arXiv subjects

Joost de Graaf

Publications and source records attributed to Joost de Graaf.

At least 19 recordsLinked to original sources

arXiv2026

Projection-Based Solver for Viscoelastic Stokes Flow using FFTs

Understanding the flow of complex media is relevant for a wide range of research fields and industrial applications. Several numerical approaches exist by which approximate solutions can be determined for the Stokes equations that describe microhydrodynamic flows at the continuum level. However, achieving efficiency and accuracy for an incompressible fluid remains challenging. Here, we present an algorithm for solving the Stokes equations for an Oldroyd-B fluid using Fourier transforms. We gain efficiency by leveraging the 'Fastest Fourier Transform in the West' (FFTW). We validate our approach for the well-characterized four-roll mill, which exhibits nearly singular points of stress at the extensional points of the flow. We capture this divergence and showcase the potential of our method without making the usual diffusive renormalization. We also focus on characterizing the power-law behavior and numerically assess the divergence criterion. Future work will concentrate on active systems, the introduction of moving boundaries, and application to microfluidic devices.

physics.flu-dyn↗

arXiv2026

Phase-Field Models for Particle-Stabilised Emulsions

Particle-stabilised emulsions are a cornerstone of soft matter science due to their broad application and fundamental relevance. Computer simulations provide key insights into the formation and behaviour of these emulsions, yet current methods are limited by the spatiotemporal scales accessible for study. The principal issue is that particles are resolved individually. In this work, an alternative strategy is introduced based on phase-field theory, for which we establish the framework. By evolving continuous fields, large-scale dynamics can be simulated in a computationally efficient manner. Our approach is then applied to model the complex formation of a bicontinuous interfacially jammed emulsion gel (bijel) via solvent-transfer induced phase separation (STrIPS). By resolving the coupled dynamics of liquid phase separation and nanoparticle adsorption, the model allows for the characterisation of the influence of nanoparticles on the morphology. Higher concentrations of nanoparticles are found to reduce the average domain size of STrIPS bijels, in line with previous experimental evidence. The presented phase-field model thus represents a promising approach for the morphological investigation of complex particle-stabilised emulsions.

cond-mat.soft↗

arXiv2026

The Geometry behind the Glass Transition and Frictional Jamming in Systems of Two-Dimensional Hard Disks

The relation between dynamics and structure in systems of Brownian bidisperse 2D hard disks with arrested dynamics is examined using numerical simulations. Surprisingly, the suspensions show dynamic arrest at an area fraction of ϕ {\approx} 0.777 over a wide range of disk-size ratios. This is in close agreement with the experimental findings of [Nat. Mater. 18, 1118 (2019)] (ϕ {\approx} 0.776) for a quasi-2D colloidal suspension of spheres with large-to-small size ratio of approximately 1.4. Intriguingly, this also matches a jamming transition (ϕ {\approx} 0.773 to 0.777) found experimentally in a 2D bidisperse granular packing of disks for a similar aspect ratio [Powders and Grains (2025)]. Adopting a geometric viewpoint allows for the identification of the floret pentagonal tiling (ϕ {\approx} 0.777343), which is comprised of congruent (elongated) pentagonal tiles. In analogy to foam and tissue models, it is the presence of this congruent reference state that induces a dynamical transition in the disordered fluid of the disks. That is, the change in dynamics observed both in a uniformly compressed granular medium and a colloidal one at finite temperature are implied to be caused by the same topological mechanism. Extending this reasoning to a honeycomb lattice could also explain the experimentally observed onset of caging dynamics (ϕ {\approx} 0.6) in a similar bidisperse, quasi-2D system of colloidal spheres [Nature 587, 225 (2020)]. An outlook is provided on how this concept may be applied to 3D: removing one in four particles from a face-centered-cubic arrangement leads to a square bipyramidal honeycomb} with associated volume fraction η {\approx} 0.55536. The ideas put forward here thus also provide a possible origin for random loose packing of (frictional) hard spheres in 3D and can potentially shed light onto the nature of the glass transition.

cond-mat.soft↗

arXiv2025

Cell Competition Driven by Secreted Ligands: Modeling Liver Metastasis of Colorectal Cancer

Cell competition in multicellular organisms has been shown to play a critical role during the development of organisms, cancer progression, and in the establishment and maintenance of tissue homeostasis. Various mechanisms of cell competition have been identified, including active elimination via mechanical forces or induced apoptosis, as well as competition for nutrients and other beneficial factors. A recent experiment demonstrated hallmarks of cell competition, associated with cell cycle dynamics, between liver progenitor cells and colorectal cancer cells [Krotenberg Garcia et al., iScience 27, 109718 (2024)]. However, a mechanistic explanation for this form of competition remains lacking. Here, we present a mean-field model of competition for signaling ligands, coupled with cell cycle dynamics, to provide such an understanding. Our model captures the salient features of the experiment, including population dynamics and cell cycle variations. We demonstrate that secretion of a beneficial factor by cells, coupled with the enhanced uptake efficiency of cancer cells, suffices to reproduce the experimental outcome. Our model, reminiscent of competition for secreted growth factors, provides insight into the minimal level of complexity required to achieve the observed competitive outcome as well as its link to cell cycle dynamics. It can also serve as a general framework for studying biological populations with growth-stage-dependent competition over consumer-produced products.

physics.bio-ph↗

arXiv2025

Hydrodynamic Interactions in Particle Suspensions: A Perspective on Stokesian Dynamics

Stokesian Dynamics (SD) is a numerical framework used for simulating hydrodynamic interactions in particle suspensions at low Reynolds number. It combines far-field approximations with near-field lubrication corrections, offering a balance between accuracy and efficiency. This work reviews SD and provides a perspective on future directions for this approach. We outline the mathematical foundations, the method's strengths and weaknesses, and the computational challenges that need to be overcome to work with SD effectively. We also discuss recent advancements that improve the algorithm's efficiency, including the use of iterative solvers and matrix-free approaches. In addition, we highlight the limitations of making stronger, albeit more cost-effective approximations to studying hydrodynamic interactions in dense suspensions than made in SD, such as the two-body Rotne-Prager-Yamakawa (RPY) approximation. To overcome these issues, we propose a hybrid framework that replaces SD's full many-body computations with a neural network trained on SD data. That is, we correct the RPY approximation, while avoiding costly matrix inversions. We demonstrate the potential of this method on a simple system, where we find a close match to SD data while algorithmically outperforming RPY. Our work provides an outlook on the way in which large-scale simulations of particle suspensions can be performed in the foreseeable future.

physics.flu-dyn↗

arXiv2025

Python-JAX-based Fast Stokesian Dynamics

Stokesian Dynamics (SD) is a powerful computational framework for simulating the motion of particles in a viscous Newtonian fluid under Stokes-flow conditions. Traditional SD implementations can be computationally expensive as they rely on the inversion of large mobility matrices to determine hydrodynamic interactions. Recently, however, the simulation of thermalized systems with large numbers of particles has become feasible [Fiore and Swan, J. Fluid. Mech. $\textbf{878}$, 544 (2019)]. Their ``fast Stokesian dynamics'' (FSD) method leverages a saddle-point formulation to ensure overall scaling of the algorithm that is linear in the number of particles $\mathcal{O}(N)$; performance relies on dedicated graphics-processing-unit computing. Here, we present a different route toward implementing FSD, which instead leverages the Just-in-Time (JIT) compilation capabilities of Google JAX. We refer to this implementation as JFSD and perform benchmarks on it to verify that it has the right scaling and is sufficiently fast by the standards of modern computational physics. In addition, we provide a series of physical test cases that help ensure accuracy and robustness, as the code undergoes further development. Thus, JFSD is ready to facilitate the study of hydrodynamic effects in particle suspensions across the domains of soft, active, and granular matter.

physics.flu-dyn↗

arXiv2024

Fluid-Derived Lattices for Unbiased Modeling of Bacterial Colony Growth

Bacterial colonies can form a wide variety of shapes and structures based on ambient and internal conditions. To help understand the mechanisms that determine the structure of and the diversity within these colonies, various numerical modeling techniques have been applied. The most commonly used ones are continuum models, agent-based models, and lattice models. Continuum models are usually computationally fast, but disregard information at the level of the individual, which can be crucial to understanding diversity in a colony. Agent-based models resolve local details to a greater level, but are computationally costly. Lattice-based approaches strike a balance between these two limiting cases. However, this is known to come at the price of introducing undesirable artifacts into the structure of the colonies. For instance, square lattices tend to produce square colonies even where an isotropic shape is expected. Here, we aim to overcome these limitations and therefore study lattice-induced orientational symmetry in a class of hybrid numerical methods that combine aspects of lattice-based and continuum descriptions. We characterize these artifacts and show that they can be circumvented through the use of a disordered lattice which derives from an unstructured fluid. The main advantage of this approach is that the lattice itself does not imbue the colony with a preferential directionality. We demonstrate that our implementation enables the study of colony growth involving millions of individuals within hours of computation time on an ordinary desktop computer, while retaining many of the desirable features of agent-based models. Furthermore, our method can be readily adapted for a wide range of applications, opening up new avenues for studying the formation of colonies with diverse shapes and complex internal interactions.

cond-mat.soft↗

arXiv2024

The motion of catalytically active colloids approaching a surface

Catalytic microswimmers typically swim close to walls due to hydrodynamic and/or phoretic effects. The walls in turn are known to affect their propulsion, making it difficult to single out the contributions that stem from particle-based catalytic propulsion only, thereby preventing an understanding of the propulsion mechanism. Here, we use acoustic tweezers to lift catalytically active Janus spheres away from the wall to study their motion in bulk and when approaching a wall. Mean-squared displacement analysis shows that diffusion constants at different heights match with Faxén's prediction for the near-wall hydrodynamic mobility. Both particles close to a substrate and in bulk show a decrease in velocity with increasing salt concentration, suggesting that the dominant factor for the decrease in speed is a reduction of the swimmer-based propulsion. The velocity-height profile follows a hydrodynamic scaling relation as well, implying a coupling between the wall and the swimming speed. The observed speed reduction upon addition of salt matches expectations from a electrokinetic theory, except for experiments in 0.1 wt% hydrogen peroxide in bulk, which could indicate contributions from a different propulsion mechanism. Our results help with the understanding of ionic effects on microswimmers in 3D and point to a coupling between the wall and the particle that affects its self-propulsion speed.

cond-mat.soft↗

arXiv2024

The Cellular Potts Model on Disordered Lattices

The Cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems, and this is known to introduce artifacts in the structure and dynamics of the model tissues. That is, on regular lattices, cells can assume shapes that are dictated by the symmetries of the underlying lattice. Here, we developed a variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition and is different from the glass/jamming transitions commonly reported for the vertex and active Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular Cellular Potts model.

cond-mat.soft↗

arXiv2024

Delayed Gravitational Collapse of Attractive Colloidal Suspensions

Colloidal gels have strong industrial relevance as they can behave liquid- and solid-like. The latter allows them to support the buoyant weight against gravity. However, the system is intrinsically out-of-equilibrium, which means that the colloids must eventually settle out of the suspension. The process of settling has been captured theoretically, but the presence of a delay time during which the gel appears relatively unaffected by gravity has not. Here, we modify existing frameworks to capture this delay, by treating the gel as a continuum with viscoelastic response that is based on the local bond density. We can solve our model numerically to obtain the evolution of the colloid density profile and recover qualitatively the accumulation of a dense layer on top of the settling gel, as is experimentally observed in depletion gels. This numerical study is complemented by a theoretical analysis that allows us to identify an emergent time and length scale that set the dynamics of the gel. Our model provides a solid foundation for future studies that incorporate hydrodynamic erosion and tackle industrially relevant geometries.

cond-mat.soft↗

arXiv2023

Hydrodynamic Lubrication in Colloidal Gels

Colloidal gels are elasto-plastic materials composed of an out-of-equilibrium, self-assembled network of micron-sized (solid) particles suspended in a fluid. Recent work has shown that far-field hydrodynamic interactions do not change gel structure, only the rate at which the network forms and ages. However, during gel formation, the interplay between short-ranged attractions leading to gelation and equally short-ranged hydrodynamic lubrication interactions remains poorly understood. Here, we therefore study gelation using a range of hydrodynamic descriptions: from single-body (Brownian Dynamics), to pairwise (Rotne-Prager-Yamakawa), to (non-)lubrication-corrected many-body (Stokesian Dynamics). We confirm the current understanding informed by simulations accurate in the far-field. Yet, we find that accounting for lubrication can strongly impact structure at low colloid volume fraction. Counterintuitively, strongly dissipative lubrication interactions also accelerate the aging of a gel, irrespective of colloid volume fraction. Both elements can be explained by lubrication forces facilitating collective dynamics and therefore phase-separation. Our findings indicate that despite the computational cost, lubricated hydrodynamic modeling with many-body far-field interactions is needed to accurately capture the evolution of the gel structure.

cond-mat.soft↗

arXiv2023

Hydrodynamic Stability Criterion for Colloidal Gelation under Gravity

Attractive colloids diffuse and aggregate to form gels, solid-like particle networks suspended in a fluid. Gravity is known to strongly impact the stability of gels once they are formed. However, its effect on the process of gel formation has seldom been studied. Here, we simulate the effect of gravity on gelation using both Brownian dynamics and a lattice-Boltzmann algorithm that accounts for hydrodynamic interactions. We work in a confined geometry to capture macroscopic, buoyancy-induced flows driven by the density mismatch between fluid and colloids. These flows give rise to a stability criterion for network formation, based on an effective accelerated sedimentation of nascent clusters at low volume fractions that disrupts gelation. Above a critical volume fraction, mechanical strength in the forming gel network dominates the dynamics: the interface between the colloid-rich and colloid-poor region moves downward at an ever decreasing rate. Finally, we analyze the asymptotic state, the colloidal gel-like sediment, which we find not to be appreciably impacted by the vigorous flows that can occur during the settling of the colloids. Our findings represent the first steps toward understanding how flow during formation affects the life span of colloidal gels.

cond-mat.soft↗

arXiv2022

Structuring Colloidal Gels via Micro-Bubble Oscillations

Locally (re)structuring colloidal gels $\unicode{x2013}$ micron-sized particles forming a connected network with arrested dynamics $\unicode{x2013}$ enables precise tuning of the micromechanical and -rheological properties of the system. A recent experimental study [B. Saint-Michel, G. Petekidis, and V. Garbin, Soft Matter $\boldsymbol{18}$, 2092 (2022)] showed that rapid restructuring can occur by acoustically modulating an embedded microbubble. Here, we perform Brownian dynamics simulations to understand the mechanical effect of an oscillating microbubble on the structure of the embedding colloidal gel. Our simulations reveal a hexagonal-close-packed restructuring in a range that is comparable to the amplitude of the oscillations. However, we were unable to reproduce the unexpectedly long-ranged modification of the gel structure $\unicode{x2013}$ dozens of amplitudes $\unicode{x2013}$ observed in experiment. This suggests including long-ranged effects, such as fluid flow, should be considered in future work.

cond-mat.soft↗

arXiv2021

Amphibious Transport of Fluids and Solids by Soft Magnetic Carpets

One of the major challenges in modern robotics is controlling micromanipulation by active and adaptive materials. In the respiratory system, such actuation enables pathogen clearance by means of motile cilia. While various types of artificial cilia have been engineered recently, they often involve complex manufacturing protocols and focus on transporting liquids only. Here, we create soft magnetic carpets via an easy self-assembly route based on the Rosensweig instability. These carpets can transport liquids but also solid objects that are larger and heavier than the artificial cilia, using a crowd-surfing effect. This amphibious transportation is locally and reconfigurably tuneable by simple micromagnets or advanced programmable magnetic fields with a high degree of spatial resolution. We identify and model two surprising cargo reversal effects due to collective ciliary motion and non-trivial elastohydrodynamics. While our active carpets are generally applicable to integrated control systems for transport, mixing and sorting, these effects could also be exploited for microfluidic viscosimetry and elastometry.

physics.app-ph↗

arXiv2021

Regulating Aggregation of Colloidal Particles in an Electro-Osmotic Micropump

Unrestricted particle transport through microfluidic channels is of paramount importance to a wide range of applications, including lab-on-a-chip devices. In this article, we study using video microscopy the electro-osmotic aggregation of colloidal particles at the opening of a micrometer-sized silica channel in presence of a salt gradient. Particle aggregation eventually leads to clogging of the channel, which may be undone by a time-adjusted reversal of the applied electric potential. We numerically model our system via the Stokes-Poisson-Nernst-Planck equations in a geometry that approximates the real sample. This allows us to identify the transport processes induced by the electric field and salt gradient and to provide evidence that a balance thereof leads to aggregation. We further demonstrate experimentally that a net flow of colloids through the channel may be achieved by applying a square-waveform electric potential with an appropriately tuned duty cycle. Our results serve to guide the design of microfluidic and nanofluidic pumps that allow for controlled particle transport and provide new insights for anti-fouling in ultra-filtration.

cond-mat.soft↗

arXiv2021

Activity-induced microswimmer interactions and cooperation in one-dimensional environments

Cooperative motion in biological microswimmers is crucial for their survival as it facilitates adhesion to surfaces, formation of hierarchical colonies, efficient motion, and enhanced access to nutrients. Synthetic microswimmers currently lack truly cooperative behavior that originates from activity-induced interactions. Here, we demonstrate that catalytic microswimmers show a variety of cooperative behaviors along one-dimensional paths. We show that their speed increases with the number of swimmers, while the activity induces a preferred distance between swimmers. Using a minimal model, we ascribe this behavior to an effective activity-induced potential that stems from a competition between chemical and hydrodynamic coupling. These interactions further induce active self-assembly into trains as well as compact chains that can elongate, break-up, become immobilized and remobilized. We identify the crucial role that environment morphology and swimmer directionality play on these highly dynamic chain behaviors. These activity-induced interactions open the door towards exploiting cooperation for increasing the efficiency of, as well as provide temporal and spatial control over, microswimmer motion, thereby enabling them to perform intricate tasks inside complex environments.

cond-mat.soft↗

arXiv2020

Height Distribution and Orientation of Colloidal Dumbbells Near a Wall

Geometric confinement strongly influences the behavior of microparticles in liquid environments. However, to date, nonspherical particle behaviors close to confining boundaries, even as simple as planar walls, remain largely unexplored. Here, we measure the height distribution and orientation of colloidal dumbbells above walls by means of digital in-line holographic microscopy. We find that while larger dumbbells are oriented almost parallel to the wall, smaller dumbbells of the same material are surprisingly oriented at preferred angles. We determine the total height-dependent force acting on the dumbbells by considering gravitational effects and electrostatic particle-wall interactions. Our modeling reveals that at specific heights both net forces and torques on the dumbbells are simultaneously below the thermal force and energy, respectively, which makes the observed orientations possible. Our results highlight the rich near-wall dynamics of nonspherical particles, and can further contribute to the development of quantitative frameworks for arbitrarily-shaped microparticle dynamics in confinement.

cond-mat.soft↗

arXiv2020

Autonomously Probing Viscoelasticity in Disordered Suspensions

Recent experiments show a strong rotational-diffusion enhancement for self-propelled microrheological probes in colloidal glasses. Here, we provide microscopic understanding using simulations with a frictional probe-medium coupling that converts active translation into rotation. Diffusive enhancement emerges from the medium's disordered structure and peaks at a second-order transition in the number of contacts. Our results reproduce the salient features of the colloidal glass experiment and support an effective description that is applicable to a broader class of viscoelastic suspensions.

cond-mat.soft↗