Hydrodynamic Screening Research Articles

A generalized Zimm model: Hydrodynamic screening in polymer solutions

This work presents a phenomenological theory for the single-chain dynamics in semidilute and concentrated polymer solutions and allows to describe the crossover from Zimm to Rouse-like behavior both in time domain and in spatial domain. The polymer solution is described as a set of oscillators fixed in space and submerged in an incompressible fluid. It is shown that the coupled equations of motion of such a polymer system give rise to the time dependence of the Oseen-like tensor and, as a consequence, the time-dependent hydrodynamic screening length. Monomer mean-square displacements and the single-chain dynamic structure factor are calculated.

Self-diffusion of a sphere in an effective medium of rods

Self-diffusion of a sphere in a network of rods is analyzed theoretically. Hydrodynamic interactions are taken into account according to the model of Dhont et al. [J. Chem. Phys. 122, 044905 (2005); ibid.124, 044907 (2006); ibid.126, 214501 (2007)] based on the Debye-Bueche-Brinkman equation. The hydrodynamic screening length of the effective medium is assumed to be much larger than the sphere radius and the rod thickness. The self-diffusion coefficient, given by Dhont et al. in terms of four-dimensional integrals, is in this work expressed in terms of a single integral only and therefore evaluated numerically with a high precision. Moreover, simple expressions for the self-diffusion coefficient are derived and shown to be independent of the rod length. They can be useful for experimental verification of the model.

Nonlinear Response of Grafted Semiflexible Polymers in Shear Flow

Using Brownian-hydrodynamic and lattice-Boltzmann simulations, we study the nonlinear response of grafted semiflexible polymers to shear flow as a function of shear rate, grafting density, and chain stiffness. Simulation results for brush height and flow stagnation layer height agree well with a mean-field theory that incorporates the interplay of hydrodynamic screening and drag-induced polymer deformation. Our predictions for the stagnation height show excellent agreement with recent experiments on the nonlinear hydrodynamic drag of DNA-grafted colloids held in a laser trap.

Topological character of hydrodynamic screening in suspensions of hard spheres: An example of universal phenomenon

Although in the case of polymer solutions the existence of hydrodynamic screening was theoretically established some time ago, use of the same methods for suspensions of hard spheres thus far have failed to produce similar results. In this work we reconsider this problem. Using superposition of topological and London-style qualitative arguments we prove the existence of screening in hard sphere suspensions. Even though some of these arguments were employed initially for treatments of superconductivity and superfluidity, we find analogs of these phenomena in non-traditional settings such as in colloidal suspensions, turbulence, magnetohydrodynamics, etc. In particular, in suspensions, we demonstrate that the hydrodynamic screening is an exact analog of Meissner effect in superconductors. The extent of screening depends on the volume fraction of hard spheres. The zero volume fraction limit corresponds to the normal state. The case of finite volume fractions-to the mixed state typical for superconductors of the second kind with such a state becoming fully “superconducting” at the critical volume fraction φ ∗ for which the (zero frequency) relative viscosity η ( relative ) diverges. Brady and, independently, Bicerano et al using scaling-type arguments predicted that for φ close to φ ∗ the viscosity η ( relative ) behaves as C ( 1 − φ / φ ∗ ) − 2 with C being some constant. Their prediction is well supported by experimental data. In this work we explain such a behavior of viscosity in terms of a topological-type transition which, mathematically can be made isomorphic to the more familiar Bose–Einstein condensation transition. Because of this, the results and methods of this work are not limited to suspensions. In the concluding section we describe other applications ranging from turbulence and magnetohydrodynamics to high temperature superconductors and QCD, etc.

Hydrodynamic flow induced anisotropy in colloid adsorption

The possibility to induce structure in layers of colloid particles by using the hydrodynamic blocking effect is investigated both experimentally and by using Monte Carlo simulations. Latex particles with diameters of 1.1 μ m and 0.46 μ m are deposited on 3-amino-propyltriethoxysilane (APTES) functionalized substrates under shear flow conditions. The spatial particle distribution in the adsorbed layers is analyzed using a two-dimensional map of the pair correlation function obtained from image analysis of optical micrographs. This pair correlation map (PCM) enables visualization of the exclusion zone and allows determination of its length as a function of the Peclet number. We find that this shadow length scales with the Peclet number with an exponent less than one due to attractive particle–surface interactions. Results obtained by Monte Carlo simulations using a random sequential adsorption (RSA) model are analyzed using the same PCM and show qualitative agreement with the experiments. The reduced particle density behind particles in the flow direction promises the possibility to selectively deposit particles in these locations after reducing the hydrodynamic screening of the surface. Simulations show that it is indeed possible to self-assemble particle pairs by performing consecutive depositions under different flow conditions on the same surface.

Visualizing phase separation in polystyrene/polystyrene homo‐IPNs via sulfonation

AbstractBACKGROUND: Polystyrene/polystyrene (PS/PS) interpenetrating polymer networks (IPNs) represent ideal homo‐IPNs. Whether phase separation occurs in this system has been a long‐standing problem, which is closely related to the self‐organization mechanism in IPN formation and is important to the exploration of new polymer morphologies and properties by topological isomerism.RESULTS: A series of bead samples of PS/PS sequential IPNs with the same nominal divinylbenzene contents were synthesized by suspension polymerization, followed by sulfonation. Scanning electron micrographs and energy‐dispersive X‐ray mapping show unique distinctive topography on both surfaces and fractured surfaces and large heterogeneity in sulfonation of the PS/PS IPN beads, which for the first time provide visual evidence for dual‐phase continuity in PS/PS IPNs.CONCLUSION: The phase separation behavior is proposed to be due to hydrodynamic screening, architectural asymmetry and excluded volume interactions between network I and the precursor chains of network II. This is considered to represent pure IPN effects in sequential formation and may shed light on the general constitution mechanism and molecular design of IPN materials. Copyright © 2009 Society of Chemical Industry

Polyelectrolytes in electric fields: measuring the dynamical effective charge and effective friction

We use a coarse-grained molecular dynamics model to study the electrophoretic behaviour of flexible polyelectrolyte chains. We first characterize the static properties of the model with respect to the chain length, the polyelectrolyte concentration, additional salt and the influence of an applied external field. Next we investigate the dynamic behaviour in the oligomer range and find excellent correspondence of simulations to experimental observations when hydrodynamic interactions are accounted for in the simulations. We then present novel estimators for the dynamical effective charge during free-solution electrophoresis and compare them to static estimators. We find complete agreement between the static and the dynamic estimators. We further evaluate the scaling behaviour of the effective friction of the polyelectrolyte-counterion complex with the surrounding fluid. We identify a hydrodynamic screening length beyond which the friction during electrophoresis is linear depending on the chain length resulting in a constant mobility for long polyelectrolyte chains. Our results show a convincing agreement with experimental data and demonstrate that it is possible to model dynamic behaviour of polyelectrolytes using coarse-grained models, provided they include the effects of hydrodynamical interactions.

Diffusion of DNA in Nanoslits

We observed the free diffusion of individual 10 kbp, (1/2)λ (24.2 kbp), and λ (48.5 kbp) double-stranded deoxyribonucleic acid (DNA) molecules in fused-silica nanoslits with depths from 541 to 24 nm using epifluorescence video microscopy. Diffusivity, D, scaled with nanoslit depth, h, according to D ∝ hα, where α was 0.47 ± 0.05, 0.51 ± 0.06, and 0.47 ± 0.05 for 10 kbp, (1/2)λ, and λ DNA, respectively, in disagreement with the value of two-thirds predicted by blob theory. We observed no change in scaling behavior for h less than the persistence length of DNA, as predicted by reflecting rod theory. The scaling of D with DNA length, N, followed D ∝ N−1, indicating hydrodynamic screening in accordance with Rouse dynamics. Our results establish these scaling exponents for smaller h and greater DNA confinement than previous studies.

Hydrodynamic screening and axisymmetric turbulence in the transient sedimentation of a dilute suspension at small Reynolds number

A theory of settling of a dilute suspension of identical spherical particles in a viscous incompressible fluid is developed on the basis of the equations of transient Stokesian dynamics. The equations describe hydrodynamic interactions between particles moving under the influence of a constant force, starting to act at a particular instant of time. For a dilute suspension, a monopole approximation can be used. It is argued that the growth of velocity fluctuations is bounded by a combination of two effects, destructive interference of the flow patterns of individual particles, and a rearrangement of particle positions leading to a time-dependent microstructure of the suspension. After a long time, the microstructure tends to a steady state. The corresponding structure factor is described phenomenologically. The corresponding pair correlation function and the velocity correlation functions describing axisymmetric turbulence on the length scale of the mean distance between particles are evaluated.

Computer simulations of the dynamics of polymer solutions

A method for simulating the dynamics of polymer–solvent systems is described. The fluid is simulated via lattice Boltzmann and the polymer chains via Molecular Dynamics. The two parts are coupled by a simple dissipative point–particle force, and the system is driven by Langevin stochastic forces added to both the fluid and the polymers. This method is applied to a semidilute system of chains of length N = 1000. We observe the crossover from Zimm dynamics at short length and time scales to Rouse dynamics at long length and time scales. Moreover, we find “incomplete screening”, i. e. Zimm–like behavior at short times but large length scales. This behavior can be nicely described in terms of the de Gennes picture, which explains hydrodynamic screening as a result of entanglements. An analogous simulation approach has been developed for electrostatics, where the interaction is described by a dynamic Maxwell field coupled to the system of charges. This method is briefly outlined as well, with emphasis on the analogy between hydrodynamics and electrostatics.

Long‐range hydrodynamic response of particulate liquids and liquid‐laden solids

AbstractIn viscous particulate liquids, such as suspensions and polymer solutions, the large‐distance steady‐state flow due to a local disturbance is commonly described in terms of hydrodynamic screening—beyond a correlation length ξ the response drops from that of the pure solvent, characterized by its viscosity η0, to that of the macroscopic liquid with viscosity η > η0 For cases where η >> η0 we show, based on general conservation arguments, that this screening picture, while being asymptotically correct, should be refined in an essential way. The crossover between the microscopic and macroscopic behaviors occurs gradually over a wide range of distances, ξ < r < (η / η0)1/2 ξ In liquid‐laden solids, such as colloidal glasses, gels, and liquid‐filled porous media, where η → ∞, this intermediate behavior takes over the entire large‐distance response. The intermediate flow field, arising from the effect of mass displacement rather than momentum diffusion, has several unique characteristics: (i) It has a dipolar shape with l/r3 spatial decay, negative transverse components, and vanishing angular average. (ii) Its amplitude depends on the liquid properties through η0 and ξ alone; thus, in cases where ξ is fixed by geometry (e.g., for particulate liquids tightly confined in solid matrices), the large‐distance response is independent of particle concentration. (iii) The intermediate field builds up non‐diffusively, with a distance‐independent relaxation rate, making it dominant at large distances before steady state has been reached. We demonstrate these general properties in three model systems.

Sedimentation, Péclet number, and hydrodynamic screening

The sedimentation of hard spheres in a Newtonian solvent is studied as a function of Péclet number in the low-concentration limit. Two functional forms for the sedimentation velocity as a function of particle concentration are realized in the limit of high and low Péclet numbers. We argue that a more ordered phase occurs for large Péclet numbers. Measurements of settling in sheared suspensions support these contentions. Recent explanations of sedimentation in suspensions are examined in light of these results.

Anomalous Microfluidic Phonons Induced by the Interplay of Hydrodynamic Screening and Incompressibility

We investigate the acoustic normal modes ("phonons") of a 1D microfluidic droplet crystal at the crossover between 2D flow and confined 1D plug flow. The unusual phonon spectra of the crystal, which arise from long-range hydrodynamic interactions, change anomalously under confinement. The boundaries induce weakening and screening of the interactions, but when approaching the 1D limit we measure a marked increase in the crystal sound velocity, a sign of interaction strengthening. This nonmonotonous behavior of the phonon spectra is explained theoretically by the interplay of screening and plug flow.

Experimental study of internal gravity waves generated by supercritical topography

Oscillatory tides flowing over rough topography on the ocean floor generate internal gravity waves, which are a major source of ocean mixing. Linear inviscid theory can describe waves generated by gentle topography with slopes that are less steep than the propagation angle of the internal waves; such topography is termed subcritical. However, a clear physical picture of internal waves generated by topography with slopes steeper than the angle of internal waves (supercritical topography) is lacking. In this paper we present an experimental study at Reynolds number ∼O(100) of internal gravity waves generated by a circular cylinder that oscillates horizontally (at a frequency Ω), thus mimicking barotropic tidal flow over bottom topography. Fundamental waves of frequency Ω emanate from locations on the cylinder where the topographic slope equals the slope of internal waves. For small oscillating amplitude A (weak forcing), our experimental results compare well with predictions of the viscous linear theory of D. G. Hurley and G. Keady [J. Fluid Mech. 351, 119 (1997)]. The width of the wave beams is determined by competition between forcing and viscous smoothing, and hydrodynamic screening of the steep part of the topography extends the cylinder’s horizontal length scale. Beyond the weak forcing regime, harmonic waves of frequency nΩ (with integer n>1 and nΩ<N, where N is the buoyancy frequency) are generated mainly by nonlinear interaction involving the overlapping fundamental waves. For moderate forcing we find that the intensity of the fundamental and second harmonic waves scales linearly and quadratically with A, respectively.

Hydrodynamic screening of star polymers in shear flow

The mutual effects of the conformations of a star polymer in simple shear flow and the deformation of the solvent flow field are investigated by a hybrid mesoscale simulation technique. We characterize the flow field near the star polymer as a function of its functionality (arm number) f . A strong screening of the imposed flow is found inside the star polymer, which increases with increasing f . To elucidate the importance of hydrodynamic screening, we compare results for hydrodynamic and random solvents. The dependence of the polymer orientation angle on the Weissenberg number shows a power law behavior with super-universal exponent --independent of hydrodynamic and excluded-volume interactions. In contrast, the polymer rotation frequency changes qualitatively when hydrodynamic interactions are switched on.

Diffusion of spheres in isotropic and nematic networks of rods: Electrostatic interactions and hydrodynamic screening

Translational diffusion of a small charged tracer sphere in isotropic and nematic suspensions of long and thin charged rods is investigated as a function of ionic strength and rod concentration. A theory for the diffusive properties of a small sphere is developed, where both (screened) hydrodynamic interactions and charge interactions between the tracer sphere and the rod network are analyzed. Hydrodynamic interactions are formulated in terms of the hydrodynamic screening length. As yet, there are no independent theoretical predictions for the hydrodynamic screening length for rod networks. Experimental tracer-diffusion data are presented for various ionic strengths as a function of the rod concentration, both in the isotropic and nematic states. Orientational order parameters are measured for the same ionic strengths as a function of the rod concentration. The hydrodynamic screening length is determined from these experimental data and scaling relations obtained from the above mentioned theory. For the isotropic networks, a master curve is found for the hydrodynamic screening length as a function of the rod concentration. For the nematic networks the screening length turns out to be a very sensitive function of the orientational order parameter.

Collective diffusion in charge-stabilized suspensions: Concentration and salt effects

The authors present a joint experimental-theoretical study of collective diffusion properties in aqueous suspensions of charge-stabilized fluorinated latex spheres. Small-angle x-ray scattering and x-ray photon correlation spectroscopy have been used to explore the concentration and ionic-strength dependence of the static and short-time dynamic properties including the hydrodynamic function H(q), the wave-number-dependent collective diffusion coefficient D(q), and the intermediate scattering function over the entire accessible range. They show that all experimental data can be quantitatively described and explained by means of a recently developed accelerated Stokesian dynamics simulation method, in combination with a modified hydrodynamic many-body theory. In particular, the behavior of H(q) for de-ionized and dense suspensions can be attributed to the influence of many-body hydrodynamics, without any need for postulating hydrodynamic screening to be present, as it was done in earlier work. Upper and lower boundaries are provided for the peak height of the hydrodynamic function and for the short-time self-diffusion coefficient over the entire range of added salt concentrations.

Time domain effects in the single-chain dynamics of semidilute and concentrated polymer solutions

Single-chain dynamics in semidilute polymer solutions is Zimm-like on short time scales and Rouse-like on long time scales. The crossover is due to time-dependent screening of hydrodynamic interactions. We present a generalized Zimm theory for polymer dynamics in an elastic polymer network. We show that the coupled equations of motion of the polymer network–fluid system lead to a generalized Oseen tensor with a time-dependent hydrodynamic screening length. The time correlation function of the Rouse modes, monomer mean-square displacements and the single-chain dynamical structure factor are calculated.

Dynamics and Transport of Molecules in Polymer and Colloidal-Rod Networks

ABSTRACTRe-orientational dynamics of liquid crystal molecules in a polymer network subjected to an electric field is studied by means of light diffraction [1]. When the optical pitch of the electric-field induced cholesteric phase is small compared to the optical wavelength of light, dynamic light scattering (DLS) can be performed to extract the relaxation dynamics of the chiral nematic molecules in the presence of the polymer network. Intriguingly, the reactive mesogenic type of polymer network exhibits a confinement effect, which can be probed within the limited range of scattering angles that comply with the structural correlation length in the system [2].Diffusive mass transport of molecules through a rod network can be studied via fluorescence correlation spectroscopy (FCS) and DLS. Long time self-diffusion of tracer spheres (silica and proteins) in isotropic and nematic colloidal-rod networks (fd-viruses) is systematically studied for various tracer-sphere sizes as compared to the mesh size of the network [3]. In addition, by varying the salt concentration, the relative contribution of electrostatic interactions can be varied. A theory is developed where the diffusion coefficient is expressed in terms of the hydrodynamic screening length of the highly entangled rod-network. The hydrodynamic screening length of rod networks is extracted from diffusion data as a function of the rod concentration both for isotropic and nematic networks [4-5].

Double-Stranded DNA Diffusion in Slitlike Nanochannels

We present an experimental study of double-stranded DNA diffusion in slitlike channels. The channel heights span the regime from moderate confinement (height ∼ bulk radius of gyration of the DNA) to strong confinement (height ∼ persistence length). Scalings of diffusivity with channel height differ from blob model predictions. The diffusivity scales inversely with molecular weight when the channel height is smaller than the bulk radius of gyration. This scaling is indicative of hydrodynamic screening. A scaling analysis shows that the screening of hydrodynamic interactions arises from a combination of two mechanisms. After using a Zimm preaverage approximation, the unique symmetry of the thin-slit disturbance velocity and the isotropic nature of the polymer conformation together cause a cancellation of hydrodynamic interactions due to symmetry. We also find that the algebraic decay of the far-field velocity magnitude is sufficient to eliminate large-length scale hydrodynamic cooperativity in diffusion of ...