Theory of Brownian motion in a Jeffreys fluid

Raǐkher, Yu. L.; Rusakov, V. V.

doi:10.1134/s1063776110110191

Cited by 22 publications

(29 citation statements)

References 17 publications

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“…In rheophysics, this combination is known as Jeffreys viscoelastic fluid [17]. Let us construct an equivalent scheme for this medium [27,28]. The initial model (see Fig.…”

Section: Classical Models Of the Fluids With Complex Rheologymentioning

confidence: 99%

Brownian Motion in the Fluids with Complex Rheology

Rusakov

Raǐkher

Perzynski

2015

Math. Model. Nat. Phenom.

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Theory of Brownian motion of a fine particle in a viscoelastic fluid continuum is developed. The rheology of the embedding medium is described in terms of classical structure (spring-and-damper) schemes. It is shown that a great variety of conceivable ramifications of such structures could be reduced to an effective Jeffreys model: a Maxwell chain shunted by a damper. This scheme comprises just three material parameters: two for viscosities (fast and slow) and one for elasticity. For the thermal motion of a particle in such a fluid, the set of Langevin equations is derived. In the cases of 1D translational and 2D orientational (rotation about fixed axis) motions, the time dependencies of mean-square displacements are found analytically. It is shown that in a Jeffreys fluid, the Brownian motion has three regimes: fast diffusion (short times), slow diffusion (long times) and a crossover of those resulting in virtual localization (dynamic confinement) of the particle. Experimental evidence for that taken from the literature is presented. The developed formalism is applied to the particles with "frozen-in" dipole moments, whose orientational motion is a combination of Brownian diffusion and regular excitation by an AC field. The dynamic susceptibilities are calculated for the ensembles of particles liable for either 2D or 3D rotations. Comparison shows that the out-of-phase part of the susceptibility χ ′′ (ω) in 3D case differs considerably from that of 2D case. Function χ(ω) for the forced 3D rotary diffusion in a Jeffreys fluid is found for the first time. In our view, it would be useful for realistic theoretical interpretation of microrheology data and the more so for estimating the particle-mediated AC field-induced heating (magnetic hyperthermia) in viscoelastic fluid media.

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“…In rheophysics, this combination is known as Jeffreys viscoelastic fluid [17]. Let us construct an equivalent scheme for this medium [27,28]. The initial model (see Fig.…”

Section: Classical Models Of the Fluids With Complex Rheologymentioning

confidence: 99%

Brownian Motion in the Fluids with Complex Rheology

Rusakov

Raǐkher

Perzynski

2015

Math. Model. Nat. Phenom.

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“…12 an example was given demonstrating that formula (11) is well capable of describing the motion of probing microparticles in a "living polymer", i.e., a concentrated solution of wormlike micelles. 12 an example was given demonstrating that formula (11) is well capable of describing the motion of probing microparticles in a "living polymer", i.e., a concentrated solution of wormlike micelles.…”

Section: Langevin Equations and Mean-square Displacementmentioning

confidence: 99%

“…The pertinent set of equations was obtained in our preceding work:12 The pertinent set of equations was obtained in our preceding work:12 …”

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confidence: 99%

Brownian motion in a viscoelastic medium modelled by a Jeffreys fluid

2013

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Theory of Brownian motion of a particle in a viscoelastic Jeffreys fluid is extended for the case of rotational motion. The employed rheological model combines two viscous mechanisms (instantaneous and retarded) and, in contrast to the Maxwell model, does not produce artifacts and works robustly when applied to diffusion of tracer particles in real complex fluids. With the aid of it, specific features of the dynamic susceptibility of a magnetic Jeffreys suspension and the viscous power losses induced by an ac field are analyzed deriving the conclusions valid for active microrheology and magnetic hyperthermia. In general aspect, it is shown that the developed phenomenology provides an archetypal "frame" for a number of mesoscopic models used to describe confined random walk transport processes in a variety of systems of both biological and inorganic origin.

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“…To get deeper insight into the sample property, different models describing a linear viscoelastic fluid have been developed. Foremost among these, is the Maxwell model [23,24] which has been further developed into the generalized Maxwell model or Jeffreys' model [25,26]. The high degree of simplification [27][28][29] used in the Maxwell model ease out calculations, but the model sometimes fails to interpret experimental results.…”

Section: Introductionmentioning

confidence: 99%

Active microrheology to determine viscoelastic parameters of Stokes-Oldroyd B fluids using optical tweezers

2019

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We use active microrheology to determine the frequency dependent moduli of a linear viscoelastic fluid in terms of the polymer time constant (λ), and the polymer (μ p ) and solvent viscosity (μ s ), respectively. We measure these parameters from the response function of an optically trapped Brownian probe in the fluid under an external perturbation, and at different dilutions of the viscoelastic component in the fluid. This is an improvement over bulk microrheology measurements in viscoelastic Stokes-Oldroyd B fluids which determine the complex elastic modulus G(ω) of the fluid, but do not, however, reveal the characteristics of the polymer chains and the Newtonian solvent of the complex fluid individually. In a recent work (Paul et al 2018 J. Phys. Condens. Matter 30, 345101), we linearized the Stokes-Oldroyd B fluid model and thereby explicitly formulated the frequency dependent moduli in terms of μ p , μ s and λ which we now extend to account for an external sinusoidal force applied to the probe particle. We measure λ, μ p , and μ s experimentally, and compare with the existing λ values in the literature for the same fluid at some of the dilution levels, and obtain good agreement. Further, we use these parameters to calculate the complex elastic modulus of the fluid again at certain dilutions and verify successfully with existing data. This establishes our method as an alternate approach in the active microrheology of complex fluids which should reveal information about the composition of such fluids in significantly greater detail and high signal to noise.

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Theory of Brownian motion in a Jeffreys fluid

Cited by 22 publications

References 17 publications

Brownian Motion in the Fluids with Complex Rheology

Brownian Motion in the Fluids with Complex Rheology

Brownian motion in a viscoelastic medium modelled by a Jeffreys fluid

Active microrheology to determine viscoelastic parameters of Stokes-Oldroyd B fluids using optical tweezers

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