Inhomogeneities in the velocity field of a moving fluid are dampened by the inherent viscous behaviour of the system. Both bulk and shear effects, related to the divergence and the curl of the velocity field, are relevant. On molecular time scales, beyond the Navier-Stokes description, memory plays an important role. We demonstrate here on the basis of molecular and overdamped Brownian dynamics many-body simulations that analogous viscous effects act on the acceleration field. This acceleration viscous behaviour is associated with the divergence and the curl of the acceleration field and it can be quantitatively described using simple exponentially decaying memory kernels. The simultaneous use of velocity and acceleration fields enables the description of fast dynamics on molecular scales.
Viscous phenomena are the hallmark of the hydrodynamic flow exhibited by Dirac fermions in clean graphene at high enough temperatures. We report a quantitative calculation of the electronic shear and Hall viscosities in graphene based on the kinetic theory combined with the renormalization group providing a unified description at arbitrary doping levels and non-quantizing magnetic fields. At charge neutrality, the Hall viscosity vanishes, while the field-dependent shear viscosity decays from its zero-field value saturating to a nonzero value in classically strong fields. Away from charge neutr…
Using Mathematica package, we derive analytical closed-form expressions for the shear and the bulk viscosity coefficients in multicomponent relativistic gases with constant cross sections, being the relativistic generalization for the hard spheres model. Some of them are cumbersome and require symbolic manipulations in an algebraic package. The constant cross sections are of the elastic processes, while the inelastic (or number-changing) processes (collisions or decays) are considered only partly. As examples, we find explicit expressions of the correct single-component first-order shear visco…
We concentrate on calculation of the shear and bulk viscosities of the hadron gas. They define its dissipative dynamics and influence its experimentally measurable elliptic flow. Due to difficulty of this calculation the relaxation time approximation (RTA) was used in previous works. As those results have approached the realistic ones, there is a need to find out how accurate the RTA is. For this sake we calculate the viscosities in the RTA using cross sections extracted from the ultrarelativistic quantum molecular dynamics (UrQMD) model and compare them with the same ones calculated without t…
Recent experiments report that slowly-sheared noncolloidal particle suspensions can exhibit unexpected rate($ω$)-dependent complex viscosities in oscillatory shear, despite a constant relative viscosity in steady shear. Using a minimal hydrodynamic model, we show that a weak interparticle attraction reproduces this behavior. At volume fractions $ϕ=20\sim50$%, the complex viscosities in both experiments and simulations display power-law reductions in shear, with a $ϕ$-dependent exponent maximum at $ϕ=40$%, resulting from the interplay between hydrodynamic, collision and adhesive interactions. F…
We study effective shear viscosity $μ^\star$ and effective extensional viscosity $λ^\star$ of concentrated non-colloidal suspensions of rigid spherical particles. The focus is on the spatially disordered arrays. We use recently developed discrete network approximation techniques to obtain asymptotic formulas for the viscosities as the typical inter-particle distance $δ$ tends to zero. For disordered arrays, the volume fraction alone does not determine the effective viscosity. Use of the network approximation allows us to study the dependence of the effective viscosities on variable distances b…
Effects of surface viscosities on the motion of a droplet enclosing a translating particle
Santa Clara University（圣克拉拉大学）；Towson University（托森大学）；National University of Singapore（新加坡国立大学）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；New Jersey Institute of Technology（新泽西理工学院）
The shear and the bulk viscosities of the hadron gas at low temperatures are studied in the model with constant elastic cross sections being relativistic generalization of the hard spheres model. One effective radius ${r=0.4 fm}$ is chosen for all elastic collisions. Only elastic collisions are considered which are supposed to be dominant at temperatures ${T\leq 120-140 MeV}$. The calculations are done in the framework of the Boltzmann equation with the Boltzmann statistics distribution functions and the ideal gas equation of state. The applicability of these approximations is discussed. It's …
Interfacial standing wave-patterns disentangle dilatational and shear surface viscous effects
Imperial College London（帝国理工学院）；Abdullah Al Salem University（阿卜杜拉·萨勒姆大学）；Université Paris Saclay（巴黎萨克雷大学）；Hongik University（弘益大学）；University of Cambridge（剑桥大学）
A very famous result of gauge/gravity duality is the universality of the ratio of shear viscosity to entropy density in every field theory holographically dual to classical, two-derivative (Einstein) gravity. We present a way to obtain deviation form this universality by breaking the rotational symmetry spontaneously. In anisotropic fluids additional shear modes exist and their corresponding shear viscosities may be non-universal. We confirm this by explicitly calculating the shear viscosities in a transversely isotropic background, a p-wave superfluid, and study its critical behavior. This is…
In the present paper, we address the important point of the proportionality between the longitudinal integral lengthscale ($L$) and the characteristic mean flow width ($δ$) using experimental data of an axisymmetric wake and a turbulent planar jet. This is a fundamental hypothesis when deriving the self-similar scaling laws in free shear flows, irrespective of turbulence dissipation scaling. We show that $L/δ$ is indeed constant, at least in a range of streamwise distances between 15 and 50 times the characteristic inlet dimension ($L_{ref}$, nozzle width or wake generator size). Furthermore, …
Elaborated calculations of the shear and the bulk viscosities in the hadron gas, using the ultrarelativistic quantum molecular dynamics (UrQMD) model cross sections, are made. These cross sections are analyzed and improved. A special treatment of the resonances is implemented additionally. All this allows for better hydrodynamical description of the experimental data. The previously considered approximation of one constant cross section for all hadrons is justified. It's found that the bulk viscosity of the hadron gas is much larger than the bulk viscosity of the pion gas while the shear visco…
We analyze both theoretically and experimentally the breakup of a pendant water droplet loaded with Sodium Dodecyl Sulfate (SDS). The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the full Navier-Stokes equations for different values of the shear and dilatational surface viscosities. This comparison shows the small but measurable effect of the surface viscous stresses on the system dynamics for sufficiently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear…
The effective dilatational and shear viscosities of a particle-laden fluid interface are computed in the dilute limit under the assumption of an asymptotically vanishing viscosity ratio between both fluids. Spherical particles with a given contact angle of the fluid interface at the particle surface are considered. A planar fluid interface and a small Reynolds number are assumed. The theoretical analysis is based on a domain perturbation expansion in the deviation of the contact angle from $90^\circ$ up to the second order. The resulting effective dilatational viscosity shows a stronger depend…
We experimentally and theoretically study impacts into dense cornstarch and water suspensions. We vary impact speed as well as intruder size, shape, and mass, and we characterize the resulting dynamics using high-speed video and an onboard accelerometer. We numerically solve previously proposed models, most notably the added-mass model as well as a class of {viscous-like} models. In the {viscous-like models}, the intruder dynamics are dominated by {large, viscous-like forces} at the boundary of the jammed front {where large shear rates and accompanying large viscosities are present.} We find t…
Cilia and flagella are hair-like appendages that protrude from the surface of a variety of eukaryotic cells and deform in a wavelike fashion to transport fluids and propel cells. Motivated by the ubiquity of non-Newtonian fluids in biology, we address mathematically the role of shear-dependent viscosities on both the waving flagellar locomotion and ciliary transport by metachronal waves. Using a two-dimensional waving sheet as model for the kinematics of a flagellum or an array of cilia, and allowing for both normal and tangential deformation of the sheet, we calculate the flow field induced b…
The Lagrangian (LA) and Eulerian Acceleration (EA) properties of fluid particles in homogeneous turbulence with uniform shear and uniform stable stratification are studied using direct numerical simulations. The Richardson number is varied from $Ri=0$, corresponding to unstratified shear flow, to $Ri=1$, corresponding to strongly stratified shear flow. The probability density functions (pdfs) of both LA and EA have a stretched-exponential shape and they show a strong and similar influence on the Richardson number. The extreme values of the EA are stronger than those observed for the LA. Geomet…
The traditional approach in the study of hydrodynamic stability of stratified fluids includes the stick boundary conditions between layers. However, this rule may be violated in polymer systems and as a consequence various instabilities may arise. The main objective of this paper is to analyze theoretically the influence of slip boundary conditions on the hydrodynamic stability of the interface between two immiscible viscous layers subjected to simple shear flow. It is found that the growth rate of long-wave disturbances is fairly sensitive to the slip at the interface between layers as well a…
When a drop of fluid hits a small solid target of comparable size, it expands radially until reaching a maximum diameter and subsequently recedes. In this work, we show that the expansion process of liquid sheets is controlled by a combination of shear (on the target) and biaxial extensional (in the air) deformations. We propose an approach toward a rational description of the phenomenon for Newtonian and viscoelastic fluids by evaluating the viscous dissipation due to shear and extensional deformations, yielding a prediction of the maximum expansion factor of the sheet as a function of the re…
Micro-organisms expend energy moving through complex media. While propulsion speed is an important property of locomotion, efficiency is another factor that may determine the swimming gait adopted by a micro-organism in order to locomote in an energetically favorable manner. The efficiency of swimming in a Newtonian fluid is well characterized for different biological and artificial swimmers. However, these swimmers often encounter biological fluids displaying shear-thinning viscosities. Little is known about how this nonlinear rheology influences the efficiency of locomotion. Does the shear-t…
