Posters
A multiscale approach to learn of constitutive equations for dilute polymeric solutions
David Nieto Simavilla, Pep Español (UNED), Marco Ellero (Basque Center for Applied Mathematics)
Abstract:
Polymer solutions display complex viscoelastic behaviour due to the orientation and stretching of chains. As a result, the simulation of polymer solutions requires a multiscale approach to avoid the high computational cost of resolving the materials’ microscopic details. At the macroscopic level, viscoelasticity is included via a closure constitutive equation for the polymeric stress. A novel approach is to use Machine Learning (ML) to establish the closure equations. However, arbitrary choices for the structure-property relationships – that determine the constitutive equations – result in a black box connection between microscale and macroscale simulations.
We present a general data-driven constitutive learning approach, where the local chain conformation tensor c is sufficient to describe the rheology of the system. For our microscopic system, we use SDPD particles joined by FENE springs to create chains that introduce viscoelasticity. In this physics guided approach the polymeric stress – as a function of the conformation tensor – is the only to-be-learned constitutive relation. On one hand, we show that in the miscrocopic simulation data the information rests on the polymeric entropy, a function of the eigenvalues of c alone. On the other hand, the evolution of the eigenvectors of c allows us to evaluate slip in the reversible part of the evolution equation for c – an assumption often taken for granted. We find good agreement at low Weissenberg numbers between our simulation results and the Oldroyd-B model predictions. Finally, we test our learning approach comparing microscopic and macroscopic Couette flow.
References
[1]P. Español, M. Revenga, Phys. Rev. E, 67, 026705 (2003)
[2]A. Vázquez-Quesada, M. Ellero, P. Español, Phys. Rev. E, 79, 056707 (2009)
[3]D. Simavilla, M. Ellero, Journal of Non-Newtonian Fluid Mechanics, 104811 (2022)
A tour of StochasticHydroTools
Brennan Sprinkle, Raul Perez (UAM), Aleksandar Donev (NYU), Florencio Balboa Usabiaga (BCAM), Blaise Delmotte (LadHyX, Ecole Polytechnique), Ondrej Maxian (NYU)
Abstract:
In suspensions of many small particles, a concert of random (Brownian) motion and inter-particle forces will often activate new and fascinating dynamics. In a lab we can harness these kinds of collective, microscopic effects to drive systems of synthetic micro-machines. Our own cells use fluctuations and a dense, interconnected network of fibers (the cytoskeleton) to move and divide themselves. This poster will illustrate some simulation techniques for investigating these types of driven, fluctuating suspensions - all of which are implemented in the open source software https://github.com/stochasticHydroTools. These numerical methods are designed around strict adherence to physical principles (e.g detailed ballance), and this posted will describe how they are made efficient through careful mathematical considerations (e.g stochastic temporal integration schemes). The poster will emphasize how we can use simulations in conjunction with data and experiments to answer foundational questions about synthetic and biological micro-systems.
Complex Fluids Modelling Using Lagrangian Heterogeneous Multiscale Methods
Nicolas Moreno, Marco Ellero (Basque Center for Applied Mathematics)
Abstract:
We propose a fully Lagrangian heterogeneous multiscale framework to model complex fluids in arbitrary flow configurations. This multiscale method bypasses the need to approximate constitutive relations for the stress by using microscopic information derived on the fly. We use Smoothed Dissipative Particle Dynamics[1] (SDPD) to model the fluid at both macro and microscales. This Lagrangian heterogeneous scheme naturally track memory effects, that are otherwise cumbersome to account in simple Eulerian discretizations. SDPD discretizes the fluctuating Navier-Stokes equations and allows us to incorporate various complex physical models in the microscales such as polymer solution, colloidal suspensions, and multiphase flows. Moreover, at the microscales, we adopted arbitrary boundary conditions[2] to be able to simulate mixed flows (shear and extensional). We construct different benchmark configurations to validate our framework (reverse Poiseuille flow, flow passing a cylinder array, and flow around a square cavity) for Newtonian and non-Newtonian fluids. We modelled complex fluids at the microscale using multiphase systems, polymer melts, and polymer solutions. For multiphase flows, we adopt a modified version of SDPD[3] using pairwise forces between particles in different phases. We showed that stresses are adequately captured and passed from micro to macroscales, leading to richer fluid response at the continuum. In general, the proposed methodology provides a natural link between variations at a macroscale, whereas accounting for memory effects of microscales
References
[1]P. Español, M. Revenga, Phys. Rev. E, 67, 026705 (2003)
[2]N. Moreno, M. Ellero, Physics of Fluids, 33, 012006 (2021)
[3]H. Lei, N. Baker, L. Wu, G. Schenter, C. Mundy, A. Tartakovsky, Phys. Rev. E, 94, 023304 (2016)
Complex aggregation modelling using Smoothed Dissipative Particle Dynamics
Elnaz Zohravi, Nicolas Moreno (BCAM), Marco Ellero (BCAM)
Abstract:
Complex hierarchical aggregation mediated by diffusion and reaction is ubiquitous to many naturally occurring phenomena. The aggregates typically exhibit a fractal behaviour or non-integer size scaling compared to their intrinsic dimensionality (1-3 dimensions). Such fractal aggregates have attracted attention in studying biological (i.e. bronchi and nervous system morphogenesis, blood clotting) and synthetic (i.e. colloids, polymers, catalysts, nano-dendrites) systems [1,2]. Despite the similarity between different biological systems, the computational simulation of aggregation processes ranging from atomistic to continuum scale is hard to achieve. Typically approaches involve the use of different discretizations and telescoped time scales. Herein, we introduce an aggregation framework based on the smoothed dissipative particle dynamic (SDPD) method that incorporates hydrodynamic, permanent binding and surface tension effects to simulate the aggregate's growth [3].
This framework systematically allows us to identify characteristic biomarkers such as the fractal dimension, aggregates connectivity and stability for various initial conditions and system parameters. Using simulations in 2 and 3 dimensions, we deduced the dependency of the fractal dimension of the aggregates with the initial concentration of aggregating particles. Characteristic correlations between aggregates fractal dimension, number of aggregated particles, and bond number were identified for the temporal evolution of the aggregates and their final steady-state condition. The presented computational model serves as a tool to further explore complex aggregation mechanisms related to blood coagulation at different scales, ranging from fibrin network formation to platelet aggregation.
References
[1]S. Bhattacharya, J. Kieffer, The Journal of Chemical Physics, 122, 094715 (2005)
[2]M. Brown, D. Curtis, P. Rees, H. Summers, K. Hawkins, P. Evans, P. Williams, Chaos, Solitons & Fractals, 45, 1025-1032 (2012)
[3]P. Español, M. Revenga, Phys. Rev. E, 67, 026705 (2003)
Modeling swelling effects during coffee extraction with smoothed particle hydrodynamics
Chaojie Mo, Luciano Navarini (Illycaffe` S.p.A), Furio Suggi Liverani (Illycaffe` S.p.A), Marco Ellero (Basque Center for Applied Mathematics)
Abstract:
It is commonly assumed that coffee particles swell during filtration, but it has not been clarified how different degrees of swelling affect the extraction. In this article, we propose a grain swelling model to investigate the influences of swelling on both intra-grain and inter-grain transport. The swelling is modelled through a diffusion process of excess water into the grains. The geometric expansion of the grains is connected to the local concentration of excess water through a specified deformation gradient tensor. Diffusion of soluble compounds inside the grains is coupled with the swelling dynamics through a modified diffusion equation. Inter-grain transport is modelled by solving the Navier-Stokes equation and diffusion equations. This model is solved numerically in the framework of smoothed particle hydrodynamics and it is used to simulate the extraction of a minimal coffee bed setup, and to investigate the effect of a small degree of particle swelling (<8% in size) on the extraction kinetics. It is found that under the normal operating parameter regime of espresso filtration, swelling affects the extraction mainly through the change of inter-grain transport. Swelling also alters the diffusion inside the grains, but this process has a secondary effect on the extraction. In general, swelling slightly impedes the extraction rate, but enhances the strength considerably at both fixed brewing time and fixed brewing volume. Our results justify the endeavour in the literatures to clarify the effect of possible swelling on brewing and preparation variables during coffee extraction.
Modelling biological matter as active nematic fluids
Liam Ruske, Julia Yeomans (University of Oxford)
Abstract:
It is increasingly becoming apparent that the physical concepts of forces and flows play an important role in understanding living active matter, from the invasive spread of cancer to morphogenesis, the development of organisms. In this talk/poster, I will explain how active liquid crystal hydrodynamics can be used to model biological matter, in which a continuous influx of energy on a single-particle level leads to striking collective behaviour eminiscent of many processes observed in nature.
References
Passive transport of SARS-CoV-2
Daniela Moreno-Chaparro, Nicolas Moreno (Basque Center for Applied Mathematics (BCAM)), Florencio Balboa-Usabiaga (Basque Center for Applied Mathematics (BCAM)), Marco Ellero (Basque Center for Applied Mathematics (BCAM))
Abstract:
Since 2019, the virus SARS-CoV-2 has been a critical topic worldwide because of its health impact on millions of people. Currently, different studies about virus genetics, biochemistry, infectivity, physics, and dynamics have been addressed. Here, we investigate the diffusion of SARS-CoV-2 virions using computational simulations. Due to the morphological features, virions can be seen as decorated nanoparticles and are characterized according to their translational and rotational diffusivity. We used the Rigid Multi-Blob (RMB) [1] methodology and Smoothed Dissipative Particle Dynamics (SDPD) [2] to simulate the effect of the spike proteins in the virions transport.
Using RMB, we construct virion models by discretizing the structures as a set of rigidly connected spherical beads; later, we compute their mobility tensor to determine the diffusion. The results revealed the effect of spike arrangement, number, and morphology on virion transport and shed light on its possible effects on viral infectivity. In general, randomness in the distribution of the spike decreases the hydrodynamic drag of the particles facilitating their transport. Using the same blob discretization of RMB, we conduct SDPD simulations without the rigid-body restriction between envelope and spikes. This approach allowed us to characterize the effects of spike motion and localization on the rotational diffusivity of the virion. We identify that passive microrheology can provide relevant information about viruses and offer potential novel biomarkers.
References
[1] F. Balboa Usabiaga, B. Kallemov, B. Delmotte, A. Bhalla, B. Griffith, and A. Donev, Hydrodynamics of suspensions of passive and active rigid particles: a rigid multiblob approach. Communications in Applied Mathematics and Computational Science, 2017, 11(2), 217-296.
[2] Espanol, P., & Revenga, M. (2003). Smoothed dissipative particle dynamics. Physical Review E, 67(2), 026705.
Spontaneous polarization and locomotion of an active particle with surface-mobile enzymes
Marco De Corato (Universidad de Zaragoza)
Abstract:
We examine a mechanism of locomotion of active particles whose surface is uniformly coated with mobile enzymes. The enzymes catalyze a reaction that drives phoretic flows but their homogeneous distribution forbids locomotion by symmetry. We find that the ability of the enzymes to migrate over the surface combined with self-phoresis can lead to a spontaneous symmetry-breaking instability whereby the homogeneous distribution of enzymes polarizes and the particle propels. The instability is driven by the advection of enzymes by the phoretic flows and occurs above a critical Péclet number. The transition to polarized motile states occurs via supercritical or subcritical pitchfork bifurcations, the latter of which enables hysteresis and coexistence of uniform and polarized states.
References
[1]M. De Corato, I. Pagonabarraga, L. Abdelmohsen, S. Sánchez, M. Arroyo, Phys. Rev. Fluids, 5, 122001 (2020)
[2]S. Song, A. Mason, R. Post, M. De Corato, R. Mestre, N. Yewdall, S. Cao, R. van der Hofstad, S. Sanchez, L. Abdelmohsen, J. van Hest, Nat. Commun., 12, 6897 (2021)
The role of hydrodynamics in the diffusion of passive tracers in random networks
Nerea Alcázar-Cano, Rafael Delgado-Buscalioni (Universidad Autónoma de Madrid)
Abstract:
The first natural consequence of the extra reduction in mobility near a wall induced by hydrodynamic interactions (HI) is to decrease the diffusion coefficient. While this statement is true, the role of HI in the diffusion of tracer particles in random media presents other many unexpected faces, some of them still not fully explored. The present study highlights the role of the network structure: we have considered cubic networks formed by randomly placed mutually orthogonal rods, randomly distributed polymeric fibers, and irregular thicker walls formed by colloidal gels. We unveil the relevance of both HI and the obstacle configuration by analyzing the “history” of the particle diffusion, evidenced in the van Hove distribution P(∆,t) of the tracer jumps ∆ after a lag time t.
As expected, at short times, the probability of small jumps is larger if HI are included (added friction). However at longer times, we observe that the diffusion coefficient of mobile particles in simulations including hydrodynamic interactions (HI) become gradually similar to that of purely Brownian walkers (BD). This “HI-induced” enhancement of diffusion at long times is more clearly observed close to the critical percolation threshold, i.e., when particles diffuse along single (or very few) fractal paths traversing the system.
References
[1]N. Alcázar-Cano, R. Delgado-Buscalioni, Soft Matter, 18, 1941-1954 (2022)
UAMMD: Complex fluids in the GPU era
Raul Perez Pelaez, Rafael Delgado-Buscalioni (Universidad Autónoma de Madrid)
Abstract:
Complex fluids is an umbrella where solute particles and liquid phase coexist, embracing inorganic and organic soft matter, nanoparticles, polymers, colloids, membranes, interfaces, and hydrodynamics at different spatio-temporal regimes. To face the challenge of simulating them, we present the ``Universally Adaptable Multiscale Molecular Dynamics'' code (UAMMD) [1], a novel, open-source, massive parallel, software infrastructure for soft matter simulations in Graphical Procesor Units (GPU). Starting from few nanometers up, UAMMD allows for Lagrangian simulations (MD, DPD, SPH, Brownian hydrodynamics, etc.) and also hybrid Eulerian-Lagrangian schemes.
One of the strongholds of UAMMD is to couple continuum fields with particles. Using the immersed-boundary formalism, Landau-Lifshitz fluctuating hydrodynamics are coupled to MD and this idea is generalized to other fields to model opto-hydrodynamics, charge dynamics, magnetic nanoparticles, etc. UAMMD naturally embraces coarse-grained models of proteins and any other tailored model. I will introduce UAMMD and expose my attempts to push the boundaries of numerical simulation of complex fluids, revisiting old and new schemes in the eyes of a GPU.
Reference