arXiv subjects

Sascha Hilgenfeldt

Publications and source records attributed to Sascha Hilgenfeldt.

At least 19 recordsLinked to original sources

arXiv2025

Controlled particle displacement by hydrodynamic obstacle interaction in non-inertial flows

Systematic deflection of microparticles off of initial streamlines is a fundamental task in microfluidics, aiming at applications including sorting, accumulation, or capture of the transported particles. In a large class of setups, including Deterministic Lateral Displacement and porous media filtering, particles in non-inertial (Stokes) flows are deflected by an array of obstacles. We show that net deflection of force-free particles passing an obstacle in Stokes flow is possible solely by hydrodynamic interactions if the flow and obstacle geometry break fore-aft symmetries. The net deflection is maximal for certain initial conditions and we analytically describe its scaling with particle size, obstacle shape, and flow geometry, confirmed by direct trajectory simulations. For realistic parameters, separation by particle size is comparable to what is found assuming contact (roughness) interactions. Our approach also makes systematic predictions on when short-range attractive forces lead to particle capture or sticking. In separating hydrodynamic effects on particle motion strictly from contact interactions, we provide novel, rigorous guidelines for elementary microfluidic particle manipulation and filtering.

physics.flu-dyn↗

arXiv2025

Principles of hydrodynamic particle manipulation in internal Stokes flow

Manipulation of small-scale particles across streamlines is the elementary task of microfluidic devices. Many such devices operate at very low Reynolds numbers and deflect particles using arrays of obstacles, but a systematic quantification of relevant hydrodynamic effects has been lacking. Here, we explore an alternate approach, rigorously modeling the displacement of force-free spherical particles in vortical Stokes flows under hydrodynamic particle-wall interaction. Certain Moffatt-like eddy geometries with broken symmetry allow for systematic deflection of particles across streamlines, leading to particle accumulation at either Faxen field fixed points or limit cycles. Moreover, particles can be forced onto trajectories approaching channel walls exponentially closely, making quantitative predictions of particle capture (sticking) by short-range forces possible. This rich, particle size-dependent behavior suggests the versatile use of inertial-less flow in devices with a long particle residence time for concentration, sorting, or filtering.

physics.flu-dyn↗

arXiv2025

Cell Deformation Signatures along the Apical-Basal Axis: A 3D Continuum Mechanics Shell Model

Two-dimensional (2D) mechanical models of confluent tissues have related the mechanical state of a monolayer of cells to the average perimeter length of the cell cross sections, predicting floppiness or rigidity of the material. For the well-studied system of in-vitro MDCK epithelial cells, however, we find experimentally that cells in mechanically rigid tissues display long perimeters characteristic of a floppy state in 2D models. We suggest that this discrepancy is due to mechanical effects in the third (apical-basal) dimension, including those caused by actin stress fibers near the basal membrane. To quantitatively understand cell deformations in 3D, we develop a continuum mechanics model of epithelial cells as elastic cylindrical shells, with appropriate boundary conditions reflecting both the passive confinement of neighboring cells and the active stress of actomyosin contractility. This formalism yields analytical solutions predicting cell cross sections along the entire cylinder axis. Deconvolution microscopy experimental data confirm the significant and systematic change in cell shape parameters in this apical-basal direction. In addition to providing a wealth of detailed information on deformation on the subcellular scale, the results of the approach alter our understanding of how active tissues balance requirements of their stiffness and integrity, suggesting they are more robust against loss of rigidity than previously inferred.

cond-mat.soft↗

arXiv2024

A thermodynamic approach to adhesion and deformation of DNA-bound droplets

Here we derive and experimentally test a free energy functional that captures the adhesion of DNA-coated emulsion droplets. Generalizing previous approaches, the theory combines important energetic and entropic effects of microscopic DNA mechanics and droplet elasticity. It simultaneously predicts adhesion size, morphology, and binder concentration as a function of experimental control parameters. Notably, droplets transition from undeformed binding to flat droplet interfaces at a characteristic DNA coverage. These equilibrium predictions agree quantitatively with experiments on droplet-substrate and droplet-droplet binding, revealing a weak effective binding strength of $3.7\pm0.3\text{k}_{\text{B}}\text{T}$ owing to entropic costs. Our results open the path to rich design strategies for making colloidal architectures.

cond-mat.soft↗

arXiv2024

Exceptionally Dense and Resilient Polydisperse Disk Packings

Understanding the way disordered particle packings transition between jammed (rigid) and unjammed (fluid) states is of both great practical importance and strong fundamental interest. The values of critical packing fraction (and other state variables) at the jamming transition are protocol dependent. Here, we demonstrate that this variability can be systematically traced to structural measures of packing, as well as to energy measures inside the jamming regime. A novel generalized simultaneous particle swap algorithm constructs overjammed states of desired energy, which upon decompression lead to predictable critical packing fractions. Thus, for a given set of particle sizes, states with extraordinarily high critical packing fractions can be found efficiently, which sustain substantial shear strain and preserve their special structure over the entire jammed domain. The close relation revealed here between the energy landscape of overjammed soft-particle packings and the behavior near the jamming transition points towards new ways of understanding and constructing disordered materials with exceptional properties.

cond-mat.soft↗

arXiv2023

Density-contrast induced inertial forces on particles in oscillatory flows

Oscillatory flows have become an indispensable tool in microfluidics, inducing inertial effects for displacing and manipulating fluid-borne objects in a reliable, controllable, and label-free fashion. However, the quantitative description of such effects has been confined to limit cases and specialized scenarios. Here we develop an analytical formalism yielding the equation of motion of density-mismatched spherical particles in arbitrary background flows, generalizing previous work. Inertial force terms are systematically derived from the geometry of the flow field together with analytically known Stokes number dependences. Supported by independent, first-principles direct numerical simulations, we find that these forces are important even for nearly density-matched objects such as cells or bacteria, enabling their fast displacement and separation. Our formalism thus generalizes the Maxey--Riley equation, encompassing not only particle inertia, but consistently recovering, in the limit of large Stokes numbers, the Auton modification to added mass as well as the far-field acoustofluidic secondary radiation force.

physics.flu-dyn↗

arXiv2021

DNA self-organization controls valence in programmable colloid design

Just like atoms combine into molecules, colloids can self-organize into predetermined structures according to a set of design principles. Controlling valence -- the number of inter-particle bonds -- is a prerequisite for the assembly of complex architectures. The assembly can be directed via solid `patchy' particles with prescribed geometries to make, for example, a colloidal diamond. We demonstrate here that the nanoscale ordering of individual molecular linkers can combine to program the structure of microscopic assemblies. Specifically, we experimentally show that covering initially isotropic microdroplets with $N$ mobile DNA linkers results in spontaneous and reversible self-organization of the DNA into $Z(N)$ binding patches, selecting a predictable valence. We understand this valence thermodynamically, deriving a free energy functional for droplet-droplet adhesion that accurately predicts the equilibrium size of and molecular organization within patches, as well as the observed valence transitions with $N$. Thus, microscopic self-organization can be programmed by choosing the molecular properties and concentration of binders. These results are widely applicable to the assembly of any particle with mobile linkers, such as functionalized liposomes or protein interactions in cell-cell adhesion.

cond-mat.soft↗

arXiv2021

Predicting the Characteristics of Defect Transitions on Curved Surfaces

The energetically optimal position of lattice defects on intrinsically curved surfaces is a complex function of shape parameters. For open surfaces, a simple condition predicts the critical size for which a central disclination yields lower energy than a boundary disclination. In practice, this transition is modified by activation energies or more favorable intermediate defect positions. Here it is shown that these transition characteristics (continuous or discontinuous, first or second order) can also be inferred from analytical, general criteria evaluated from the surface shape. A universal scale of activation energy is found, and the criterion is generalized to predict transition order as symmetries such as that of the shape are broken. The results give practical insight into structural transitions to disorder in many cellular materials of technological and biological importance.

cond-mat.soft↗

arXiv2021

An unrecognized force in inertial microfluidics

Describing effects of small but finite inertia on suspended particles is a fundamental fluid dynamical problem that has never been solved in full generality. Modern microfluidics has turned this academic problem into a practical challenge through the use of high-frequency oscillatory flows, perhaps the most efficient way to take advantage of inertial effects at low Reynolds numbers, to precisely manipulate particles, cells and vesicles without the need for charges or chemistry. The theoretical understanding of flow forces on particles has so far hinged on the pioneering work of Maxey and Riley (MR in the following), almost 40 years ago. We demonstrate here theoretically and computationally that oscillatory flows exert previously unexplained, significant and persistent forces, that these emerge from a combination of particle inertia and spatial flow variation, and that they can be quantitatively predicted through a generalization of MR.

physics.flu-dyn↗

arXiv2020

Size-dependent particle migration and trapping in 3D microbubble streaming flows

Acoustically actuated sessile bubbles can be used as a tool to manipulate microparticles, vesicles and cells. In this work, using acoustically actuated sessile semi-cylindrical microbubbles, we demonstrate experimentally that finite-sized microparticles undergo size-sensitive migration and trapping towards specific spatial positions in three dimensions with high reproducibility. The particle trajectories are successfully reproduced by passive advection of the particles in a steady three-dimensional streaming flow field augmented with volume exclusion from the confining boundaries. For different particle sizes, this volume exclusion mechanism leads to three regimes of qualitatively different migratory behavior, suggesting applications for separating, trapping, and sorting of particles in three dimensions.

physics.flu-dyn↗

arXiv2020

A simple, general criterion for onset of disclination disorder on curved surfaces

Determining the positions of lattice defects on elastic surfaces with Gaussian curvature is a non-trivial task of mechanical energy optimization, particularly for surfaces with boundaries. We introduce a simple way to predict the onset of disclination disorder from the shape of bounded surfaces. The criterion fixes the value of a weighted integral Gaussian curvature to a universal constant and proves accurate across a great variety of shapes, even when previously suggested criteria fail. It is an easy avenue to improved understanding of the limitations to crystalline order in many materials.

cond-mat.soft↗

arXiv2019

Flow topology during multiplexed particle manipulation using a Stokes Trap

Trapping and manipulation of small particles underlies many scientific and technological applications. Recently, the precise manipulation of multiple small particles was demonstrated using a Stokes trap that relies only on fluid flow without the need for optical or electric fields. Active flow control generates complex flow topologies around suspended particles during the trapping process, yet the relationship between the control algorithm and flow structure is not well understood. In this work, we characterize the flow topology during active control of particle trajectories using a Stokes trap. Our results show that optimal control of two particles unexpectedly relies on flow patterns with zero or one stagnation points, as opposed to positioning two particles using two distinct stagnation points. We characterize the sensitivity of the system with respect to the parameters in the control objective function, thereby providing a systematic understanding of the trapping process. Overall, these results will be useful in guiding applications involving the controlled manipulation of multiple colloidal particles and the precise deformation of soft particles in defined flow fields.

physics.flu-dyn↗

arXiv2015

Growth control of sessile microbubbles in PDMS devices

In a microfluidic environment, the presence of bubbles is often detrimental to the functionality of the device, leading to clogging or cavitation, but microbubbles can also be an indispensable asset in other applications such as microstreaming. In either case, it is crucial to understand and control the growth or shrinkage of these bodies of air, in particular in common soft-lithography devices based on polydimethylsiloxane (PDMS), which is highly permeable to gases. In this work, we study the gas transport into and out of a bubble positioned in a microfluidic device, taking into account the direct gas exchange through PDMS as well as the transport of gas through the liquid in the device. Hydrostatic pressure regulation allows for the quantitative control of growth, shrinkage, or the attainment of a stable equilibrium bubble size. We find that the vapor pressure of the liquid plays an important role for the balance of gas transport, accounting for variability in experimental conditions and suggesting additional means of bubble size control in applications.

physics.flu-dyn↗

arXiv2015

Three-dimensional phenomena in microbubble acoustic streaming

Ultrasound-driven oscillating micro-bubbles have been used as active actuators in microfluidic devices to perform manifold tasks such as mixing, sorting and manipulation of microparticles. A common configuration consists on side-bubbles, created by trapping air pockets in blind channels perpendicular to the main channel direction. This configuration consists of acoustically excited bubbles with a semi-cylindrical shape that generate significant streaming flow. Due to the geometry of the channels, such flows have been generally considered as quasi two-dimensional. Similar assumptions are often made in many other microfluidic systems based on \emph{flat} micro-channels. However, in this paper we show that microparticle trajectories actually present a much richer behavior, with particularly strong out-of-plane dynamics in regions close to the microbubble interface. Using Astigmatism Particle Tracking Velocimetry, we reveal that the apparent planar streamlines are actually projections of a \emph{streamsurface} with a pseudo-toroidal shape. We therefore show that acoustic streaming cannot generally be assumed as a two-dimensional phenomenon in confined systems. The results have crucial consequences for most of the applications involving acoustic streaming as particle trapping, sorting and mixing.

physics.flu-dyn↗

arXiv2011

Analytical Results for Size-Topology Correlations in 2D Disc and Cellular Packings

Random tilings or packings in the plane are characterized by a size distribution of individual elements (domains) and by the statistics of neighbor relations between the domains. Most systems occurring in nature or technology have a unimodal distribution of both areas and number of neighbors. Empirically, strong correlations between these distributions have been observed and formulated as universal laws. Using only the local, correlation-free granocentric model approach with no free parameters, we construct accurate analytical descriptions for disc crystallization, size-topology correlations, and Lemaître's law.

cond-mat.soft↗

arXiv2010

Trapping, focusing and sorting of microparticles through bubble streaming

Ultrasound-driven microbubbles rectify oscillatory motion into strong steady streaming flow [1, 2]. In this fluid dynamics video, we show size-dependent trapping, focusing and sorting of microparticles, utilizing the interaction between bubble streaming and the induced streaming around the mobile particles. This mechanism is purely passive and is selective for sizes and size differentials far smaller than any scale imposed by the device geometry.

physics.flu-dyn↗

arXiv1998

Response of bubbles to diagnostic ultrasound: a unifying theoretical approach

The scattering of ultrasound from bubbles of micrometer-sized radius, such as used in contrast enhancers for ultrasound diagnostics, is studied. We show that sound scattering and ``active'' emission of sound from oscillating bubbles are not contradictory, but are just two different aspects derived from the same physics. Treating the bubble as a nonlinear oscillator, we arrive at general formulas for scattering and absorption cross sections. We show that several well-known formulas are recovered in the linear limit of this ansatz. In the case of strongly nonlinear oscillations, however, the cross sections can be larger than those for linear response by several orders of magnitude. The major part of the incident sound energy is then converted into emitted sound, unlike what happens in the linear case, where the absorption cross sections exceed the scattering cross sections.

cond-mat.soft↗

arXiv1998

Analysis of Rayleigh-Plesset dynamics for sonoluminescing bubbles

Recent work on single bubble sonoluminescence (SBSL) has shown that many features of this phenomenon, especially the dependence of SBSL intensity and stability on experimental parameters, can be explained within a hydrodynamic approach. More specifically, many important properties can already be derived from an analysis of bubble wall dynamics. This dynamics is conveniently described by the Rayleigh-Plesset (RP) equation. In this work we derive analytical approximations for RP dynamics and subsequent analytical laws for parameter dependences. These results include (i) an expression for the onset threshold of SL, (ii) an analytical explanation of the transition from diffusively unstable to stable equilibria for the bubble ambient radius (unstable and stable sonoluminescence), and (iii) a detailed understanding of the resonance structure of the RP equation. It is found that the threshold for SL emission is shifted to larger bubble radii and larger driving pressures if surface tension is enlarged, whereas even a considerable change in liquid viscosity leaves this threshold virtually unaltered. As an enhanced viscosity stabilizes the bubbles against surface oscillations, we conclude that the ideal liquid for violently collapsing, surface stable SL bubbles should have small surface tension and large viscosity, although too large viscosity (>40 times the viscosity of water) will again preclude collapses.

chao-dyn↗