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Two alternative routes are taken to derive, on the basis of the dynamics of a finite number of dumbbells, viscoelasticity in terms of a conformation tensor with fluctuations. The first route is a direct approach using stochastic calculus only, and it serves as a benchmark for the second route, which is guided by thermodynamic principles. In the latter, the Helmholtz free energy and a generalized relaxation tensor play a key role. It is shown that the results of the two routes agree only if a finite-size contribution to the Helmholtz free energy of the conformation tensor is taken into account. Using statistical mechanics, this finite-size contribution is derived explicitly in this paper for a large class of models; this contribution is non-zero whenever the number of dumbbells in the volume of observation is finite. It is noted that the generalized relaxation tensor for the conformation tensor does not need any finite-size correction.

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We investigate the flow of a concentrated suspension of colloidal particles at deformation rates higher than the discontinuous shear-thickening transition shear rate. We show that, under its own weight, a jet of a concentrated enough colloidal suspension, simultaneously flows while it sustains tensile stress and transmits transverse waves. This results in a new flow instability of jets of shear-thickening suspensions: the jet is submitted to rapid transverse oscillations, that we characterize.

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We present a direct numerical simulation (DNS) study of buoyancy-driven bubbly flows in two dimensions. We employ the volume of fluid (VOF) method to track the bubble interface. To investigate the spectral properties of the flow, we derive the scale-by-scale energy budget equation. We show that the Galilei number (Ga) controls different scaling regimes in the energy spectrum. For high Galilei numbers, we find the presence of an inverse energy cascade. Our study indicates that the density ratio of the bubble with the ambient fluid or the presence of coalescence between the bubbles does not alter the scaling behaviour.

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The physical properties of an aqueous solution of a macromolecule primarily depend on its chemical structure and the mesoscopic aggregates formed by many of such molecules. Ionic liquids (ILs) are the macromolecules that have caught significant research interests for their enormous industrial and biomedical applications. In the present paper, the physical properties, such as density, viscosity, ionic conductivity of aqueous solutions of various ILs, have been investigated. These properties are found to systematically depend on the shape and size of the anion and the cation along with the solution concentration. The ionic conductivity and viscosity behavior of the solutions do not strictly follow the Walden rule that relates the conductivity to the viscosity of the solution. However, the modified Walden rule could explain the behavior. A simple calculation based on the geometry of a given molecule could shed the light on the observed results.

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We study how the stability of a homogeneous incompressible fluid flow over a saturated Brinkman porous medium is affected by a change in porosity. We produce neutral curves using the shooting method in the area of bimodality. When the porosity decreases, the topology of these curves changes because of the interplay between two instability modes. The long-wave instability is dominant if the medium is highly porous. In contrast, the short-wave instability is the most significant at low porosity because of high tangential stress at the fluid-medium interface. We identify a stability gap between the neutral curve branches within a narrow range of porosity values. The calculated results show the development and disappearance of this gap when the porosity changes.

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The fluctuation theorem is considered intrinsically linked to reversibility and therefore its phenomenological consequence, the fluctuation relation, is sometimes considered not applicable. Nevertheless here is considered the paradigmatic example of irreversible evolution, the 2D Navier-Stokes incompressible flow, to show how universal properties of fluctuations in systems evolving irreversibily could be predicted in a general context. Together with a formulation of the theoretical framework several open questions are formulated and a few more simulations are provided to illustrate the results and to stimulate further checks.

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Fluctuating viscoelasticity for conformation-tensor-based models is studied at equilibrium, in simple-shear deformation, and in uniaxial extension. The models studied are the upper-convected Maxwell model, the FENE-P model with finite chain-extensibility, and the Giesekus model with anisotropic drag. Using numerical simulations, the models are compared in detail both with each other and with analytical predictions for the Maxwell model. At equilibrium, the models differ only marginally, both in terms of static and dynamic characteristics. When deformed, the average mechanical response of the Maxwell model is unaffected by the strength of thermal fluctuations, while the mechanical response of the FENE-P and Giesekus models show a slight decrease the stronger the fluctuations in simple shear, whereas the decrease in uniaxial extension is marginal. For all models, the standard deviation of the mechanical response increases with increasing strength of fluctuations, and the magnitude of the standard deviation relative to the average for given fluctuation strength generally decreases the stronger the deformation, this effect being stronger for uniaxial extension than for simple-shear deformation.

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An erythrocytes sedimentation rate (ESR) measures how fast a blood sample sediments along a test tube in one hour in a clinical laboratory. Since elevated level of ESR is associated with inflammatory diseases, ESR is one of the routine hematology test in a clinical laboratory. In this paper, the physics of erythrocyte (RBC) sedimentation rate as well as the dynamics of the RBC is explored by modeling the dynamics of the cells as the motion of Brownian particle moving in a viscous medium. The viscous friction of blood γ is considered to decrease as the temperature of the medium increases. The results obtained in this work show that the ESR increases as the number of red blood cells (that bind together in the sedimentation process) steps up. The room temperature also affects the sedimentation rate. As the room temperature rises up, the ESR steps up. Furthermore the dynamics of the RBC along a Westergren pipet that is held in an upright position is explored. The exact analytic result depicts that the velocity of cells increases as the number of cells that form rouleaux steps up. Since our study is performed by considering physiological parameters, the results obtained in this work not only can be justified experimentally but also helps to understand most hematological experiments that are conducted in vitro.

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A capillary tube model reveals that the surface tension at the air-water interface cannot cause the instability of gravity-driven unsaturated slow flow in sandy soils.

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Turbulent wind patterns over a two-dimensional isolated downsized barchan dune under the influence of sinusoidal inflow with different amplitudes and periods are simulated. The evolution rules of wind velocity over time at different positions are revealed. The flow reattachment distance and turbulence intensity distribution are also compared. The results show that wind velocities at different positions of the dune whose similar evolvement process of going from short-term fast adjustment transition to long-term stable sinusoidal fluctuation, can be reasonably estimated by the present simulation. It is found that, for the leeward toe of a dune with complex reversed flow, the balance position value of the sinusoidal wind velocity fluctuation is no longer close to the value of the steady wind velocity but shows a velocity deviation of about 0.40m/s. The flow reattachment distances under different unsteady inflows ultimately show a sinusoidal fluctuation with time, and their values are all larger than that of the steady flow. These synthetically predict that the unsteady flow has a stronger shaping effect on the leeward side of the dune body by enhancing sand transport. In addition, the predicted distribution comparison between unsteady wind velocity and turbulence intensity indicates that the unsteady wind velocity has a dominant effect on the turbulence intensity.

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Compared to nanofluids with spherical particles, nanofluids with anisotropic particles possess higher thermal conductivity and present a better enhancement option in heat transfer applications. The viscosity variation of such nanofluids becomes of great importance in evaluating their pumping power in thermal systems. This paper presents a comprehensive review of the experimental and theoretical studies on the viscosity of nanofluids with anisotropic particles. The internal mechanisms of viscosity evolution are investigated considering three aspects: particle clustering, particle interactions, and Brownian motion. In experimental studies, important factors including classification and synthetic methods for particle preparation, base fluid, particle loading, particle shape and size, temperature, p H, shear stress and electric field are investigated in detail. Classical theoretical models and empirical relations of the effective viscosity of suspensions are discussed. Some crucial factors such as maximum particle packing fraction, fractal index and intrinsic viscosity models, are examined. A comparison of predictions and experimental results shows that the classical models underestimate suspension viscosity. A comprehensive combination of the modified Krieger-Dougherty (K-D) model with intrinsic viscosity relations for different aspect ratios is suggested for low particle loadings, and the modified Maron-Pierce model (M-D) is recommended for high particle loadings. Possible directions for future works are discussed.

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Windbreak wall over railway subgrades is an effective and widely used measure to reduce the impact of high-speed wind in northwest China and central Asia. For the railway crossing sandy/Gobi desert, there exists serious sand accumulation over subgrade behind windbreak walls, causing great harm to the normal railway operation. So far, many measures have been tried to prevent sand accumulation. However, due to lack of understanding on causes of sand accumulation, they are often ineffective. To explore the characteristics of wind-blown sand flow around railway subgrades and the causes of sand accumulation, we set up a turbulent flow-sand particle-terrain coupling model and calculated sand particles' motion features around a typical windbreak wall in Lanxin railway line using the Lagrangian particle-tracing model. The results show that in sandy desert, although inflow sand particles are difficult to fly over windbreak wall, due to presence of a large reflux zone behind the windbreak wall where "reverse" wind-blown sand flow is generated, sand particles are blown up and rolled back to the subgrade under the effect of vertical wind velocity and reflux. By contrast, in the Gobi desert, sand particles are much easier to fly over windbreak wall and possess different motion features under different wind speeds. To solve the problem of sand accumulation on railway subgrade, we should comprehensively consider both wind speed and underlying conditions and then take appropriate measures.

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The correlations detected by the mutual information in the propensities of a molecular viscous liquid are studied by molecular-dynamics simulations. Dynamic heterogeneity is evidenced and two particle fractions with different mobility and relaxation identified. The two fractions exhibit the scaling of their relaxation in terms of the rattling amplitude of the particle trapped in the cage of the first neighbours 〈u2〉 . The scaling master curve does not differ from the one found for bulk systems, thus confirming identical results previously reported in other systems with strong dynamic heterogeneity as thin molecular films. The excitation of planar and globular structures at short and long times with respect to structural relaxation, respectively, is revealed. Some of the globular structures are different from the ones evidenced in atomic mixtures. States with equal 〈u2〉 are found to have identical time dependence of several quantities, referring to both bulk and the two fractions with heterogeneous dynamics, at least up to the structural relaxation time [Formula: see text].

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It has been shown recently that the coupled dynamics of micro-particles in a viscous fluid has many interesting aspects including motional resonance which can be used to perform two-point micro-rheology. However, it is expected that this phenomenon in a viscoelastic fluid is much more interesting due to the presence of the additional frequency-dependent elasticity of the medium. Thus, a theory describing the equilibrium dynamics of two hydrodynamically coupled Brownian harmonic oscillators in a viscoelastic Maxwell fluid has been derived which appears with new and impressive characteristics. Initially, the response functions have been calculated and then the fluctuation-dissipation theorem has been used to calculate the correlation functions between the coloured noises present on the concerned particles placed in a Maxwell fluid due to the thermal motions of the fluid molecules. These correlation functions appear to be in a linear relationship with the delta-correlated noises in a viscous fluid. Consequently, this reduces the statistical description of a simple viscoelastic fluid to the statistical representation for an extended dynamical system subjected to delta-correlated random forces. Thereupon, the auto and cross-correlation functions in the time domain and frequency domain and the mean-square displacement functions of the particles have been calculated which are perfectly consistent with their corresponding established forms in a viscous fluid and emerge with exceptional features.

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We address the problem of glass-forming of liquids by superpressing. We study the pressure-induced dynamic change of the fragile van der Waals liquid propylene carbonate towards the glassy state in the equilibrium regime by measuring the diffusivity of the fluorescent probe Coumarin 1 embedded in the host liquid. The probe diffusivity is measured by the fluorescence recovery after photobleaching (FRAP) technique across a bleached volume generated by the near-field diffracted pattern of a laser beam. The recovered fluorescence intensity fits to a stretched exponential with the diffusive time [Formula: see text] and the stretched exponent [Formula: see text] as free parameters. In the pressure range [0.3-1.0]GPa the diffusivity decouples from the Stokes-Einstein relation. The decoupling correlates well to a decrease of [Formula: see text]. The variation of [Formula: see text] is non-monotonous with [Formula: see text] showing a minimum at [Formula: see text] s. We evidence an isochronal superpositioning over about 3 decades of [Formula: see text] between ∼ 10 s and [Formula: see text] s and a density scaling in the whole investigated pressure range. The pressure at which [Formula: see text] is minimum coincides to the dynamical crossover pressure measured by other authors. This crossover pressure is compatible with the critical point of MCT theory. As our studied pressure range encompasses the critical pressure, the non-monotonous variation of [Formula: see text] opens new insight in the approach to the critical point.

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A common simplification used in different physical contexts by both experimentalists and theoreticians when dealing with essentially non-spherical drops is treating them as ellipsoids or, in the axisymmetric case, spheroids. In the present theoretical study, we are concerned with such a spheroidal approximation for free viscous shape relaxation of strongly deformed axisymmetric drops towards a sphere. A general case of a drop in an immiscible fluid medium is considered, which includes the particular cases of high and low inside-to-outside viscosity ratios (e.g., liquid drops in air and bubbles in liquid, respectively). The analysis involves solving for the accompanying Stokes (creeping) flow inside and outside a spheroid of an evolving aspect ratio. Here this is accomplished by an analytical solution in the form of infinite series whose coefficients are evaluated numerically. The study aims at the aspect ratios up to about 3 at most in both the oblate and prolate domains. The inconsistency of the spheroidal approximation and the associated non-spheroidal tendencies are quantified from within the approach. The spheroidal approach turns out to work remarkably well for the relaxation of drops of relatively very low viscosity (e.g., bubbles). It is somewhat less accurate for drops in air. A semi-heuristic result encountered in the literature, according to which the difference of the squares of the two axes keeps following the near-spherical linear evolution law even for appreciable deformations, is put into context and verified against the present results.

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In stationary nonequilibrium states coupling between hydrodynamic modes causes thermal fluctuations to become long ranged inducing nonequilibrium Casimir pressures. Here we consider nonequilibrium Casimir pressures induced in liquids by a velocity gradient. Specifically, we have obtained explicit expressions for the magnitude of the shear-induced pressure enhancements in a liquid layer between two horizontal plates that complete and correct results previously presented in the literature. In contrast to nonequilibrium Casimir pressures induced by a temperature or concentration gradient, we find that in shear nonequilibrium contributions from short-range fluctuations are no longer negligible. In addition, it is noted that currently available computer simulations of model fluids in shear observe effects from molecular correlations at nanoscales that have a different physical origin and do not probe shear-induced pressures resulting from coupling of long-wavelength hydrodynamic modes. Even more importantly, we find that in actual experimental conditions, shear-induced pressure enhancements are caused by viscous heating and not by thermal velocity fluctuations. Hence, isothermal computer simulations are irrelevant for the interpretation of experimental shear-induced pressure enhancements.

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We report new results on the liquid to solid phase transition of benzene. We determine experimentally and investigate the properties of a number of parameters of the benzene metastable state under different pressures (from 0.1 up to 2200atm). It is shown that the supercooling, pressure drop, incubation period, time of abrupt transition from the metastable state to the crystalline state, and time of isothermal freezing all decrease as the external pressure increases, then they all vanish at 2200atm and 356K which may mark the end-point of metastability. Quadratic interpolation formulas for these parameters are provided. The densities and molar heat capacities of supercooled benzene under different pressures have been calculated too.

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Microflows are intensively used for investigating and controlling the dynamics of particles, including soft particles such as biological cells and capsules. A classic result is the tank-treading motion of elliptically deformed soft particles in linear shear flows, which do not migrate across straight streamlines in the bulk. However, soft particles migrate across straight streamlines in Poiseuille flows. In this work we describe a new mechanism of cross-streamline migration by using soft capsules with a spherical equilibrium shape. If the viscosity varies perpendicular to the streamlines then the soft particles migrate across streamlines towards regions of a lower viscosity, even in linear shear flows. An interplay with the repulsive particle-boundary interaction causes then focusing of particles in linear shear flows with the attractor streamline closer to the wall in the low viscosity region. Viscosity variations perpendicular to the streamlines in Poiseuille flows leads either to a shift of the particle attractor or even to a splitting of particle attractors, which may give rise to interesting applications for particle separation. The location of attracting streamlines depend on the particle properties, like their size and elasticity. The cross-stream migration induced by viscosity variations is explained by analytical considerations, Stokesian dynamics simulations with a generalized Oseen tensor and lattice-Boltzmann simulations.

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In this study, structures and behaviours of acoustic cavitation bubbles induced by a high-intensity focused ultrasound (HIFU) transducer, operating at its resonance frequency of 250kHz, are experimentally explored with corresponding observations captured by a high-speed video camera system. The experiments were conducted in an open-top Perspex water tank with deionized water, and illumination was provided by a LED spotlight which is placed beside the water tank throughout the whole experiment. Experimental results show that the structure of ultrasonically generated bubbles forms in a conical shape with several concentric bubble rings above the transducer. The distance between the adjacent rings with equal spacing as determined by the driving frequency of the HIFU transducer is experimentally measured and compared with the theoretical value. Then, the distribution of acoustic pressure in the acoustically driven liquid is further studied to investigate the behaviours of cavitation bubbles generated in a HIFU field. Additionally, the analysis of Bjerknes forces on the bubble surface which are induced by the gradient of acoustic pressure and the adjacent oscillating bubbles is quantitatively carried out, and the radius and velocity of a typical larger bubble are measured to characterize the behaviours of ultrasonically induced bubbles. Particularly, the physical phenomena of large bubbles including the coalescence, attraction or repulsion between adjacent bubbles, as well as the jumping of an acoustic bubble from the lower concentric ring level to the higher level, are analysed. The moving trajectory of the bubble is next obtained, and some conclusions are summarized to provide a greater understanding of the complex behaviours of the ultrasonically generated bubbles.