Timm Krüger

Efficient and accurate simulations of deformable particles immersed in a fluid using a combined immersed boundary lattice Boltzmann finite element method

The deformation of an initially spherical capsule, freely suspended in simple shear flow, can be computed analytically in the limit of small deformations [D. Barthes-Biesel, J.M. Rallison, The time-dependent deformation of a capsule freely suspended in a linear shear flow, J. Fluid Mech. 113 (1981) 251-267]. Those analytic approximations are used to study the influence of the mesh tessellation method, the spatial resolution, and the discrete delta function of the immersed boundary method on the numerical results obtained by a coupled immersed boundary lattice Boltzmann finite element method. For the description of the capsule membrane, a finite element method and the Skalak constitutive model [R. Skalak, A. Tozeren, R.P. Zarda, S. Chien, Strain energy function of red blood cell membranes, Biophys. J. 13 (1973) 245-264] have been employed. Our primary goal is the investigation of the presented model for small resolutions to provide a sound basis for efficient but accurate simulations of multiple deformable particles immersed in a fluid. We come to the conclusion that details of the membrane mesh, as tessellation method and resolution, play only a minor role. The hydrodynamic resolution, i.e., the width of the discrete delta function, can significantly influence the accuracy of the simulations. The discretization of the delta function introduces an artificial length scale, which effectively changes the radius and the deformability of the capsule. We discuss possibilities of reducing the computing time of simulations of deformable objects immersed in a fluid while maintaining high accuracy.

Shear stress in lattice Boltzmann simulations

A thorough study of shear stress within the lattice Boltzmann method is provided. Via standard multiscale Chapman-Enskog expansion we investigate the dependence of the error in shear stress on grid resolution showing that the shear stress obtained by the lattice Boltzmann method is second-order accurate. This convergence, however, is usually spoiled by the boundary conditions. It is also investigated which value of the relaxation parameter minimizes the error. Furthermore, for simulations using velocity boundary conditions, an artificial mass increase is often observed. This is a consequence of the compressibility of the lattice Boltzmann fluid. We investigate this issue and derive an analytic expression for the time dependence of the fluid density in terms of the Reynolds number, Mach number, and a geometric factor for the case of a Poiseuille flow through a rectangular channel in three dimensions. Comparison of the analytic expression with results of lattice Boltzmann simulations shows excellent agreement.

Numerical simulations of complex fluid-fluid interface dynamics

Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually deformable and their shapes are not known a priori. Since experiments do not provide access to all observables of interest, computer simulations pose attractive alternatives to gain insight into the physics of interfaces. In the present article, we restrict ourselves to systems with dimensions comparable to the lateral interface extensions. We provide a critical discussion of three numerical schemes coupled to the lattice Boltzmann method as a solver for the hydrodynamics of the problem: (a) the immersed boundary method for the simulation of vesicles and capsules, the Shan-Chen pseudopotential approach for multi-component fluids in combination with (b) an additional advection-diffusion component for surfactant modelling and (c) a molecular dynamics algorithm for the simulation of nanoparticles acting as emulsifiers.

Assembling Ellipsoidal Particles at Fluid Interfaces Using Switchable Dipolar Capillary Interactions

How to dynamically tune an assembly of anisotropic colloidal particles adsorbed at fluid-fluid interfaces using dipolar capillary interactions is demonstrated. A previously discovered first-order phase transition is exploited and it is shown how to spontaneously turn off these dipolar capillary interactions by exceeding a critical field strength, providing unprecedented control of the bottom-up fabrication of soft materials.

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 effective suspension stress to the characteristic cell membrane stress exceeds a certain value and does not explicitly depend on volume fraction or 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 transition, but rather follows a simple scaling law independent of volume fraction.

Interplay of inertia and deformability on rheological properties of a suspension of capsules

The interplay of inertia and deformability has a substantial impact on the transport of soft particles suspended in a fluid. However, to date a thorough understanding of these systems is still missing, and only a limited number of experimental and theoretical studies are available. We combine the finite-element, immersed-boundary and lattice-Boltzmann methods to simulate three-dimensional suspensions of soft particles subjected to planar Poiseuille flow at finite Reynolds numbers. Our findings confirm that the particle deformation and inclination increase when inertia is present. We observe that the Segre‐Silberberg effect is suppressed with respect to the particle deformability. Depending on the deformability and strength of inertial effects, inward or outward lateral migration of the particles takes place. In particular, for increasing Reynolds numbers and strongly deformable particles, a hitherto unreported distinct flow focusing effect emerges, which is accompanied by a non-monotonic behaviour of the apparent suspension viscosity and thickness of the particle-free layer close to the channel walls. This effect can be explained by the behaviour of a single particle and the change of the particle collision mechanism when both deformability and inertia effects are relevant.

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 this 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 (WSS) gradients exist. We propose two possible mechanisms to account for the observed increase in velocity and WSS between P5 and P6: (i) the measured reduction in typical vessel diameter between both time points and (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.

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, 2007, 19, 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.

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 characterize 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 this work, we apply the three-band diagram (TBD) analysis due to Gizzi et al. (Gizzi et al. 2011 Three-band decomposition analysis of wall shear stress in pulsatile flows. Phys. Rev. E 83, 031902. (doi:10.1103/PhysRevE.83.031902)) 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 0.94–1.56 Pa, where the results of the TBD analysis of the rheology models considered differs. Otherwise, we observe no significant differences.

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.