60th Annual Report on Research 2015

The present project proposed two main topics of research: 1) Effects of hydrodynamics on colloidal gellation and 2) Particles in a turbulent flow. A summary of the advances so far follows.

Role of hydrodynamics in gelation. Some authors claim that hydrodynamic interactions between colloids is able to reduce the colloid volume fraction f for gellation to occur and even alter the structure of a colloidal gel. To falsify this statement computational work are required (as indeed experiments cannot turn-out hydrodynamics). During the first year of research we were devoted to: i) reproduce the studies done so far ii) develop hydrodynamic tools and Monte Carlo codes for thermodynamic information, post-processing and visualization tools and iii) enlarge bibliographical study and design definitive research plans.

Concerning i) we have checked two main papers on the computaional field claiming the relevance of hydrodynamics on cluster formation and gelation. Whitmer and Luijten [J. Phys. Chem. B 2011, 115, 7294–7300 ] working with depletion potentials (short ranged attracting) and Cao et al. [J. Colloid and Interface Sci. 368, 86–96 (2012)] considering DLVO-like interaction (short range atraction and long range repulsion). These colloidal interactions lead to different gelation routes forming monomer gels or cluster phase in the case of repulsive DLVO. This ACS ND project started with Adolfo Vazquez-Quesada, who moved soon after to Swansea University (UK). We performed a throrough analysis of the work of Whitmer and Luijten, using different computational techniques: Monte Carlo (NVT), Brownian dynamics without hydrodynamics (BD)and our colloidal hydrodynamic code (FLUAM based on Stochastic Immersed Boundary Method). We also prepared [Vazquez-Quesada et al. J. Chem. Phys. 141, 204102 (2014)] a multiblob model for FLUAM with lubrication. Surprisingly, all these different methods produced the same outcome (cluster distribution), in clear contradiction with the conclusions of Whitmer et al. This new result prove that, at least in this case, hydrodynamics does not alter the cluster structure (although it does alter the time scale for cluster formation). After Adolfo's departure, in March 2015 we finally welcome Mingzhou Yu, a new postdoc student from China. For training purposes, we first analyzed Cao et al. graph on the probability of the angle between just 3 colloids, discovering it contains errors. Hydrodynamic delays bond formation, but the process is essentially governed by a Kramer escape time ruled by the jump in the (angle dependent) free energy (see Figure 1). Lubrication will be studied along with Aleksandar Donev at Courant Institute. Angel Nuñez, a new postdoc in the group is determining the gelation threshold, which requires all the techniques in the field and substantial GPU time. We found percolating structures at lower volume fractions than reported, indicating that Cao's results are based on too short runs and small boxes. Currently we are analyzing the role of hydrodynamics in the different gelation routes (see Figure 2).

We pursue a broader scenario where to place our main question: “under what circustances does dynamics affect gelation?”. Gelation can be reversible (cluster network forming and breaking under equilibrium) or irreversible (under large attractive interaction). Friction forces cannot alter a real equilibrium state so hydrodynamics might, at most, be relevant in irreversible gelation. Irreversible gelation takes place at low temperatures, below the coexistence line for gas and liquid-like colloidal order and requires preliminar thermodynamic analyses. We will focus on Frenkel's law of corresponding states (gelation is governed by the second virial coefficient) corroborated in a relevant paper [Nature, 453, 499 (2008)] under reversible gelation. In long range repulsion potentials we will study the regime where clusters (and not monomers) are the interacting units (Nature, 432, 492, 2004). During my Master lectures, I met Raúl Pérez Pelaez, a smart graduate student willing to work in this nice project. We hired him by July 2015 with the ACS grant funds. As a training, he soon coded his own Monte Carlo tools (isobaric and Gibbs Ensembles) to locate the coexistence line for arbitrary colloid-colloid interactions. In 2 months he also produced new visualization tools and several extensions in FLUAM. Raul Perez is learning fast and next year we will start a study on a gellation problem where flow is relevant: wax formation induced by gellation of micron-size paraffine crystals.

Particle turbulence. In collaboration with Anne Dejoan (CIEMAT, Spain) we prepared FLUAM code to run in other architectures (ZETA GPU cluster) and tested its limits in this highly memory demanding problem: decaying turbulence. Figure 3 (a) shows the turbulent kinetic energy and disipation rate time histories for the unladen flow for two values of the Reynolds number based on the caracteristic Taylor length scale. These turbulence statistics are computed from numerical integration of the energy spectrum and dissipation spectrum. Results are in agreement with previous studies, in particular the decay exponent approaches a consistent value with previous works (see Burton & Eaton, J. Fluid Mech., 2005 and references in). An instantaneous picture of the vorticity field is represented in Fig. 3 (b). Next part of the work considered particle-laden turbulent flows with different particle inertia. The particle RMS velocity in Fig. 3 (c) show that Lagrangian fluid tracers (excess density rp=0) perfectly agree with Eulerian statistics. RMS velocity of inertial particles represented by particles with diameter as small as the Kolmogorov length scale are close to fluid tracers after the Stokes inertial time as expected. However, when described by the multi-blob model (particle diameter larger then the Kolmogorov length), the RMS velocity decreases in agreement with the low-pass filtering effect reported in previous studies (J. Fluid. Mech. 651, 81, 2010). We will focus in determining the cross-over from the Stokes inertia to inertia dominated by either finite size and/or excess density effects. We expect to continue this research next year, the rate depending on the availability of our collaboration node in CIEMAT.

Illustration 1: Gellation processes for the DLVO potential and structrure factor

Illustration 3: Three colloids under DLVO potential.

Illustration 2: Swarm of colloids in decaying turbulence