards to structural anisotropies that develop in the sheared fluid. Figure 1(b) shows the evolution in tr{Z} (i.e. the coordination number) and the deviatoric components of the fabric tensor as a function of the accumulated strain in the start-up of steady shear flow over a wide range of shear rates.

After validating the capability of the model in reproducing realistic and precise microstructural information and macroscopic properties of a model TEVP fluid, we present in the second part of this work a Time-Peclet-Transformation (TPT) procedure to construct dynamical phase diagram for attractive systems of different mechanical properties. Using spherical particles, and the dimensionless ratio of the shear forces to attractive forces between the particles (Peclet number) as the key dimensionless group, we identify the interdependent roles of different deformation parameters such as strain and strain rate, on the final state of the system.

In this work we will show that a mesoscale model that conserves mass and momentum both locally and globally, and thus preserves multi-body hydrodynamics intrinsically, successfully reproduces the key features of a model TEVP fluid including flow instabilities and coarsening dynamics at rest. In addition to reproducing the experimental results for these fluids, our model provides a detailed description of the microstructure that results in such rich rheological behavior. The fabric tensor provides a quantitative microstructural measure of the system that correlates to the macroscopic stress response in a TEVP fluid in both steady and transient states. The evolution in the components of Z with strain provides quantitative insight on the flow instabilities and secondary structures that develop in the sheared microstructure. The TPT procedure provides a mechanism to systematically develop phase map for attractive systems, based on their flow and mechanical properties. This will pave the way for exploiting the largely-unexplored rheology of such systems, for designing novel materials with engineered properties.

References:

1. C. J. Dimitriou and G. H. McKinley, Soft Matter, 10(35):6619-6644 (2014).

2. T. Olsen and K. Kamrin, Soft Matter, 11(19):3875-3883 (2015).