Faxén's theorem for nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow

Vázquez-Quesada, Adolfo; Ellero, Marco; Español, Pep

doi:10.1103/physreve.87.032301

Cited by 2 publications

(2 citation statements)

References 32 publications

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“…Effects of probe inertia and fluid inertia, including possible implications for data analysis, have been discussed in detail elsewhere [33][34][35][36]. At even shorter time scales, compressibility effects may in addition become relevant, and these have been studied [37], prompted by recent developments of experiments capable of resolving the very-short-time probe motion [38]. It has to be noted, however, that these studies typically still model the fluid as a viscoelastic continuum, implying its structural length scales to be well separated from the probe size a.…”

Section: Theoretical Model For Microrheologymentioning

confidence: 99%

Microrheology of colloidal systems

Puertas

Voigtmann

2014

J. Phys.: Condens. Matter

105

110

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Microrheology was proposed almost twenty years ago as a technique to obtain rheological properties in soft matter from the microscopic motion of colloidal tracers used as probes, either freely diffusing in the host medium, or subjected to external forces. The former case is known as passive microrheology, and is based on generalizations of the Stokes-Einstein relation between the friction experienced by the probe and the host-fluid viscosity. The latter is termed active microrheology, and extends the measurement of the friction coefficient to the nonlinear-response regime of strongly driven probes. In this review article, we discuss theoretical models available in the literature for both passive and active microrheology, focusing on the case of single-probe motion in model colloidal host media. A brief overview of the theory of passive microrheology is given, starting from the work of Mason and Weitz. Further developments include refined models of the host suspension beyond that of a Newtonian-fluid continuum, and the investigation of probe-size effects. Active microrheology is described starting from microscopic equations of motion for the whole system including both the host-fluid particles and the tracer; the many-body Smoluchowski equation for the case of colloidal suspensions. At low fluid densities, this can be simplified to a two-particle equation that allows the calculation of the friction coefficient with the input of the density distribution around the tracer, as shown by Brady and coworkers. The results need to be upscaled to agree with simulations at moderate density, in both the case of pulling the tracer with a constant force or dragging it at a constant velocity. The full many-particle equation has been tackled by Fuchs and coworkers, using a mode-coupling approximation and the scheme of integration through transients, valid at high densities. A localization transition is predicted for a probe embedded in a glass-forming host suspension. The nonlinear probe-friction coefficient is calculated from the tracer's position correlation function. Computer simulations show qualitative agreement with the theory, but also some unexpected features, such as superdiffusive motion of the probe related to the breaking of nearest-neighbor cages. We conclude with some perspectives and future directions of theoretical models of microrheology.

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Section: Theoretical Model For Microrheologymentioning

confidence: 99%

Microrheology of colloidal systems

Puertas

Voigtmann

2014

J. Phys.: Condens. Matter

105

110

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“…This finally allows to better understand the frequency-dependence of particle pair interactions. With this paper we therefore combine recent advancements in hydrodynamic theory [17,19,24,25], computer simulations and experiments of single particles in (viscoelastic) fluids [21][22][23] and non-Markovian modeling [26,27].…”

Section: Introductionmentioning

confidence: 99%

Frequency-dependent hydrodynamic interaction between two solid spheres

Jung

Schmid

2017

Physics of Fluids

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Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that the compressibility of the fluid has a significant impact on frequency-dependent pair interactions.The predictions of the hydrodynamic theory are compared to molecular dynamics simulations of two solid spheres in a Lennard-Jones fluid. For this system we reconstruct memory functions by extending the inverse Volterra technique. The simulation data agree very well with the theory, therefore, the theory can be used to implement dynamically consistent hydrodynamic interactions in the increasingly popular field of non-Markovian modeling.

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Faxén's theorem for nonsteady motion of a sphere through a compressible linear viscoelastic fluid in arbitrary flow

Cited by 2 publications

References 32 publications

Microrheology of colloidal systems

Microrheology of colloidal systems

Frequency-dependent hydrodynamic interaction between two solid spheres

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