Zsigmond Varga

Linear viscoelasticity of attractive colloidal dispersions

The rheology of a semidilute dispersion of colloids having short-ranged attractions is studied. A depletion potential is chosen as a model for the attractive interaction and arises from nonadsorbing polymer dispersed with the colloids. The complex viscosity of these materials can be calculated by investigating their response to weak oscillatory shear. A first order expansion in small rates of deformation is used to solve for the microstructure and stress in the dispersion. Additionally, the effect of hydrodynamic interactions is studied via the excluded annulus model, which views the radius at which hard-sphere interactions occur as a barrier that resides beyond the hydrodynamic radius of the particles. This treatment allows a continuous variation of the hydrodynamic interaction strength. The viscoelastic response exhibits a sharp transition when going from weak attraction to strong attraction. Below a critical strength, increasing the interparticle attraction reduces the low frequency viscosity. Strong a...

Normal modes of weak colloidal gels

The normal modes and relaxation rates of weak colloidal gels are investigated in calculations using different models of the hydrodynamic interactions between suspended particles. The relaxation spectrum is computed for freely draining, Rotne-Prager-Yamakawa, and accelerated Stokesian dynamics approximations of the hydrodynamic mobility in a normal mode analysis of a harmonic network representing several colloidal gels. We find that the density of states and spatial structure of the normal modes are fundamentally altered by long-ranged hydrodynamic coupling among the particles. Short-ranged coupling due to hydrodynamic lubrication affects only the relaxation rates of short-wavelength modes. Hydrodynamic models accounting for long-ranged coupling exhibit a microscopic relaxation rate for each normal mode, λ that scales as l^{-2}, where l is the spatial correlation length of the normal mode. For the freely draining approximation, which neglects long-ranged coupling, the microscopic relaxation rate scales as l^{-γ}, where γ varies between three and two with increasing particle volume fraction. A simple phenomenological model of the internal elastic response to normal mode fluctuations is developed, which shows that long-ranged hydrodynamic interactions play a central role in the viscoelasticity of the gel network. Dynamic simulations of hard spheres that gel in response to short-ranged depletion attractions are used to test the applicability of the density of states predictions. For particle concentrations up to 30% by volume, the power law decay of the relaxation modulus in simulations accounting for long-ranged hydrodynamic interactions agrees with predictions generated by the density of states of the corresponding harmonic networks as well as experimental measurements. For higher volume fractions, excluded volume interactions dominate the stress response, and the prediction from the harmonic network density of states fails. Analogous to the Zimm model in polymer physics, our results indicate that long-ranged hydrodynamic interactions play a crucial role in determining the microscopic dynamics and macroscopic properties of weak colloidal gels.

Large scale anisotropies in sheared colloidal gels

The steady shear of weak colloidal gels results in vorticity aligned density fluctuations. These have been measured in neutron scattering and flow dichroism experiments and observed with microscopy coupled with rheometer tools of varying geometry. The origins of this instability remain a mystery, and discrete element simulations of colloidal gels have to date failed to reproduce the phenomena. Novel Brownian Dynamics simulations with hydrodynamic interactions show that this instability is fluid mechanical in origin, and results from long-ranged hydrodynamic interactions, which stabilize the vorticity aligned flocs under flow. Squeeze flows between vorticity aligned flocs prevent collisions and realignment under flow, thus promoting stability of large-scale, vorticity aligned density fluctuations. A single force scale—the most probable rupture force for the intercolloid bonds—collapses the microstructural and rheological data, including the characteristic size of the vorticity aligned flocs and the virial ...

Structure and Relaxation in Solutions of Monoclonal Antibodies

Reversible self-association of therapeutic antibodies is a key factor in high protein solution viscosities. In the present work, a coarse-grained computational model accounting for electrostatic, dispersion, and long-ranged hydrodynamic interactions of two model monoclonal antibodies is applied to understand the nature of self-association, predicting the solution microstructure and resulting transport properties of the solution. For the proteins investigated, the structure factor across a range of solution conditions shows quantitative agreement with neutron-scattering experiments. We observe a homogeneous, dynamical association of the antibodies with no evidence of phase separation. Calculations of self-diffusivity and viscosity from coarse-grained dynamic simulations show the appropriate trends with concentration but, respectively, over- and under-predict the experimentally measured values. By adding constraints to the self-associated clusters that rigidify them under flow, prediction of the transport properties is significantly improved with respect to experimental measurements. We hypothesize that these rigidity constraints are associated with missing degrees of freedom in the coarse-grained model resulting from patchy and heterogeneous interactions among coarse-grained domains. These results demonstrate how structural anisotropy and anisotropy of interactions generated by features at the 2-5 nm length scale in antibodies are sufficient to recover the dynamics and rheological properties of these important macromolecular solutions.

Modelling a hydrodynamic instability in freely settling colloidal gels

Attractive colloidal dispersions, suspensions of fine particles which aggregate and frequently form a space spanning elastic gel are ubiquitous materials in society with a wide range of applications. The colloidal networks in these materials can exist in a mode of free settling when the network weight exceeds its compressive yield stress. An equivalent state occurs when the network is held fixed in place and used as a filter through which the suspending fluid is pumped. In either scenario, hydrodynamic instabilities leading to loss of network integrity occur. Experimental observations have shown that the loss of integrity is associated with the formation of eroded channels, so-called streamers, through which the fluid flows rapidly. However, the dynamics of growth and subsequent mechanism of collapse remain poorly understood. Here, a phenomenological model is presented that describes dynamically the radial growth of a streamer due to erosion of the network by rapid fluid back flow. The model exhibits a finite-time blowup -- the onset of catastrophic failure in the gel -- due to activated breaking of the inter-colloid bonds. Brownian dynamics simulations of hydrodynamically interacting and settling colloids in dilute gels are employed to examine the initiation and propagation of this instability, which is in good agreement with the theory. The model dynamics are also shown to accurately replicate measurements of streamer growth in two different experimental systems. The predictive capabilities and future improvements of the model are discussed and a stability-state diagram is presented providing insight into engineering strategies for avoiding settling instabilities in networks meant to have long shelf lives.