arXiv subjects

Timm Krüger

Publications and source records attributed to Timm Krüger.

At least 19 recordsLinked to original sources

arXiv2026

Boundary-velocity error and stability of the accelerated multi-direct-forcing immersed boundary method

The multi-direct-forcing immersed boundary method allows for a small velocity error of the no-slip condition in moving-particle problems but suffers from numerical instability if simulation parameters are not carefully chosen. This study investigates the boundary-velocity error and numerical stability of the accelerated multi-direct-forcing immersed boundary method. An analysis of the discretized equations of body motion in moving boundary problems identifies a critical parameter that solely determines the numerical stability for the body motion. Additionally, numerical simulations reveal the optimal acceleration parameter that minimizes the velocity error of the no-slip condition and is independent of details of the boundary discretisation, the boundary shape, and spatial dimensionality. This study provides a guideline for establishing numerically stable simulations of moving boundary problems at optimal boundary-velocity error.

physics.flu-dyn↗

arXiv2020

Spatio-temporal dynamics of dilute red blood cell suspensions in a microchannel flow at low Reynolds number

Microfluidic technologies are commonly used for the manipulation of red blood cell (RBC) suspensions and analyses of flow-mediated biomechanics. To enhance the performance of microfluidic devices, understanding the dynamics of the suspensions processed within is crucial. We report novel aspects of the spatio-temporal dynamics of RBC suspensions flowing through a typical microchannel at low Reynolds number. Through experiments with dilute RBC suspensions, we find an off-centre two-peak (OCTP) profile of cells contrary to the centralised distribution commonly reported for low-inertia flows. This is reminiscent of the well-known "tubular pinch effect" which arises from inertial effects. However, given the conditions of negligible inertia in our experiments, an alternative explanation is needed for this OCTP profile. Our massively-parallel simulations of RBC flow in real-size microfluidic dimensions using the immersed-boundary-lattice-Boltzmann method (IB-LBM) confirm the experimental findings and elucidate the underlying mechanism for the counterintuitive RBC pattern. By analysing the RBC migration and cell-free layer (CFL) development within a high-aspect-ratio channel, we show that such a distribution is co-determined by the spatial decay of hydrodynamic lift and the global deficiency of cell dispersion in dilute suspensions. We find a CFL development length greater than 46 and 28 hydraulic diameters in the experiment and simulation, respectively, exceeding typical lengths of microfluidic designs. Our work highlights the key role of transient cell distribution in dilute suspensions, which may negatively affect the reliability of experimental results if not taken into account.

physics.flu-dyn↗

arXiv2019

Modelling ternary fluids in contact with elastic membranes

We present a thermodynamically consistent model of a ternary fluid interacting with elastic membranes. Following a free-energy modelling approach and taking into account the thermodynamics laws, we derive the equations governing the ternary fluid flow and dynamics of the membranes. We also provide the numerical framework for simulating such fluid-structure interaction problems. It is based on the lattice Boltzmann method, employed for resolving the evolution equations of the ternary fluid in an Eulerian description, coupled to the immersed boundary method, allowing for the membrane equations of motion to be solved in a Lagrangian system. The configuration of an elastic capsule placed at a fluid-fluid interface is considered for validation purposes. Systematic simulations are performed for a detailed comparison with reference numerical results obtained by Surface Evolver, and the Galilean invariance of the proposed model is also proven. The proposed approach is versatile, and a wide range of geometries can be simulated. To demonstrate this, the problem of a capillary bridge formed between two deformable capsules is investigated here.

cond-mat.soft↗

arXiv2017

Mesoscopic Modelling and Simulation of Soft Matter

The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance computing and community codes for soft matter simulation.

cond-mat.soft↗

arXiv2017

Anisotropic permeability in deterministic lateral displacement arrays

We uncover anisotropic permeability in microfluidic deterministic lateral displacement (DLD) arrays. A DLD array can achieve high-resolution bimodal size-based separation of microparticles, including bioparticles, such as cells. For an application with a given separation size, correct device operation requires that the flow remains at a fixed angle to the obstacle array. We demonstrate via experiments and lattice-Boltzmann simulations that subtle array design features cause anisotropic permeability. Anisotropic permeability indicates the microfluidic array's intrinsic tendency to induce an undesired lateral pressure gradient. This can cause an inclined flow and therefore local changes in the critical separation size. Thus, particle trajectories can become unpredictable and the device useless for the desired separation task. Anisotropy becomes severe for arrays with unequal axial and lateral gaps between obstacle posts and highly asymmetric post shapes. Furthermore, of the two equivalent array layouts employed with the DLD, the rotated-square layout does not display intrinsic anisotropy. We therefore recommend this layout over the easier-to-implement parallelogram layout. We provide additional guidelines for avoiding adverse effects of anisotropy on the DLD.

physics.flu-dyn↗

arXiv2016

Effect of body deformability on microswimming

In this work we consider the following question: given a mechanical microswimming mechanism, does increased deformability of the swimmer body hinder or promote the motility of the swimmer? To answer this we study a microswimmer model composed of deformable beads connected with springs. We determine the velocity of the swimmer analytically, starting from the forces driving the motion and assuming that the oscillations in the effective radii of the beads are known and are much smaller than the radii themselves. We find that to the lowest order, only the driving frequency mode of the surface oscillations contributes to the swimming velocity, and that this velocity may both rise and fall with the deformability of the beads depending on the spring constant. To test these results, we run immersed boundary lattice Boltzmann simulations of the swimmer, and show that they reproduce both the velocity-promoting and velocity-hindering effects of bead deformability correctly in the predicted parameter ranges. Our results mean that for a general swimmer, its elasticity determines whether passive deformations of the swimmer body, induced by the fluid flow, aid or oppose the motion.

physics.bio-ph↗

arXiv2016

Setting the pace of microswimmers: when increasing viscosity speeds up self-propulsion

It has long been known that some microswimmers seem to swim counter-intuitively faster when the viscosity of the surrounding fluid is increased, whereas others slow down. This conflicting dependence of the swimming velocity on the viscosity is poorly understood theoretically. Here we explain that any mechanical microswimmer with an elastic degree of freedom in a simple Newtonian fluid can exhibit both kinds of response to an increase in the fluid viscosity for different viscosity ranges, if the driving is weak. The velocity response is controlled by a single parameter $\varGamma$, the ratio of the relaxation time of the elastic component of the swimmer in the viscous fluid and the swimming stroke period. This defines two velocity-viscosity regimes, which we characterize using the bead-spring microswimmer model and analyzing the different forces acting on the parts of this swimmer. The analytical calculations are supported by lattice-Boltzmann simulations, which accurately reproduce the two velocity regimes for the predicted values of $\varGamma$.

cond-mat.soft↗

arXiv2016

Ternary Free Energy Lattice Boltzmann Model with Tunable Surface Tensions and Contact Angles

We present a new ternary free energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also describe how the model here presented here can be extended to include an arbitrary number of fluid components.

physics.comp-ph↗

arXiv2015

Effect of tube diameter and capillary number on platelet margination and near-wall dynamics

The effect of tube diameter $D$ and capillary number $Ca$ on platelet margination in blood flow at $\approx 37\%$ tube haematocrit is investigated. The system is modelled as three-dimensional suspension of deformable red blood cells and nearly rigid platelets using a combination of the lattice-Boltzmann, immersed boundary and finite element methods. Results show that margination is facilitated by a non-diffusive radial platelet transport. This effect is important near the edge of the cell-free layer, but it is only observed for $Ca > 0.2$, when red blood cells are tank-treading rather than tumbling. It is also shown that platelet trapping in the cell-free layer is reversible for $Ca \leq 0.2$. Only for the smallest investigated tube ($D = 10 μ\text{m}$) margination is essentially independent of $Ca$. Once platelets have reached the cell-free layer, they tend to slide rather than tumble. The tumbling rate is essentially independent of $Ca$ but increases with $D$. Tumbling is suppressed by the strong confinement due to the relatively small cell-free layer thickness at $\approx 37\%$ tube haematocrit.

cond-mat.soft↗

arXiv2015

Breakdown of deterministic lateral displacement efficiency for non-dilute suspensions: a numerical study

We investigate the effect of particle volume fraction on the efficiency of deterministic lateral displacement (DLD) devices. DLD is a popular passive sorting technique for microfluidic applications. Yet, it has been designed for treating dilute suspensions, and its efficiency for denser samples is not well known. We perform 3D simulations based on the immersed-boundary, lattice-Boltzmann and finite-element methods to model the flow of red blood cells (RBCs) in different DLD devices. We quantify the DLD efficiency in terms of appropriate "failure" probabilities and RBC counts in designated device outlets. Our main result is that the displacement mode breaks down upon an increase of RBC volume fraction, while the zigzag mode remains relatively robust. This suggests that the separation of larger particles (such as white blood cells) from a dense RBC background is simpler than separating smaller particles (such as platelets) from the same background. The observed breakdown stems from non-deterministic particle collisions interfering with the designed deterministic nature of DLD devices. Therefore, we postulate that dense suspension effects generally hamper efficient particle separation in devices based on deterministic principles.

cond-mat.soft↗

arXiv2015

Fluctuations and diffusion in sheared athermal suspensions of deformable particles

We analyze fluctuations of particle displacements and stresses in a sheared athermal suspension of elastic capsules (red blood cells). Upon variation of the volume fraction from the dilute up to the highly concentrated regime, our numerical simulations reveal different characteristic power-law regimes of the fluctuation variances and relaxation times. In the jammed phase and at high shear rates, anomalous scaling exponents are found that deviate from pure dimensional predictions. The observed behavior is rationalized via kinetic arguments and a dissipation balance model that takes into account the local fluid flows between the particles. Our findings support the view that the rheology of dense suspensions is essentially governed by the non-affine displacements.

cond-mat.soft↗

arXiv2014

Interface deformations affect the orientation transition of magnetic ellipsoidal particles adsorbed at fluid-fluid interfaces

Manufacturing new soft materials with specific optical, mechanical and magnetic properties is a significant challenge. Assembling and manipulating colloidal particles at fluid interfaces is a promising way to make such materials. We use lattice-Boltzmann simulations to investigate the response of magnetic ellipsoidal particles adsorbed at liquid-liquid interfaces to external magnetic fields. We provide further evidence for the first-order orientation phase transition predicted by Bresme and Faraudo [Journal of Physics: Condensed Matter 19 (2007), 375110]. We show that capillary interface deformations around the ellipsoidal particle significantly affect the tilt-angle of the particle for a given dipole-field strength, altering the properties of the orientation transition. We propose scaling laws governing this transition, and suggest how to use these deformations to facilitate particle assembly at fluid-fluid interfaces.

cond-mat.soft↗

arXiv2014

Detachment Energies of Spheroidal Particles from Fluid-Fluid Interfaces

The energy required to detach a single particle from a fluid-fluid interface is an important parameter for designing certain soft materials, for example, emulsions stabilised by colloidal particles, colloidosomes designed for targeted drug delivery, and bio-sensors composed of magnetic particles adsorbed at interfaces. For a fixed particle volume, prolate and oblate spheroids attach more strongly to interfaces because they have larger particle-interface areas. Calculating the detachment energy of spheroids necessitates the difficult measurement of particle-liquid surface tensions, in contrast with spheres, where the contact angle suffices. We develop a simplified detachment energy model for spheroids which depends only on the particle aspect ratio and the height of the particle centre of mass above the fluid-fluid interface. We use lattice Boltzmann simulations to validate the model and provide quantitative evidence that the approach can be applied to simulate particle-stabilized emulsions, and highlight the experimental implications of this validation.

cond-mat.soft↗

arXiv2014

Impact of blood rheology on wall shear stress in a model of the middle cerebral artery

Perturbations to the homeostatic distribution of mechanical forces exerted by blood on the endothelial layer have been correlated with vascular pathologies including intracranial aneurysms and atherosclerosis. Recent computational work suggests that in order to correctly characterise such forces, the shear-thinning properties of blood must be taken into account. To the best of our knowledge, these findings have never been compared against experimentally observed pathological thresholds. In the current work, we apply the three-band diagram (TBD) analysis due to Gizzi et al. to assess the impact of the choice of blood rheology model on a computational model of the right middle cerebral artery. Our results show that, in the model under study, the differences between the wall shear stress predicted by a Newtonian model and the well known Carreau-Yasuda generalized Newtonian model are only significant if the vascular pathology under study is associated with a pathological threshold in the range 0.94 Pa to 1.56 Pa, where the results of the TBD analysis of the rheology models considered differs. Otherwise, we observe no significant differences.

cs.CE↗

arXiv2014

Computer simulations reveal complex distribution of haemodynamic forces in a mouse retina model of angiogenesis

There is currently limited understanding of the role played by haemodynamic forces on the processes governing vascular development. One of many obstacles to be overcome is being able to measure those forces, at the required resolution level, on vessels only a few micrometres thick. In the current paper, we present an in silico method for the computation of the haemodynamic forces experienced by murine retinal vasculature (a widely used vascular development animal model) beyond what is measurable experimentally. Our results show that it is possible to reconstruct high-resolution three-dimensional geometrical models directly from samples of retinal vasculature and that the lattice-Boltzmann algorithm can be used to obtain accurate estimates of the haemodynamics in these domains. We generate flow models from samples obtained at postnatal days (P) 5 and 6. Our simulations show important differences between the flow patterns recovered in both cases, including observations of regression occurring in areas where wall shear stress gradients exist. We propose two possible mechanisms to account for the observed increase in velocity and wall shear stress between P5 and P6: i) the measured reduction in typical vessel diameter between both time points, ii) the reduction in network density triggered by the pruning process. The methodology developed herein is applicable to other biomedical domains where microvasculature can be imaged but experimental flow measurements are unavailable or difficult to obtain.

cs.CE↗

arXiv2014

Deformability-based red blood cell separation in deterministic lateral displacement devices - a simulation study

We show, via three-dimensional immersed-boundary-finite-element-lattice-Boltzmann simulations, that deformability-based red blood cell (RBC) separation in deterministic lateral displacement (DLD) devices is possible. This is due to the deformability-dependent lateral extension of RBCs and enables us to predict a priori which RBCs will be displaced in a given DLD geometry. Several diseases affect the deformability of human cells. Malaria-infected RBCs or sickle cells, for example, tend to become stiffer than their healthy counterparts. It is therefore desirable to design microfluidic devices which can detect those diseases based on the cells' deformability fingerprint, rather than preparing samples using expensive and time-consuming biochemical preparation steps. Our findings should be helpful in the development of new methods for sorting cells and particles by deformability.

cond-mat.soft↗

arXiv2013

Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells

Via computer simulations, we provide evidence that the shear rate induced red blood cell tumbling-to-tank-treading transition also occurs at quite high volume fractions, where collective effects are important. The transition takes place as the ratio of suspension stress to the characteristic cell membrane stress exceeds a certain value, independent of volume fraction and cell deformability. This value coincides with that for a transition from an orientationally less ordered to a highly ordered phase. The average cell deformation does not show any signature of the transition, but rather follows a simple scaling law independent of volume fraction.

cond-mat.soft↗

arXiv2013

Choice of boundary condition for lattice-Boltzmann simulation of moderate Reynolds number flow in complex domains

Modeling blood flow in larger vessels using lattice-Boltzmann methods comes with a challenging set of constraints: a complex geometry with walls and inlet/outlets at arbitrary orientations with respect to the lattice, intermediate Reynolds number, and unsteady flow. Simple bounce-back is one of the most commonly used, simplest, and most computationally efficient boundary conditions, but many others have been proposed. We implement three other methods applicable to complex geometries (Guo, Zheng and Shi, Phys Fluids (2002); Bouzdi, Firdaouss and Lallemand, Phys. Fluids (2001); Junk and Yang Phys. Rev. E (2005)) in our open-source application \HemeLB{}. We use these to simulate Poiseuille and Womersley flows in a cylindrical pipe with an arbitrary orientation at physiologically relevant Reynolds (1--300) and Womersley (4--12) numbers and steady flow in a curved pipe at relevant Dean number (100--200) and compare the accuracy to analytical solutions. We find that both the Bouzidi-Firdaouss-Lallemand and Guo-Zheng-Shi methods give second-order convergence in space while simple bounce-back degrades to first order. The BFL method appears to perform better than GZS in unsteady flows and is significantly less computationally expensive. The Junk-Yang method shows poor stability at larger Reynolds number and so cannot be recommended here. The choice of collision operator (lattice Bhatnagar-Gross-Krook vs.\ multiple relaxation time) and velocity set (D3Q15 vs.\ D3Q19 vs.\ D3Q27) does not significantly affect the accuracy in the problems studied.

physics.comp-ph↗