اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDeterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions
140
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The dynamics of macroscopically homogeneous sheared suspensions of neutrally buoyant, non-Brownian spheres is investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics. We show that the complex dynamics of sheared suspensions can be characterized as a chaotic motion in phase space and determine the dependence of the largest Lyapunov exponent on the volume fraction $phi$. The loss of memory at the microscopic level of individual particles is also shown in terms of the autocorrelation functions for the two transverse velocity components. Moreover, a negative correlation in the transverse particle velocities is seen to exist at the lower concentrations, an effect which we explain on the basis of the dynamics of two isolated spheres undergoing simple shear. In addition, we calculate the probability distribution function of the velocity fluctuations and observe, with increasing $phi$, a transition from exponential to Gaussian distributions. The simulations include a non-hydrodynamic repulsive interaction between the spheres which qualitatively models the effects of surface roughness and other irreversible effects, such as residual Brownian displacements, that become particularly important whenever pairs of spheres are nearly touching. We investigate the effects of such a non-hydrodynamic interparticle force on the scaling of the particle tracer diffusion coefficient $D$ for very dilute suspensions, and show that, when this force is very short-ranged, $D$ becomes proportional to $phi^2$ as $phi to 0$. In contrast, when the range of the non-hydrodynamic interaction is increased, we observe a crossover in the dependence of $D$ on $phi$, from $phi^2$ to $phi$ as $phi to 0$.
قيم البحث
اقرأ أيضاً
Particle suspensions, present in many natural and industrial settings, typically contain aggregates or other microstructures that can complicate macroscopic flow behaviors and damage processing equipment. Recent work found that applying uniform perio
dic shear near a critical transition can reduce fluctuations in the particle concentration across all length scales, leading to a hyperuniform state. However, this strategy for homogenization requires fine tuning of the strain amplitude. Here we show that in a model of sedimenting particles under periodic shear, there is a well-defined regime at low sedimentation speed where hyperuniform scaling automatically occurs. Our simulations and theoretical arguments show that the homogenization extends up to a finite lengthscale that diverges as the sedimentation speed approaches zero.
We present results from a series of experiments on a granular medium sheared in a Couette geometry and show that their statistical properties can be computed in a quantitative way from the assumption that the resultant from the set of forces acting i
n the system performs a Brownian motion. The same assumption has been utilised, with success, to describe other phenomena, such as the Barkhausen effect in ferromagnets, and so the scheme suggests itself as a more general description of a wider class of driven instabilities.
We propose a new look at the heat bath for two Brownian particles, in which the heat bath as a `system is both perturbed and sensed by the Brownian particles. Non-local thermal fluctuation give rise to bath-mediated static forces between the particle
s. Based on the general sum-rule of the linear response theory, we derive an explicit relation linking these forces to the friction kernel describing the particles dynamics. The relation is analytically confirmed in the case of two solvable models and could be experimentally challenged. Our results point out that the inclusion of the environment as a part of the whole system is important for micron- or nano-scale physics.
Large scale simulations and analytical theory have been combined to obtain the non-equilibrium velocity distribution, $f(v)$, of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalised to incl
ude friction. They reveal strongly anomalous but largely universal distributions which are independent of volume fraction and collision processes, which suggests a one-particle model should capture all the essential features. We have formulated this one-particle model and solved it analytically in the limit of strong damping, where we find that $f(v)$ decays as $1/v$ for multiple decades, eventually crossing over to a Gaussian decay for the largest velocities. Many particle simulations and numerical solution of the one-particle model agree for all values of the damping.
Non-Newtonian transport properties of an inertial suspension of inelastic rough hard spheres under simple shear flow are determined from the Boltzmann kinetic equation. The influence of the interstitial gas on rough hard spheres is modeled via a Fokk
er-Planck generalized equation for rotating spheres accounting for the coupling of both the translational and rotational degrees of freedom of grains with the background viscous gas. The generalized Fokker-Planck term is the sum of two ordinary Fokker-Planck differential operators in linear $mathbf{v}$ and angular $boldsymbol{omega}$ velocity space. As usual, each Fokker-Planck operator is constituted by a drag force term (proportional to $mathbf{v}$ and/or $boldsymbol{omega}$) plus a stochastic Langevin term defined in terms of the background temperature $T_text{ex}$. The Boltzmann equation is solved by two different but complementary approaches: (i) by means of Grads moment method, and (ii) by using a Bhatnagar-Gross-Krook (BGK)-type kinetic model adapted to inelastic rough hard spheres. As occurs in the case of emph{smooth} inelastic hard spheres, our results show that both the temperature and the non-Newtonian viscosity increase drastically with increasing the shear rate (discontinuous shear thickening effect) while the fourth-degree velocity moments also exhibit an $S$-shape. In particular, while high levels of roughness may slightly attenuate the jump of the viscosity in comparison to the smooth case, the opposite happens for the rotational temperature. As an application of these results, a linear stability analysis of the steady simple shear flow solution is also carried out showing that there are regions of the parameter space where the steady solution becomes linearly unstable.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
