Direct numerical simulations of a microswimmer in a viscoelastic fluid.

This study presents the application of the smoothed profile (SP) method to perform direct numerical simulations for the motion of both passive and active "squirming" particles in Newtonian and viscoelastic fluids. We found that fluid elasticity has a significant impact on both the transient behavior and the steady-state velocity of the particles. Specifically, we observe that the swirling flow generated by the squirmer's surface velocity significantly enhances their swimming speed as the Weissenberg number increases, regardless of the swimming type. Furthermore, we find that pushers outperform pullers in Oldroyd-B fluids, suggesting that the speed of a squirmer depends on the swimmer type. To understand the physical origin of the phenomenon of swirling flow enhancing the swimming speed, we investigate the velocity field and polymer conformation around non-swirling and swirling neutral squirmers in viscoelastic fluids. Our investigation reveals that the velocity field around the neutral swirling squirmers exhibits pusher-like extensional flow characteristics, as well as an asymmetric polymer conformation distribution, which gives rise to this increased propulsion. This is confirmed by the investigation of the force on a fixed squirmer, which revealed that the polymer stress, particularly its diagonal components, plays a critical role in enhancing the swimming speed of swirling squirmers in viscoelastic fluids. Additionally, our results demonstrate that the maximum swimming speeds of swirling squirmers occur at an intermediate value of the fluid viscosity ratio for all swimmer types. These findings have important implications for understanding the behavior of particles and micro-organisms in complex fluids.

Nonlinear dielectric decrement of electrolyte solutions: An effective medium approach.

HYPOTHESIS: The dielectric constant of an electrolyte solution, which determines electrostatic interactions between colloids and interfaces, depends nonlinearly on the salinity and also on the type of salt. The linear decrement at dilute solutions is due to the reduced polarizability in the hydration shell around an ion. However, the full hydration volume cannot explain the experimental solubility, which indicates the hydration volume should decrease at high salinity. Volume reduction of the hydration shell is supposed to weaken dielectric decrement and thus should be relevant to the nonlinear decrement. SIMULATIONS: According to the effective medium theory for the permittivity of heterogeneous media, we derive an equation which relates the dielectric constant with the dielectric cavities created by the hydrated cations and anions, and the effect of partial dehydration at high salinity is taken into account. FINDINGS: Analysis of experiments on monovalent electrolytes suggests that weakened dielectric decrement at high salinity originates primarily from the partial dehydration. Furthermore, the onset volume fraction of the partial dehydration is found to be salt-specific, and is correlated with the solvation free energy. Our results suggest that while the reduced polarizability of the hydration shell determines the linear dielectric decrement at low salinity, ion-specific tendency of dehydration is responsible for nonlinear dielectric decrement at high salinity.

Non-Stick Length of Polymer-Polymer Interfaces under Small-Amplitude Oscillatory Shear Measurement.

Interfaces in soft materials often exhibit deviation from non-slip/stick response and play a determining role in the rheological response of the overall system. We discuss detection techniques for the excess interface rheology using small-amplitude oscillatory shear (SAOS) measurements. A stacked bilayer of different polymers is sheared parallel to the interface and the dynamic shear response is measured. Deviation of the bilayer shear modulus from the superposition of the shear moduli of the component layers is analysed. Furthermore, we introduce a frequency-dependent non-stick length based on the bilayer SAOS response to characterize the excess interface rheology. We observe an approximate stick response in the interface in bilayers composed of the chemically same monomer as well as an apparent slip in the interface between immiscible polymers. The results suggest that the proposed non-stick length in SAOS is capable of detecting the apparent interfacial slip. The non-stick length in SAOS is readily applicable to other complex interfaces of different soft materials and offers a convenient tool to characterize the excess interface rheology.

Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles.

A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions.

Effects of viscoelasticity on shear-thickening in dilute suspensions in a viscoelastic fluid.

We investigate previously unclarified effects of fluid elasticity on shear-thickening in dilute suspensions in an Oldroyd-B viscoelastic fluid using a novel direct numerical simulation based on the smoothed profile method. Fluid elasticity is determined by the Weissenberg number Wi and by viscosity ratio 1 - ß = ηp/(ηs + ηp) which measures the coupling between the polymer stress and flow: ηp and ηs are the polymer and solvent viscosity, respectively. As 1 - ß increases, while the stresslet does not change significantly compared to that in the ß â†’ 1 limit, the growth rate of the normalized polymer stress with Wi was suppressed. Analysis of flow and conformation dynamics around a particle for different ß reveals that at large 1 - ß, polymer stress modulates flow, leading to suppression of polymer stretch. This effect of ß on polymer stress development indicates complex coupling between fluid elasticity and flow, and is essential to understand the rheology and hydrodynamic interactions in suspensions in viscoelastic media.

Differential capacitance of the electric double layer: the interplay between ion finite size and dielectric decrement.

We study the electric double layer by combining the effects of ion finite size and dielectric decrement. At high surface potential, both mechanisms can cause saturation of the counter-ion concentration near a charged surface. The modified Grahame equation and differential capacitance are derived analytically for a general expression of a permittivity ε(n) that depends on the local ion concentration, n, and under the assumption that the co-ions are fully depleted from the surface. The concentration at counter-ion saturation is found for any ε(n), and a criterion predicting which of the two mechanisms (steric vs. dielectric decrement) is the dominant one is obtained. At low salinity, the differential capacitance as function of surface potential has two peaks (so-called camel-shape). Each of these two peaks is connected to a saturation of counter-ion concentration caused either by dielectric decrement or by their finite size. Because these effects depend mainly on the counter-ion concentration at the surface proximity, for opposite surface-potential polarity either the cations or anions play the role of counter-ions, resulting in an asymmetric camel-shape. At high salinity, we obtain and analyze the crossover in the differential capacitance from a double-peak shape to a uni-modal one. Finally, several nonlinear models of the permittivity decrement are considered, and we predict that the concentration at dielectrophoretic saturation shifts to higher concentration than those obtained by the linear decrement model.

Direct numerical simulations of electrophoresis of charged colloids.

We propose a numerical method to simulate electrohydrodynamic phenomena in charged colloidal dispersions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection-diffusion, and Navier-Stokes equations so that the electrohydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters; however, our simulation predicts notable deviations in the case of dense dispersions.

Simulation method to resolve hydrodynamic interactions in colloidal dispersions.

A computational method is presented to resolve hydrodynamic interactions acting on solid particles immersed in incompressible host fluids. In this method, boundaries between solid particles and host fluids are replaced with a continuous interface by assuming a smoothed profile. This enabled us to calculate hydrodynamic interactions both efficiently and accurately, without neglecting many-body interactions. The validity of the method was tested by calculating the drag force acting on a single cylindrical rod moving in an incompressible Newtonian fluid. This method was then applied in order to simulate sedimentation process of colloidal dispersions.

Intermittency and exponent field dynamics in developed turbulence.

Spatiotemporal dynamics of intermittency in association with coarse-grained energy-dissipation rate fluctuations is discussed. This is done first by phenomenologically constructing the probability density for exponent field fluctuations that is introduced to characterize the energy-dissipation rate field, and then by proposing the Langevin dynamics derived with the projection-operator method on the basis of the Navier-Stokes equation. With a Gaussian approximation for exponent fluctuations, spatiotemporal correlation functions for coarse-grained energy-dissipation rate fluctuations are explicitly obtained.

Scaling hypothesis leading to generalized extended self-similarity in turbulence.

A scaling hypothesis leading to generalized extended self-similarity (GESS) for velocity structure functions, valid for intermediate scales in isotropic, homogeneous turbulence, is proposed. By introducing an effective scale r, monotonically depending on the physical scale r, with the use of the large deviation theory, the asymptotic forms of the probability densities for the velocity differences u(r) and for the coarse-grained energy-dissipation rate fluctuations epsilon(r), compatible with this GESS, are proposed. The probability density for epsilon(r) is shown to have the form P(r)(epsilon) approximately equal to epsilon(-1)(r/L)(S(r)[z(r)](epsilon))) with z(r)(epsilon)=ln(epsilon/epsilon(L))/ln(L/r), where L and epsilon(L) are the stirring scale and the coarse-grained energy-dissipation rate over the scale L. The concave function S(r)(z), the spectrum, plays the central role of the present approach. Comparing the results with numerical and experimental data, we explicitly obtain the fluctuation spectra S(r)(z).