Christel Hohenegger

Diffusion-induced bias in near-wall velocimetry

The Brownian fluctuations of the colloidal tracers often used in microscale velocimetry are typically isotropic in the bulk. In the near-wall region, however, these fluctuations are strongly affected by the hydrodynamic interaction with the wall and by the no-flux condition imposed by the wall. These wall effects can, under appropriate conditions, bias measurements based on colloidal tracers, potentially leading to significant overestimation of near-wall velocities. We use a Fokker–Planck description to generate probability density functions of the distances from a single wall sampled by the matched particles that are present in the same window at both the start and end of a time interval. The importance of the resulting bias for experimental parameters is then quantified in terms of the size of the imaged region and measurement interval. We conclude with a brief discussion of the implications for near-wall velocimetry measurements.

Statistical Reconstruction of Velocity Profiles for Nanoparticle Image Velocimetry

Velocities and Brownian effects at nanoscales near channel walls can be measured experimentally in an image plane parallel to the wall by evanescent wave illumination techniques [R. Sadr, M. Yoda, Z. Zheng, and A. T. Conlisk, J. Fluid Mech., 506 (2004), pp. 357–367], but the depth of field in this technique is difficult to modify. Assuming mobility of spherical particles dominated by hydrodynamic interaction between particle and wall, the out-of-plane dependence of the mobility and in-plane velocity are clearly coupled. We investigate such systems computationally, using a Milstein algorithm that is both weak- and strong-order 1. In particle image velocimetry (PIV), image pairs are cross-correlated to approximate the mean displacement of n matched particles between two windows. For comparison, we demonstrate that a maximum likelihood algorithm can reconstruct the out-of-plane velocity profile, as specified velocities at multiple points, given known mobility dependence and perfect mean measurements. We then...

Fluidparticle dynamics for passive tracers advected by a thermally fluctuating viscoelastic medium

Many biological fluids, like mucus and cytoplasm, have prominent viscoelastic properties. As a consequence, immersed particles exhibit subdiffusive behavior, which is to say, the variance of the particle displacement grows sublinearly with time. In this work, we propose a viscoelastic generalization of the LandauLifschitz NavierStokes fluid model and investigate the properties of particles that are passively advected by such a medium. We exploit certain exact formulations that arise from the Gaussian nature of the fluid model and introduce analysis of memory in the fluid statistics, marking an important step toward capturing fluctuating hydrodynamics among subdiffusive particles. The proposed method is spectral, meshless and is based on the numerical evaluation of the covariance matrix associated with individual fluid modes. With this method, we probe a central hypothesis of passive microrheology, a field premised on the idea that the statistics of particle trajectories can reveal fundamental information about their surrounding fluid environment.

DIMENSIONAL REDUCTION OF A MULTISCALE CONTINUUM MODEL OF MICROTUBULE GLIDING ASSAYS

Microtubule gliding assays, in which molecular motors anchored to a plate drive the gliding motion of filaments in a quasi--two-dimensional fluid layer, have been shown to organize into a variety of large-scale patterns. We derive a fully three-dimensional multiscale coarse-grained model of a gliding assay including the evolution of densities of rigid filaments, bound motors, and free motors, coupled to fluid equations. Our model combines continuum theories of polymeric liquids with the force spreading approach of the immersed boundary method. We use dimensional and asymptotic analysis to derive a reduced two-dimensional model and show that, to leading order, the filaments evolve in a plane, similar to what is experimentally observed. We simulate our model numerically with a GPU-based implementation and observe the same qualitative behavior as in experimental work.

Modeling aspects of two-bead microrheology

We revisit the Mason and Weitz (Phys. Rev. Lett., 74, 1995) and Levine and Lubensky (Phys. Rev. Lett., 85, 2000) analysis for one‐ and two‐bead microrheology. Our first motivation is the possibility of drawing inferences from experimental data about local diffusive properties of individual beads and nonlocal dynamic moduli of the medium separating the two beads. Our second motivation is the ability to perform direct numerical simulations of hydrodynamically coupled Brownian beads in soft matter. For both goals, we first must have a model for the coupling between these two transport properties. We reformulate the coupled generalized Langevin equations (GLE) following the scalar GLE analysis of Fricks et al. (J. Appl. Math., 2008), assuming an exponential series parametrization of both local and nonlocal memory kernels. We then show the two‐bead GLE model can be represented as a vector Ornstein‐Uhlenbeck process, which allows for a fast and statistically accurate numerical simulation of coupled bead paths (...

A Variational Characterization of Fluid Sloshing with Surface Tension

We consider the sloshing problem for an incompressible, inviscid, irrotational fluid in an open container, including effects due to surface tension on the free surface. We restrict ourselves to a constant contact angle and seek time-harmonic solutions of the linearized problem, which describes the time-evolution of the fluid due to a small initial disturbance of the surface at rest. As opposed to the zero surface tension case, where the problem reduces to a partial differential equation for the velocity potential, we obtain a coupled system for the velocity potential and the free surface displacement. We derive a new variational formulation of the coupled problem and establish the existence of solutions using the direct method from the calculus of variations. We prove a domain monotonicity result for the fundamental sloshing eigenvalue. In the limit of zero surface tension, we recover the variational formulation of the mixed Steklov-Neumann eigenvalue problem and give the first-order perturbation formula for a simple eigenvalue.

A Micro-Macro Framework for Analyzing Steric and Hydrodynamic Interactions in Gliding Assays

Macroscopic flows of filament-motor mixtures, driven by the hydrolysis of ATP, are important to many cellular processes such as cytoplasmic streaming in Drosophila oocytes and cortical flow in the first cell division of C. elegans. Gliding assays, reduced in vitro model systems where motor proteins adsorbed onto a planar substrate bind to and move filaments, recreate large-scale dynamic patterns like coherent swarming motion and density waves. These systems are sensitive to the microscopic behavior such as motor protein binding and unbinding dynamics, which take place on a faster timescale than the direct and fluid-mediated filament interactions. In this work, we present a multiscale modeling and simulation framework for gliding assays that allows detailed microscopic motor modeling as well as both steric and hydrodynamic interactions between filaments. Our model is based on continuum kinetic theory, and our implementation utilizes CPU and GPU parallelism to track the sparse but high-dimensional state spa...