Stokes friction coefficient of spherical particles in the presence of polymer depletion layers Analytical and numerical calculations, comparison with experimental data

Donath, Edwin; Krabi, A.; Nirschl, M.; Shilov, V.M.; Zharkikh, M. I.; Vincent, Brian

doi:10.1039/a603103j

Cited by 19 publications

(16 citation statements)

References 6 publications

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“…For a detailed discussion the reader is referred to Ref. (9). Donath et al consider the liquid flow in a polymer solution with viscosity r around an inert (nonadsorbing) spherical particle with radius R under creeping flow conditions (i.e.…”

Section: Diffusion Of Particles In a Polymer Solutionmentioning

confidence: 99%

“…Assuming a quasiflat surface for the sphere and taking the viscosity profile into account an expression for the velocity profile is obtained. Applying the hydrodynamic boundary conditions for the normal and tangential velocities at the surface the following expression for the effective viscosity r eff is obtained (9):…”

Section: Diffusion Of Particles In a Polymer Solutionmentioning

confidence: 99%

“…In addition we will use the diffusion behavior to obtain the thickness of the layer from which CMC is depleted from a solid-liquid interface. For this purpose we will apply a model proposed by Donath et al (9).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Effective Viscosity of Polymer Solutions: Relation to the Determination of the Depletion Thickness and Thickness of the Adsorbed Layer of Cellulose Derivatives

Hoogendam

Peters

Tuinier

et al. 1998

Journal of Colloid and Interface Science

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Section: Diffusion Of Particles In a Polymer Solutionmentioning

confidence: 99%

Section: Diffusion Of Particles In a Polymer Solutionmentioning

confidence: 99%

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Effective Viscosity of Polymer Solutions: Relation to the Determination of the Depletion Thickness and Thickness of the Adsorbed Layer of Cellulose Derivatives

Hoogendam

Peters

Tuinier

et al. 1998

Journal of Colloid and Interface Science

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“…In order to quantify the dynamic effects of a depletion layer, Donath and coworkers proposed an approximation for the hydrodynamic friction of a sphere in a non-adsorbing polymer solution by considering a slip boundary condition at the surface of the particle [22].…”

Section: Introductionmentioning

confidence: 99%

Stochastic interactions of two Brownian hard spheres in the presence of depletants

Karzar-Jeddi

Tuinier

Taniguchi

et al. 2014

The Journal of Chemical Physics

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Brownian dynamics simulation of the motion of a rigid sphere in a viscous fluid very near a wall J. Chem. Phys. 113, 9268 (2000) A quantitative analysis is presented for the stochastic interactions of a pair of Brownian hard spheres in non-adsorbing polymer solutions. The hard spheres are hypothetically trapped by optical tweezers and allowed for random motion near the trapped positions. The investigation focuses on the longtime correlated Brownian motion. The mobility tensor altered by the polymer depletion effect is computed by the boundary integral method, and the corresponding random displacement is determined by the fluctuation-dissipation theorem. From our computations it follows that the presence of depletion layers around the hard spheres has a significant effect on the hydrodynamic interactions and particle dynamics as compared to pure solvent and uniform polymer solution cases. The probability distribution functions of random walks of the two interacting hard spheres that are trapped clearly shift due to the polymer depletion effect. The results show that the reduction of the viscosity in the depletion layers around the spheres and the entropic force due to the overlapping of depletion zones have a significant influence on the correlated Brownian interactions. © 2014 AIP Publishing LLC. [http://dx

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“…An explicit, simple equation of f exists for single spheres in an ideally homogeneous medium by the Stokes law. Real systems, however, face deviations from that, caused either by a non-spherical object shape 10 11 12 13 14 15 or by anisotropic environments such as in non-ideal fluids or at surfaces/interfaces 16 17 18 19 20 , e.g. in a cell or a microchannel 21 22 23 .…”

mentioning

confidence: 99%

Rotational friction of dipolar colloids measured by driven torsional oscillations

Steinbach

Gemming

Erbe

2016

Sci Rep

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Despite its prominent role in the dynamics of soft materials, rotational friction remains a quantity that is difficult to determine for many micron-sized objects. Here, we demonstrate how the Stokes coefficient of rotational friction can be obtained from the driven torsional oscillations of single particles in a highly viscous environment. The idea is that the oscillation amplitude of a dipolar particle under combined static and oscillating fields provides a measure for the Stokes friction. From numerical studies we derive a semi-empirical analytic expression for the amplitude of the oscillation, which cannot be calculated analytically from the equation of motion. We additionally demonstrate that this expression can be used to experimentally determine the rotational friction coefficient of single particles. Here, we record the amplitudes of a field-driven dipolar Janus microsphere with optical microscopy. The presented method distinguishes itself in its experimental and conceptual simplicity. The magnetic torque leaves the local environment unchanged, which contrasts with other approaches where, for example, additional mechanical (frictional) or thermal contributions have to be regarded.Frictional forces play a fundamental role in the dynamics of mesoscopic objects, which are omnipresent in microfluidic and biological systems. The frictional interaction of moving objects with the viscous environment affects e.g. transport, demixing, diffusion, and propulsion [1][2][3][4][5] . The study of friction during these processes also gives access to the rheological and the aggregation behavior of colloids such as ferrofluids and gels [6][7][8][9] . In incompressible fluids, the key quantity is the Stokes friction coefficient f, which is the proportionality factor between the particle velocity and the drag force. Often, many-body effects in dense systems can be expressed as an expansion of the single-particle friction. An explicit, simple equation of f exists for single spheres in an ideally homogeneous medium by the Stokes law. Real systems, however, face deviations from that, caused either by a non-spherical object shape [10][11][12][13][14][15] or by anisotropic environments such as in non-ideal fluids or at surfaces/interfaces [16][17][18][19][20] , e.g. in a cell or a microchannel [21][22][23] . As most of these problems cannot be solved analytically one relies on approximate solutions 24 or on experimental measurements. Friction from translational motion behaves differently from the friction during rotational motion 16,25,26 ; for analysis sometimes both need to be decoupled 27,28 . Experimentally, the translational friction, f t , can be simply derived from the spatial displacement of a diffusing particle via optical methods. Rotational friction, f r , however, remains difficult to determine since additionally the orientation of the object has to be determined, which requires optical or shape anisotropy.For nanoscopic objects, measurement methods rely on, e.g., scattering techniques 13,29,30 , time-resolved phospho...

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Stokes friction coefficient of spherical particles in the presence of polymer depletion layers Analytical and numerical calculations, comparison with experimental data

Cited by 19 publications

References 6 publications

Effective Viscosity of Polymer Solutions: Relation to the Determination of the Depletion Thickness and Thickness of the Adsorbed Layer of Cellulose Derivatives

Effective Viscosity of Polymer Solutions: Relation to the Determination of the Depletion Thickness and Thickness of the Adsorbed Layer of Cellulose Derivatives

Stochastic interactions of two Brownian hard spheres in the presence of depletants

Rotational friction of dipolar colloids measured by driven torsional oscillations

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