61st Annual Report on Research 2016

During the second year of this proyect we have opened a novel computational route to study colloidal and polymer dynamics and built an ultra-fast GPU code to solve particle dynamics. We call it “Universally Adaptable Multiscale Molecular Dynamics”, UAMMD (https://github.com/RaulPPelaez/UAMMD). This fully Lagrangian code, which complements our Eulerian-Lagrangian FLUAM, is now being used several research programs listed below. Concerning the two initial objectives, we have concluded 1) “the study on the effects of hydrodynamics on colloidal gellation” and the results will be sent for publication over 2017. The problem 2) “particles in a turbulent flow” has been delayed due to force majeur (see below).

Project 1) Role of hydrodynamics in gelation. We have finished a first paper (to be submitted) and will submit several others over the first half of 2017. Our main conclusion is the following. Contrary to what has been recently published, we do not find evidence that hydrodynamics radically changes the medium size cluster morphology (making them more elongated). In fact, hydrodynamics do affect the rate of colloidal gelation by fastening up the encounters between clusters of typically more than 10 colloids. The hydrodynamic friction of a cluster of size “n” grows like the cluster radius, R(n) which scales like R(n) ~ n^1/b . The exponent “b” is somewhat larger than 2 and depends on the type of aggregation (diffusion or reaction limitted). Therefore, the diffusion coefficient of the cluster of size n (inverse of the friction) scales like D(n) ~ n^-1/b. By contrast, without hydrodynamics, the diffusion of the center of mass of collection of n colloids scales like 1/n, so the diffusion of a cluster “n” is enhanced by a factor n^1-1/b > n^1/2 . For small “n” (small clusters) hydrodynamics slows down diffusion due mutual friction, but it speed up the diffusion of clusters of about n>10. Other part of our work now focuses on the characteristic times for cluster formation and on finding a master curve for gellation over time, and the effects of the potential (purely attractive versus attractive at short distances and repulsive at long distances).

Project 2) Particle turbulence. This work, in collaboration with Anne Dejoan (CIEMAT, Spain) expert in particule turbulence, was interrupted due to force majeur (tenure for permanent position, who won in Sept. 2016). Last year we made a preliminary study on the effect of particle size and inertia on a relaxing turbulent field. On Jan. 2017 we will adapt FLUAM to sustain homogeneous turbulence and pursue this research.

Project 3) (new) Universally Adaptable Multiscale Molecular Dynamics.

This new computational branch of the project complements the theoretical research. It is the main research activity of Raul Pérez Pelaez, MS student (funded by the ACS-PRF grant) and excellent code developer. After implementing several useful tools (an open-source fast animation tool “superpunto” https://github.com/RaulPPelaez/superpunto see Figure. 1, and several useful tools for FLUAM) we started to develop a new code for particle simulations, using the state-of-the-art techniques in numerics, algorithmic and hard-core (machine architecture). The resulting code, UAMMD, is growing fast and it is now freely available in the web under open-source (github). UAMMD is a multiscale tool for molecular dynamics -MD (nanometers), dissipative particle dynamics -DPD (hundreds of nanometers) and Brownian hydrodynamics -BDH (tens of microns). We also plan to implement “smooth particle hydrodynamics” for macro-scale Lagrangian hydrodynamics. UAMMD runs in Graphical Processor Units (GPU’s) and are proud to say that UAMMD compares favorably with HOOMD (Fig. 1), which is one of the fastest codes for GPU. The reason is that UAMMD is adapted to the GPU architecture. The cell-list neighbor search (one of the most expensive operations) is based on a Z-ordered curve. UAMMD solves Brownian hydrodynamics (BHD) using the Rotne-Prager-Yamakawa mobility tensor for particle-particle hydrodynamic interactions. As GPU’s can multiply fast, but have limited memory; the optimal GPU-route to the square-root of the mobility is the Lanczos method which will be combined with an elegant and efficient version of the Fast Multipole Method recently developed by our coworker Aleksandar Donev (Courant, New York) (still unpublished). In summary, we expect that UAMMD will soon be one of the fastest in the field!

UAMMD-enabled ongoing projects

Gellation of micron-size paraffin crystals: we have started a problem related on the gellation in micron-size paraffine crystals. The idea is to study how paraffin nano-crystals aggregate under shear flow. We have used FLUAM in our preliminary study (see Fig. 2) and UAMMD-MD for equilibrium gellation.

Anomalous diffusion of nanoparticles in agarose gels (UAMMD-MD). This is part of a collaboration with an experimental group Miguel A. Rubio (UNED, Madrid). The task has been performed by a MS student (still BS), Nerea Alcazar.

Confined colloids (UAMMD-BHD and FLUAM). We show that the hydrodynamic enhancement of the collective diffusion coefficient of colloids confined in two-dimensions but embedded in 3D. This phenomenon is strong and ubiquitous arising from the mobility gradient.

Hydrodynamic effects on the collective diffusion of membrane lipids (with Sergio Panzuela, PhD student). By comparing MD (with explicit water), Brownian dynamics (Deserno “dry membrane” model, no hydrodynamics) and FLUAM (Deserno model with solvent hydrodynamics) we conclude that, surprisingly, the enhancement of collective diffusion is also present in membranes! We believe this is a relevant result and will be sent for publication by March 2017.

Dynamics of star polymers (UAMMD-BHD). In collaboration with Matej Praprotnik (Slovenia); publications expected for Jan.-Feb. 2017.

Dynamic coarse-graining. Star polymers. In collaboration with Vagelis Harniandakis (Crete) and BS student Virginia Arostopoulus. Using the Mori-Zwanzig formalism we measured the friction kernels to use in UAMMD-DPD for polymers. Fluid-Wall-slippage: in collaboration with Pep Español (UNED, Madrid), adapt a new coarse-graining theory to measure friction and wall-viscosities with UAMMD. The theory will be sent for publication soon.

Snapshot of a fast quench of a Lennard-Jones fluid using UAMMD (10⁶ particles, 10⁴.time steps per minute). The snapshot comes from our animation tool “superpunto” using ambient occlusion for renderization (open-source https://github.com)