arXiv subjects

Stephan Gekle

Publications and source records attributed to Stephan Gekle.

At least 37 records · Page 2Linked to original sources

arXiv2017

A boundary integral method with volume-changing objects for ultrasound-triggered margination of microbubbles

A variety of numerical methods exist for the study of deformable particles in dense suspensions. None of the standard tools, however, currently include volume-changing objects such as oscillating microbubbles in three-dimensional periodic domains. In the first part of this work, we develop a novel method to include such entities based on the boundary integral method. We show that the well-known boundary integral equation must be amended with two additional terms containing the volume flux through the bubble surface. We rigorously prove the existence and uniqueness of the solution. Our proof contains as a subset the simpler boundary integral equation without volume-changing objects (such as red blood cell or capsule suspensions) which is widely used but for which a formal proof in periodic domains has not been published to date. In the second part, we apply our method to study microbubbles for targeted drug delivery. The ideal drug delivery agent should stay away from the biochemically active vessel walls during circulation. However, upon reaching its target it should attain a near-wall position for efficient drug uptake. Though seemingly contradictory, we show that lipid-coated microbubbles in conjunction with a localized ultrasound pulse possess precisely these two properties. This ultrasound-triggered margination is due to hydrodynamic interactions between the red blood cells and the oscillating lipid-coated microbubbles which alternate between a soft and a stiff state. We find that the effect is very robust, existing even if the duration in the stiff state is more than three times lower than the opposing time in the soft state.

physics.bio-ph↗

arXiv2017

Slow rotation of a spherical particle inside an elastic tube

In this paper, we present an analytical calculation of the rotational mobility functions of a particle rotating on the centerline of an elastic cylindrical tube whose membrane exhibits resistance towards shearing and bending. We find that the correction to the particle rotational mobility about the cylinder axis depends solely on membrane shearing properties while both shearing and bending manifest themselves for the rotational mobility about an axis perpendicular to the cylinder axis. In the quasi-steady limit of vanishing frequency, the particle rotational mobility nearby a no-slip rigid cylinder is recovered only if the membrane possesses a non-vanishing resistance towards shearing. We further show that for the asymmetric rotation along the cylinder radial axis, a coupling between shearing and bending exists. Our analytical predictions are compared and validated with corresponding boundary integral simulations where a very good agreement is obtained.

physics.flu-dyn↗

arXiv2017

Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. II. Asymmetric motion

In this paper, we derive analytical expressions for the leading-order hydrodynamic mobility of a small solid particle undergoing motion tangential to a nearby large spherical capsule whose membrane possesses resistance towards shearing and bending. Together with the results obtained in the first part (Daddi-Moussa-Ider and Gekle, Phys. Rev. E {\bfseries 95}, 013108 (2017)) where the axisymmetric motion perpendicular to the capsule membrane is considered, the solution of the general mobility problem is thus determined. We find that shearing resistance induces a low-frequency peak in the particle self-mobility, resulting from the membrane normal displacement in the same way, although less pronounced, to what has been observed for the axisymmetric motion. In the zero frequency limit, the self-mobility correction near a hard sphere is recovered only if the membrane has a non-vanishing resistance towards shearing. We further compute the particle in-plane mean-square displacement of a nearby diffusing particle, finding that the membrane induces a long-lasting subdiffusive regime. Considering capsule motion, we find that the correction to the pair-mobility function is solely determined by membrane shearing properties. Our analytical calculations are compared and validated with fully resolved boundary integral simulations where a very good agreement is obtained.

physics.flu-dyn↗

arXiv2016

Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. I. Axisymmetric motion

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements which is not the case for planar membranes. In the vanishing frequency limit, the particle self-mobility near a no-slip hard sphere is recovered only when the membrane possesses a non-vanishing resistance towards shearing. We further investigate capsule motion, finding that the pair-mobility function is solely determined by membrane shearing properties. Our analytical predictions are validated by fully resolved boundary integral simulations where a very good agreement is obtained.

physics.flu-dyn↗

arXiv2016

Mobility of an axisymmetric particle near an elastic interface

Using a fully analytical theory, we compute the leading order corrections to the translational, rotational and translation-rotation coupling mobilities of an arbitrary axisymmetric particle immersed in a Newtonian fluid moving near an elastic cell membrane that exhibits resistance towards stretching and bending. The frequency-dependent mobility corrections are expressed as general relations involving separately the particle's shape-dependent bulk mobility and the shape-independent parameters such as the membrane-particle distance, the particle orientation and the characteristic frequencies associated with shearing and bending of the membrane. This makes the equations applicable to an arbitrary-shaped axisymmetric particle provided that its bulk mobilities are known, either analytically or numerically. For a spheroidal particle, these general relations reduce to simple expressions in terms of the particle's eccentricity. We find that the corrections to the translation-rotation coupling mobility are primarily determined by bending, whereas shearing manifests itself in a more pronounced way in the rotational mobility. We demonstrate the validity of the analytical approximations by a detailed comparison with boundary integral simulations of a truly extended spheroidal particle. They are found to be in a good agreement over the whole range of applied frequencies.

physics.flu-dyn↗

arXiv2016

Clustering of microscopic particles in constricted blood flow

A mixed suspension of red blood cells (RBCs) and microparticles flows through a cylindrical channel with a constriction mimicking a stenosed blood vessel. Our three-dimensional Lattice-Boltzmann simulations show that the RBCs are depleted right ahead and after the constriction. Although the RBC mean concentration (hematocrit) is 16.5% or 23.7%, their axial concentration profile is very similar to that of isolated tracer particles flowing along the central axis. Most importantly, however, we find that the stiff microparticles exhibit the opposite behavior. Arriving on a marginated position near the channel wall, they can pass through the constriction only if they find a suitable gap to dip into the dense plug of RBCs occupying the channel center. This leads to a prolonged dwell time and, as a consequence, to a pronounced increase in microparticle concentration right in front of the constriction. For biochemically active particles such as drug delivery agents or activated platelets this clustering may lead to physiologically relevant hot spots of biochemical activity.

physics.flu-dyn↗

arXiv2016

Cross-stream transport of asymmetric particles driven by oscillating shear

We study the dynamics of asymmetric, deformable particles in oscillatory, linear shear flow. By simulating the motion of a dumbbell, a ring polymer, and a capsule we show that cross-stream migration occurs for asymmetric elastic particles even in linear shear flow if the shear rate varies in time. The migration is generic as it does not depend on the particle dimension. Importantly, the migration velocity and migration direction are robust to variations of the initial particle orientation, making our proposed scheme suitable for sorting particles with asymmetric material properties.

cond-mat.soft↗

arXiv2016

Hydrodynamic interaction between particles near elastic interfaces

We present an analytical calculation of the hydrodynamic interaction between two spherical particles near an elastic interface such as a cell membrane. The theory predicts the frequency dependent self- and pair-mobilities accounting for the finite particle size up to the 5th order in the ratio between particle diameter and wall distance as well as between diameter and interparticle distance. We find that particle motion towards a membrane with pure bending resistance always leads to mutual repulsion similar as in the well-known case of a hard-wall. In the vicinity of a membrane with shearing resistance, however, we observe an attractive interaction in a certain parameter range which is in contrast to the behavior near a hard wall. This attraction might facilitate surface chemical reactions. Furthermore, we show that there exists a frequency range in which the pair-mobility for perpendicular motion exceeds its bulk value, leading to short-lived superdiffusive behavior. Using the analytical particle mobilities we compute collective and relative diffusion coefficients. The appropriateness of the approximations in our analytical results is demonstrated by corresponding boundary integral simulations which are in excellent agreement with the theoretical predictions.

physics.flu-dyn↗

arXiv2016

Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation

We study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due to the elastic energy stored in the membrane. Unlike the single-membrane case, a coupling between shearing and bending exists. The commonly used approximation of superposing two single-membrane contributions is found to give reasonable results only for motions in the parallel, but not in the perpendicular direction. We also compute analytically the membrane deformation resulting from the motion of the particle, showing that the presence of the second membrane reduces deformation. Using the fluctuation-dissipation theorem we compute the Brownian motion of the particle, finding a long-lasting subdiffusive regime at intermediate time scales. We finally assess the accuracy of the employed point-particle approximation via boundary-integral simulations for a truly extended particle. They are found to be in excellent agreement with the analytical predictions.

physics.flu-dyn↗

arXiv2016

Long-lived anomalous thermal diffusion induced by elastic cell membranes on nearby particles

The physical approach of a small particle (virus, medical drug) to the cell membrane represents the crucial first step before active internalization and is governed by thermal diffusion. Using a fully analytical theory we show that the stretching and bending of the elastic membrane by the approaching particle induces a memory in the system which leads to anomalous diffusion, even though the particle is immersed in a purely Newtonian liquid. For typical cell membranes the transient subdiffusive regime extends beyond 10 ms and can enhance residence times and possibly binding rates up to 50\%. Our analytical predictions are validated by numerical simulations.

physics.flu-dyn↗

arXiv2013

Air flow in a collapsing cavity

We experimentally study the airflow in a collapsing cavity created by the impact of a circular disk on a water surface. We measure the air velocity in the collapsing neck in two ways: Directly, by means of employing particle image velocimetry of smoke injected into the cavity and indirectly, by determining the time rate of change of the volume of the cavity at pinch-off and deducing the air flow in the neck under the assumption that the air is incompressible. We compare our experiments to boundary integral simulations and show that close to the moment of pinch-off, compressibility of the air starts to play a crucial role in the behavior of the cavity. Finally, we measure how the air flow rate at pinch-off depends on the Froude number and explain the observed dependence using a theoretical model of the cavity collapse.

physics.flu-dyn↗

arXiv2012

Collapse of a non-axisymmetric, impact-created air cavity in water

The axisymmetric collapse of a cylindrical air cavity in water follows a universal power law with logarithmic corrections. Nonetheless, it has been suggested that the introduction of a small azimuthal disturbance induces a long term memory effect, reflecting in oscillations which are no longer universal but remember the initial condition. In this work, we create non-axisymmetric air cavities by driving a metal disc through an initially-quiescent water surface and observe their subsequent gravity-induced collapse. The cavities are characterized by azimuthal harmonic disturbances with a single mode number $m$ and amplitude $a_m$. For small initial distortion amplitude (1 or 2% of the mean disc radius), the cavity walls oscillate linearly during collapse, with nearly constant amplitude and increasing frequency. As the amplitude is increased, higher harmonics are triggered in the oscillations and we observe more complex pinch-off modes. For small amplitude disturbances we compare our experimental results with the model for the amplitude of the oscillations by Schmidt et al. (2009) and the model for the collapse of an axisymmetric impact-created cavity previously proposed by Bergmann et al. (2009b). By combining these two models we can reconstruct the three-dimensional shape of the cavity at any time before pinch-off.

physics.flu-dyn↗

arXiv2010

Breakup of diminutive Rayleigh jets

Discharging a liquid from a nozzle at sufficient large velocity leads to a continuous jet that due to capillary forces breaks up into droplets. Here we investigate the formation of microdroplets from the breakup of micron-sized jets with ultra high-speed imaging. The diminutive size of the jet implies a fast breakup time scale $τ_\mathrm{c} = \sqrt{ρr^3 / γ}$ of the order of 100\,ns{}, and requires imaging at 14 million frames per second. We directly compare these experiments with a numerical lubrication approximation model that incorporates inertia, surface tension, and viscosity [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Shi, Brenner, and Nagel, Science 265, 219 (1994)]. The lubrication model allows to efficiently explore the parameter space to investigate the effect of jet velocity and liquid viscosity on the formation of satellite droplets. In the phase diagram we identify regions where the formation of satellite droplets is suppressed. We compare the shape of the droplet at pinch-off between the lubrication approximation model and a boundary integral (BI) calculation, showing deviations at the final moment of the pinch-off. Inspite of this discrepancy, the results on pinch-off times and droplet and satellite droplet velocity obtained from the lubrication approximation agree with the high-speed imaging results.

physics.flu-dyn↗

arXiv2010

Supersonic Air Flow due to Solid-Liquid Impact

A solid object impacting on liquid creates a liquid jet due to the collapse of the impact cavity. Using visualization experiments with smoke particles and multiscale simulations we show that in addition a high-speed air-jet is pushed out of the cavity. Despite an impact velocity of only 1 m/s, this air-jet attains \emph{supersonic} speeds already when the cavity is slightly larger than 1 mm in diameter. The structure of the air flow resembles closely that of compressible flow through a nozzle -- with the key difference that here the "nozzle" is a \emph{liquid} cavity shrinking rapidly in time.

physics.flu-dyn↗

arXiv2009

Collapse of Non-Axisymmetric Cavities

A round disk with a harmonic disturbance impacts on a water surface and creates a non-axisymmetric cavity which collapses under the influence of hydrostatic pressure. We use disks deformed with mode m=2 to m=6. For all mode numbers we find clear evidence for a phase inversion of the cavity wall during the collapse. We present a fluid dynamics video showing high speed imaging of different modes, pointing out the characteristic features during collapse.

physics.flu-dyn↗

arXiv2009

Generation and Breakup of Worthington Jets After Cavity Collapse

Helped by the careful analysis of their experimental data, Worthington (1897) described roughly the mechanism underlying the formation of high-speed jets ejected after the impact of an axisymmetric solid on a liquid-air interface. In this work we combine detailed boundary-integral simulations with analytical modeling to describe the formation and break-up of such Worthington jets in two common physical systems: the impact of a circular disc on a liquid surface and the release of air bubbles from an underwater nozzle. We first show that the jet base dynamics can be predicted for both systems using our earlier model in Gekle, Gordillo, van der Meer and Lohse. Phys. Rev. Lett. 102 (2009). Nevertheless, our main point here is to present a model which allows us to accurately predict the shape of the entire jet. Good agreement with numerics and some experimental data is found. Moreover, we find that, contrarily to the capillary breakup of liquid cylinders in vacuum studied by Rayleigh, the breakup of stretched liquid jets at high values of both Weber and Reynolds numbers is not triggered by the growth of perturbations coming from an external source of noise. Instead, the jet breaks up due to the capillary deceleration of the liquid at the tip which produces a corrugation to the jet shape. This perturbation, which is self-induced by the flow, will grow in time promoted by a capillary mechanism. We are able to predict the exact shape evolution of Worthington jets ejected after the impact of a solid object - including the size of small droplets ejected from the tip due to a surface-tension driven instability - using as the single input parameters the minimum radius of the cavity and the flow field before the jet emerges.

physics.flu-dyn↗

arXiv2009

Nucleation threshold and deactivation mechanisms of nanoscopic cavitation nuclei

The acoustic nucleation threshold for bubbles trapped in cavities has theoretically been predicted within the crevice theory by Atchley & Prosperetti [J. Acoust. Soc. Am. 86, 1065-1084 (1989)]. Here, we determine this threshold experimentally, by applying a single pressure pulse to bubbles trapped in cylindrical nanoscopic pits ("artificial crevices") with radii down to 50 nm. By decreasing the minimum pressure stepwise, we observe the threshold for which the bubbles start to nucleate. The experimental results are quantitatively in excellent agreement with the theoretical predictions of Atchley & Prosperetti. In addition, we provide the mechanism which explains the deactivation of cavitation nuclei: gas diffusion together with an aspherical bubble collapse. Finally, we present superhydrophobic nuclei which cannot be deactivated, unless with a high-speed liquid jet directed into the pit.

physics.flu-dyn↗

arXiv2009

Approach to Universality in Axisymmetric Bubble Pinch-Off

The pinch-off of an axisymmetric air bubble surrounded by an inviscid fluid is compared in four physical realizations: (i) cavity collapse in the wake of an impacting disc, (ii) gas bubbles injected through a small orifice, (iii) bubble rupture in a straining flow, and (iv) a bubble with an initially necked shape. Our boundary-integral simulations suggest that all systems eventually follow the universal behavior characterized by slowly varying exponents predicted in [Eggers et al., PRL 98, 094502 (2007)]. However, the time scale for the onset of this final regime is found to vary by orders of magnitude depending on the system in question: while for the impacting disc it is well in the millisecond range, for the gas injection needle universal behavior sets in only a few microseconds before pinch-off. These findings reconcile the different views expressed in recent literature about the universal nature of bubble pinch-off.

physics.flu-dyn↗