arXiv subjects

Stephan Gekle

Publications and source records attributed to Stephan Gekle.

At least 19 recordsLinked to original sources

arXiv2025

How Microplastics cross the Buoyancy Barrier: A multi-scale Study

Microplastics (MPs), though less dense than water, are frequently recovered from sediments in aqueous environments, indicating they can cross the buoyancy barrier. We quantify eco-corona mediated MP-sediment attraction and MP transport from the nanoscale to the macroscale, linking all scales to a coherent mechanism explaining how MP overcome buoyancy and settle in sediments through interaction with suspended sediment. Colloidal probe atomic force microscopy (CP-AFM) detected attractive forces (0.15 - 17 mN/m) enabling heteroaggregation. Microscale tests confirmed aggregation and on larger scales sediment retention more than doubled with an eco-corona. Simulations showed that environmental shear force ($4 \cdot 10^{-4} mN/m$) cannot disrupt aggregates. In sedimentation columns, biofilm-covered MPs settled twice as often as plain MPs in bentonite suspensions. MP retention increased by 32 %. These results demonstrate that eco-corona/biofilm-mediated heteroaggregation is a robust pathway for MP sinking, accumulation, and retention in sediment beds. By identifying physical interaction thresholds and aggregation stability, we provide mechanistic insight into MP fate, highlight probable accumulation hotspots, and offer an evidence base for improved risk assessment and environmental modelling.

cond-mat.soft↗

arXiv2023

Mechanical complexity of living cells can be mapped onto simple homogeneous equivalents

Biological cells are built up from many different constituents of varying size and stiffness which all contribute to the cell's mechanical properties. Despite this heterogeneity, in the analysis of experimental measurements such as atomic force microscopy or microfluidic characterisation a strongly simplified homogeneous cell is typically assumed and a single elastic modulus is assigned to the entire cell. This ad-hoc simplification has so far mostly been used without proper justification. Here, we use computer simulations to show that indeed a heterogeneous cell can effectively be replaced by a homogeneous equivalent cell with a volume averaged elastic modulus. To study the validity of this approach, we investigate a hyperelastic cell with a heterogeneous interior under compression as well as in shear and channel flow, mimicking atomic force and microfluidic measurements, respectively. We find that the homogeneous equivalent cell reproduces quantitatively the behavior of its inhomogeneous counterpart, and that this equality is largely independent of the stiffness or spatial distribution of the heterogeneity.

physics.bio-ph↗

arXiv2023

Cell-free layer of red blood cells in a constricted microfluidic channel under steady and time-dependent flow conditions

Constricted blood vessels in the circulatory system can severely impact the spatiotemporal organization of red blood cells (RBCs) causing various physiological complications. In lab-on-a-chip applications, constrictions are commonly used for cell sorting and plasma separation based on the formation of a cell-free layer (CFL) at the channel boundary. However, such devices usually employ a steady flow, although time-dependent and pulsatile flow conditions enhance many microfluidic operations and possess significant relevance for in-vitro studies under physiologically relevant flow conditions. In this study, we examine the CFL dynamics in a constricted microchannel under steady and time-dependent flow. Therefore, we develop an image processing routine that allows us to resolve the spatiotemporal evolution of the CFL under time-dependent driving of the flow with arbitrary waveform. First, we perform a characterization of the CFL and the cell-free area (CFA) before and after the constriction under steady flow conditions. Second, we employ our method to study the effect of the hematocrit and the parameters of the flow modulations on the CFL and CFA using a sinusoidal pressure profile. Our results highlight the dominant effects of the RBC concentration and the amplitude of the applied pressure signal predominantly on the CFA dynamics. Moreover, we observe a dampening of the CFA amplitude with increasing hematocrit or decreasing pressure amplitude, and a peculiar phase shift of the CFA oscillations pre- and post-constriction. Complementary numerical simulations reveal how the time-dependent CFA dynamics are coupled with the dynamically changing flow field at the constriction. Due to the increasing demand for investigations and applications under time-dependent flow conditions, our study provides crucial insight into the flow behavior of complex fluids in unsteady microscale flows.

physics.flu-dyn↗

arXiv2022

Predicting cell stress and strain during extrusion bioprinting

Bioprinting of living cells can cause major shape deformations, which may severely affect cell survival and functionality. While the shear stresses occurring during cell flow through the printer nozzle have been quantified to some extent, the extensional stresses occurring as cells leave the nozzle into the free printing strand have been mostly ignored. Here we use Lattice-Boltzmann simulations together with a finite-element based cell model to study cell deformation at the nozzle exit. Our simulation results are in good qualitative agreement with experimental microscopy images. We show that for cells flowing in the center of the nozzle extensional stresses can be significant, while for cells flowing off-center their deformation is dominated by the shear flow inside the nozzle. From the results of these simulations, we develop two simple methods that only require the printing parameters (nozzle diameter, flow rate, bioink rheology) to (i) accurately predict the maximum cell stress occurring during the 3D bioprinting process and (ii) approximately predict the cell strains caused by the elongational flow at the nozzle exit.

physics.bio-ph↗

arXiv2021

Red blood cell shape transitions and dynamics in time-dependent capillary flows

The dynamics of single red blood cells (RBCs) determine microvascular blood flow by adapting their shape to the flow conditions in the narrow vessels. In this study, we explore the dynamics and shape transitions of RBCs on the cellular scale under confined and unsteady flow conditions using a combination of microfluidic experiments and numerical simulations. Tracking RBCs in a comoving frame in time-dependent flows reveals that the mean transition time from the symmetric croissant to the off-centered, non-symmetric slipper shape is significantly faster than the opposite shape transition, which exhibits pronounced cell rotations. Complementary simulations indicate that these dynamics depend on the orientation of the RBC membrane in the channel during the time-dependent flow. Moreover, we show how the tank-treading movement of slipper-shaped RBCs in combination with the narrow channel leads to oscillations of the cell's center of mass. The frequency of these oscillations depends on the cell velocity, the viscosity of the surrounding fluid, and the cytosol viscosity. These results provide a potential framework to identify and study pathological changes of RBC properties.

physics.bio-ph↗

arXiv2021

On the accuracy and performance of the lattice Boltzmann method with 64-bit, 32-bit and novel 16-bit number formats

Fluid dynamics simulations with the lattice Boltzmann method (LBM) are very memory-intensive. Alongside reduction in memory footprint, significant performance benefits can be achieved by using FP32 (single) precision compared to FP64 (double) precision, especially on GPUs. Here, we evaluate the possibility to use even FP16 and Posit16 (half) precision for storing fluid populations, while still carrying arithmetic operations in FP32. For this, we first show that the commonly occurring number range in the LBM is a lot smaller than the FP16 number range. Based on this observation, we develop novel 16-bit formats - based on a modified IEEE-754 and on a modified Posit standard - that are specifically tailored to the needs of the LBM. We then carry out an in-depth characterization of LBM accuracy for six different test systems with increasing complexity: Poiseuille flow, Taylor-Green vortices, Karman vortex streets, lid-driven cavity, a microcapsule in shear flow (utilizing the immersed-boundary method) and finally the impact of a raindrop (based on a Volume-of-Fluid approach). We find that the difference in accuracy between FP64 and FP32 is negligible in almost all cases, and that for a large number of cases even 16-bit is sufficient. Finally, we provide a detailed performance analysis of all precision levels on a large number of hardware microarchitectures and show that significant speedup is achieved with mixed FP32/16-bit.

physics.comp-ph↗

arXiv2021

Analytical and computational study of cascade reaction processes in catalytic fibrous membranes

Multistep catalytic reactions use two different catalysts for the $A\to B$ and the subsequent $B\to C$ reaction, respectively. Often the employed catalysts are chemically incompatible, such as acid-base systems, which prohibits simple mixing in one solution. In this work, we study the efficiency of reactors where the incompatible catalytic sites are immobilized on fibrous membranes. We compare a lattice Boltzmann based solver for the advection-diffusion-reaction equation, a random walk particle tracking method and a simple theoretical model to investigate the reaction efficiency as a function of two dimensionless control parameters: the P\'eclet and the Damk\"ohler number. We find that, while the efficiency decreases with higher flow speed (due to the reduced reaction time), the total production nevertheless increases due to the higher mass flux in most cases. Our results further show that, even at high flow speeds, spatial proximity of the two catalysts increases reaction efficiency, which supports recent experimental efforts to locate both catalysts on a single fiber in a side-by-side geometry.

physics.comp-ph↗

arXiv2021

Vortical flow structures induced by red blood cells in capillaries

Knowledge about the flow field of the plasma around the red blood cells in capillary flow is important for a physical understanding of blood flow and the transport of micro- and nanoparticles and molecules in the flowing plasma. We conduct an experimental study on the flow field around red blood cells in capillary flow that are complemented by simulations of vortical flow between red blood cells. Red blood cells were injected in a 10x12 micrometer rectangular microchannel at a low hematocrit and the flow field around a single or two cells have been characterized thanks to a highspeed camera and by tracking 250 nm nanoparticles in flow behaving as tracers. While the flow field around a steady croissant shape is found to be relatively similar to that of a rigid sphere, the flow field around a slipper shape exhibits a small vortex at the rear of the red blood cell. Even more pronounced are vortex-like structures observed in the central region between two neighboring croissants. Conclusions: The rotation frequency of the vortices is to a good approximation, inversely proportional to the distance between the cells. Our experimental data are confirmed and complemented by numerical simulations.

physics.bio-ph↗

arXiv2020

Analytic Solution to the Piecewise Linear Interface Construction Problem and its Application in Curvature Calculation for Volume-of-Fluid Simulation Codes

The plane-cube intersection problem has been around in literature since 1984 and iterative solutions to it have been used as part of piecewise linear interface construction (PLIC) in computational fluid dynamics simulation codes ever since. In many cases, PLIC is the bottleneck of these simulations regarding compute time, so a faster, analytic solution to the plane-cube intersection would greatly reduce compute time for such simulations. We derive an analytic solution for all intersection cases and compare it to the one previous solution from Scardovelli and Zaleski (Ruben Scardovelli and Stephane Zaleski. "Analytical relations connecting linear interfaces and volume fractions in rectangular grids". In: Journal of Computational Physics 164.1 (2000), pp. 228-237.), which we further improve to include edge cases and micro-optimize to reduce arithmetic operations and branching. We then extend our comparison regarding compute time and accuracy to include two different iterative solutions as well. We find that the best choice depends on the employed hardware platform: on the CPU, Newton-Raphson is fastest with vectorization while analytic solutions perform better without. The reason for this is that vectorization instruction sets do not include trigonometric functions as used in the analytic solutions. On the GPU, the fastest method is our optimized version of the analytic SZ solution. We finally provide details on one of the applications of PLIC: curvature calculation for the Volume-of-Fluid model used for free surface fluid simulations in combination with the lattice Boltzmann method.

physics.comp-ph↗

arXiv2020

A hyperelastic model for simulating cells in flow

In the emerging field of 3D bioprinting, cell damage due to large deformations is considered a main cause for cell death and loss of functionality inside the printed construct. Those deformations, in turn, strongly depend on the mechano-elastic response of the cell to the hydrodynamic stresses experienced during printing. In this work, we present a numerical model to simulate the deformation of biological cells in arbitrary three-dimensional flows. We consider cells as an elastic continuum according to the hyperelastic Mooney-Rivlin model. We then employ force calculations on a tetrahedralized volume mesh. To calibrate our model, we perform a series of FluidFM(R) compression experiments with REF52 cells demonstrating that all three parameters of the Mooney-Rivlin model are required for a good description of the experimental data at very large deformations up to 80%. In addition, we validate the model by comparing to previous AFM experiments on bovine endothelial cells and artificial hydrogel particles. To investigate cell deformation in flow, we incorporate our model into Lattice Boltzmann simulations via an Immersed-Boundary algorithm. In linear shear flows, our model shows excellent agreement with analytical calculations and previous simulation data.

physics.bio-ph↗

arXiv2019

Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: implications for the hydrodynamics of an active microswimmer near an elastic interface

The emerging field of self-driven active particles in fluid environments has recently created significant interest in the biophysics and bioengineering communities owing to their promising future biomedical and technological applications. These microswimmers move autonomously through aqueous media where under realistic situations they encounter a plethora of external stimuli and confining surfaces with peculiar elastic properties. Based on a far-field hydrodynamic model, we present an analytical theory to describe the physical interaction and hydrodynamic couplings between a self-propelled active microswimmer and an elastic interface that features resistance toward shear and bending. We model the active agent as a superposition of higher-order Stokes singularities and elucidate the associated translational and rotational velocities induced by the nearby elastic boundary. Our results show that the velocities can be decomposed in shear and bending related contributions which approach the velocities of active agents close to a no-slip rigid wall in the steady limit. The transient dynamics predict that contributions to the velocities of the microswimmer due to bending resistance are generally more pronounced than to shear resistance. Our results provide insight into the control and guidance of artificial and synthetic self-propelling active microswimmers near elastic confinements.

physics.flu-dyn↗

arXiv2019

Computational modeling of active deformable membranes embedded in 3D flows

Active gel theory has recently been very successful in describing biologically active materials such as actin filaments or moving bacteria in temporally fixed and simple geometries such as cubes or spheres. Here we develop a computational algorithm to compute the dynamic evolution of an arbitrarily shaped, deformable thin membrane of active material embedded in a 3D flowing liquid. For this, our algorithm combines active gel theory with the classical theory of thin elastic shells. To compute the actual forces resulting from active stresses, we apply a parabolic fitting procedure to the triangulated membrane surface. Active forces are then dynamically coupled via an Immersed-Boundary method to the surrounding fluid whose dynamics can be solved by any standard, e.g. Lattice-Boltzmann, flow solver. We validate our algorithm using the Green's functions of [Berthoumieux et al. New J. Phys. 16, 065005 (2014)] for an active cylindrical membrane subjected (i) to a locally increased active stress and (ii) to a homogeneous active stress. For the latter scenario, we predict in addition a so far unobserved non-axisymmetric instability. We highlight the versatility of our method by analyzing the flow field inside an actively deforming cell embedded in external shear flow. Further applications may be cytoplasmic streaming or active membranes in blood flows.

physics.bio-ph↗

arXiv2018

Hydrodynamic coupling and rotational mobilities near planar elastic membranes

We study theoretically and numerically the coupling and rotational hydrodynamic interactions between spherical particles near a planar elastic membrane that exhibits resistance towards shear and bending. Using a combination of the multipole expansion and Faxen's theorems, we express the frequency-dependent hydrodynamic mobility functions as a power series of the ratio of the particle radius to the distance from the membrane for the self mobilities, and as a power series of the ratio of the radius to the interparticle distance for the pair mobilities. In the quasi-steady limit of zero frequency, we find that the shear- and bending-related contributions to the particle mobilities may have additive or suppressive effects depending on the membrane properties in addition to the geometric configuration of the interacting particles relative to the confining membrane. To elucidate the effect and role of the change of sign observed in the particle self and pair mobilities, we consider an example involving a torque-free doublet of counterrotating particles near an elastic membrane. We find that the induced rotation rate of the doublet around its center of mass may differ in magnitude and direction depending on the membrane shear and bending properties. Near a membrane of only energetic resistance toward shear deformation, such as that of a certain type of elastic capsules, the doublet undergoes rotation of the same sense as observed near a no-slip wall. Near a membrane of only energetic resistance toward bending, such as that of a fluid vesicle, we find a reversed sense of rotation. Our analytical predictions are supplemented and compared with fully resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied frequencies.

physics.flu-dyn↗

arXiv2018

A reciprocal theorem for the prediction of the normal force induced on a particle translating parallel to an elastic membrane

When an elastic object is dragged through a viscous fluid tangent to a rigid boundary, it experiences a lift force perpendicular to its direction of motion. An analogous lift mechanism occurs when a rigid symmetric object translates parallel to an elastic interface or a soft substrate. The induced lift force is attributed to an elastohydrodynamic coupling that arises from the breaking of the flow reversal symmetry induced by the elastic deformation of the translating object or the interface. Here we derive explicit analytical expressions for the quasi-steady state lift force exerted on a rigid spherical particle translating parallel to a finite-sized membrane exhibiting a resistance toward both shear and bending. Our analytical approach proceeds through the application of the Lorentz reciprocal theorem so as to obtain the solution of the flow problem using a perturbation technique for small deformations of the membrane. We find that the shear-related contribution to the normal force leads to an attractive interaction between the particle and the membrane. This emerging attractive force decreases quadratically with the system size to eventually vanish in the limit of an infinitely-extended membrane. In contrast, membrane bending leads to a repulsive interaction whose effect becomes more pronounced upon increasing the system size, where the lift force is found to diverge logarithmically for an infinitely-large membrane. The unphysical divergence of the bending-induced lift force can be rendered finite by regularizing the solution with a cut-off length beyond which the bending forces become subdominant to an external body force.

physics.flu-dyn↗

arXiv2018

Creeping motion of a solid particle inside a spherical elastic cavity

On the basis of the linear hydrodynamic equations, we present an analytical theory for the low-Reynolds-number motion of a solid particle moving inside a larger spherical elastic cavity which can be seen as a model system for a fluid vesicle. In the particular situation where the particle is concentric with the cavity, we use the stream function technique to find exact analytical solutions of the fluid motion equations on both sides of the elastic cavity. In this particular situation, we find that the solution of the hydrodynamic equations is solely determined by membrane shear properties and that bending does not play a role. For an arbitrary position of the solid particle within the spherical cavity, we employ the image solution technique to compute the axisymmetric flow field induced by a point force (Stokeslet). We then obtain analytical expressions of the leading order mobility function describing the fluid-mediated hydrodynamic interactions between the particle and confining elastic cavity. In the quasi-steady limit of vanishing frequency, we find that the particle self-mobility function is higher than that predicted inside a rigid no-slip cavity. Considering the cavity motion, we find that the pair-mobility function is determined only by membrane shear properties. Our analytical predictions are supplemented and validated by fully-resolved boundary integral simulations where a very good agreement is obtained over the whole range of applied forcing frequencies.

physics.flu-dyn↗

arXiv2017

Numerical-experimental observation of shape bistability of red blood cells flowing in a microchannel

Red blood cells flowing through capillaries assume a wide variety of different shapes owing to their high deformability. Predicting the realized shapes is a complex field as they are determined by the intricate interplay between the flow conditions and the membrane mechanics. In this work we construct the shape phase diagram of a single red blood cell with a physiological viscosity ratio flowing in a microchannel. We use both experimental in-vitro measurements as well as 3D numerical simulations to complement the respective other one. Numerically, we have easy control over the initial starting configuration and natural access to the full 3D shape. With this information we obtain the phase diagram as a function of initial position, starting shape and cell velocity. Experimentally, we measure the occurrence frequency of the different shapes as a function of the cell velocity to construct the experimental diagram which is in good agreement with the numerical observations. Two different major shapes are found, namely croissants and slippers. Notably, both shapes show coexistence at low (<1 mm/s) and high velocities (>3 mm/s) while in-between only croissants are stable. This pronounced bistability indicates that RBC shapes are not only determined by system parameters such as flow velocity or channel size, but also strongly depend on the initial conditions.

physics.bio-ph↗

arXiv2017

Brownian motion near an elastic cell membrane: A theoretical study

Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this chapter, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of nearby particles. In the steady limit, the diffusional behavior approaches that near a no-slip hard wall. The analytical predictions are validated and supplemented with boundary-integral simulations.

cond-mat.soft↗

arXiv2017

Hydrodynamic mobility of a sphere moving on the centerline of an elastic tube

Elastic channels are an important component of many soft matter systems, in which hydrodynamic interactions with confining membranes determine the behavior of particles in flow. In this work, we derive analytical expressions for the Green's functions associated to a point-force (Stokeslet) directed parallel or perpendicular to the axis of an elastic cylindrical channel exhibiting resistance against shear and bending. We then compute the leading order self- and pair mobility functions of particles on the cylinder axis, finding that the mobilities are primarily determined by membrane shear and that bending does not play a significant role. In the quasi-steady limit of vanishing frequency, the particle self- and pair mobilities near a no-slip hard cylinder are recovered only if the membrane possesses a non-vanishing shear rigidity. We further compute the membrane deformation, finding that deformation is generally more pronounced in the axial (radial) directions, for the motion along (perpendicular) to the cylinder centerline, respectively. Our analytical calculations for the Green's functions in an elastic cylinder can serve as a fundamental building block for future studies and are verified by fully resolved boundary integral simulations where a very good agreement is obtained.

physics.flu-dyn↗