Viscous Interaction Research Articles

Viscoelastic multiscaling in immersed networks

This paper shows how elastic and viscous microscopic interactions influence rheological responses in soft materials. Both the standard linear solid model of viscoelasticity and the Hertz model of mechanical contact can be recovered by a coarse-grained model.

Lift Force Acting on a Heavy Cylinder and a Steady Flow in an Unevenly Rotating Container

The dynamics of a heavy cylindrical body in a horizontal cylindrical cavity filled with a viscous liquid and subjected to modulated rotation is experimentally investigated. In experiment the cylinders with different moment of inertia are used. Periodic variation (modulation) of cavity rotation rate leads to the azimuthal oscillations of the body in a uniformly rotating reference frame due to viscous interaction with the cavity wall. It is found that near the cavity boundary an averaged repulsive (lift) force acts on an oscillating body. Experiments in a wide range of dimensionless frequency of rotation rate modulation demonstrate that lift force coefficient monotonically growth with frequency increase. The rotation rate modulation is found to be an effective tool to control the behavior of solids located near the rotating wall under microgravity conditions. The analysis of steady velocity field near the oscillating body reveals vortices in form of rolls localized outside the viscous boundary layers.

Wind Tunnel Investigation into the Resistance Analysis of Slender Body Catamaran

The Wind tunnel investigation of a slender body catamaran was conducted in order to determine its resistance characteristics, namely the effect of pressure and flow velocity changes for varied hull separation. The catamaran was tested in a wind tunnel belongs to Department of Mechanical Engineering, ITS, with hull separations of S/L = 0.2 to 0.4 and variation in Reynolds numbers up to 4.46 x 105. Pressure around the hull was measured using pressure tappings and the flow velocity behind the hull was also measured using a Pitôt-static tube. The experimental study shows that the pressure coefficient decreases when the hull separation declines and conversely, the flow velocity increases. The tests demonstrated a viscous interaction between the hulls, and form factors for the monohull and catamaran are derived. The demihull exhibited a form factor (1+k) of 1.265 and in the catamaran mode, the measured form factor (1+βk) was between 1.416 and 1.403. The results are in agreement with other published data.

Random vibrations of stress-driven nonlocal beams with external damping

Stochastic flexural vibrations of small-scale Bernoulli-Euler beams with external damping are investigated by stress-driven nonlocal mechanics. Damping effects are simulated considering viscous interactions between beam and surrounding environment. Loadings are modeled by accounting for their random nature. Such a dynamic problem is characterized by a stochastic partial differential equation in space and time governing time-evolution of the relevant displacement field. Differential eigenanalyses are performed to evaluate modal time coordinates and mode shapes, providing a complete stochastic description of response solutions. Closed-form expressions of power spectral density, correlation function, stationary and non-stationary variances of displacement fields are analytically detected. Size-dependent dynamic behaviour is assessed in terms of stiffness, variance and power spectral density of displacements. The outcomes can be useful for design and optimization of structural components of modern small-scale devices, such as Micro- and Nano-Electro-Mechanical-Systems (MEMS and NEMS).

The Bardeen–Petterson effect in accreting supermassive black hole binaries: a systematic approach

ABSTRACT Disc-driven migration is a key evolutionary stage of supermassive black hole binaries hosted in gas-rich galaxies. Besides promoting the inspiral, viscous interactions tend to align the spins of the black holes with the orbital angular momentum of the disc. We present a critical and systematic investigation of this problem, also known as the Bardeen–Petterson effect. We design a new iterative scheme to solve the non-linear dynamics of warped accretion discs under the influence of both relativistic frame dragging and binary companion. We characterize the impact of the disc ‘critical obliquity’, which marks regions of the parameter space where stationary solutions do not exist. We find that black hole spins reach either complete alignment or a critical configuration. Reaching the critical obliquity might imply that the disc breaks as observed in hydrodynamical simulations. Our findings are important to predict the spin configurations with which supermassive black hole binaries enter their gravitational-wave driven regime and become detectable by LISA.

On the magnetization of a dilute suspension in a uniform magnetic field: Influence of dipolar and hydrodynamic particle interactions

In this work, the magnetization of a dilute magnetic suspension undergoing a shear flow and a uniform field in the presence of dipolar and hydrodynamic interactions is investigated. Firstly, the problem of a single magnetic particle in a simple shear flow in the presence of an external uniform magnetic filed is examined. From this solution, we study the influence of non-equilibrium effects on the magnetization at condition of strong flows, including the spinning behavior of the particles. Next, we use a non-renormalized cluster expansion in order to derive the magnetization O(ϕ2) in a sheared suspension of non-Brownian magnetic from a solution of a creeping flow problem of two magnetic spherical particles interacting magnetically and hydrodynamically in the presence of a uniform applied magnetic field, where ϕ is the particle volume fraction. The numerical results suggest that under condition of strong flows the aggregative nature of the dipolar interactions may lead to a decrease in the magnetization component in the field direction. In contrast, the dispersive character of the viscous hydrodynamic interactions produces a substantial increase in the same component of magnetization even under the condition of strong flow. This result is attributed to the misalignment produced by the hydrodynamic disturbances on the particle dipoles orientated with the flow direction.

Equations and fundamental characteristics of transverse waves propagating in fluid-saturated porous materials

The main purpose of the paper is to present an extended analysis of the coupled system of linear equations describing wave propagation in fluid-saturated porous materials used for the determination of their fundamental characteristics. The present paper is the first part, mainly devoted to the analysis of the system of equations describing transverse wave propagation. The analysis of equations for compressional waves will be presented in a separate paper. The starting point of considerations are nonlinear equations describing the dynamic behavior of the medium formulated in the spirit of the theory of interacting continua in which parameters of isotropic pore space structure are explicitly present in the model, and constitutive equations are formulated for each physical component separately. They contain all fundamental mechanical couplings between components of this medium in the general nonlinear form and of clear physical meaning. Linear equations of this theory for barotropic fluid and hyperelastic skeleton are the subject of the analysis performed in the paper. They are equivalent to Biot's model, widely used in the description and analysis of wave propagation in saturated porous materials and wave interaction with the boundary of such media. A new method of analysis is proposed in the paper, based on spectral decomposition of the system of equations in the two-dimensional vector space of rotations of solid and fluid particles. It is shown that each choice of the base in this vector space defines the division of the medium into two new components and transforms the system of equation to the form describing the dynamic behavior of these components, and the requirement of the basic dynamic properties of the medium to be invariant in each chosen base uniquely determines the mass densities and bulk modules of the new components. Such an approach enabled decomposition of the system of equations for particle rotations to two uncoupled scalar equations, the only one of which describes propagation of the transverse wave. This also allowed obtaining expressions characterizing transverse wave propagation in fluid-saturated porous materials: velocity, effective mass densities and wave impedance of the medium associated with this wave and its frequency characteristics: phase velocity and attenuation coefficient. It is shown that both frequency characteristics are fully defined by the effective mass densities of both components associated with the transverse wave, the tortuosity of the pore space, and the coefficient characterizing the viscous interaction of the fluid with the skeleton.

Aeroelastic interactions and trajectory selection of vortex gusts impinging upon Joukowski airfoils

The dynamically-coupled interactions of vortex gusts encountering a symmetric Joukowski airfoil on linear elastic supports is formulated analytically and evaluated numerically using a time-dependent conformal mapping. The Brown and Michael framework models the unsteady shedding of vorticity from the airfoil into the wake, and the aeroelastic motion of the airfoil is analyzed using quasi-steady, apparent mass, and fully-unsteady aerodynamic models. Special attention is paid to the influences of the strength of the incident vortex and the airfoil natural frequency on the initial upstream placement of a vortex gust that achieves direct impingement. These results are weakly sensitive to the initial vortex position in the limits of either large or small structural natural frequency, and the initial vertical vortex position to achieve impingement changes monotonically with the vortex strength. A comparison of the numerical model with available experimental vortex gust measurements over stationary airfoils highlights the appropriate use of the point-vortex model for inviscid vortex–airfoil interaction problems without significant vortex strength decay, which occurs for predominantly viscous interactions of close vortex–airfoil encounters.

Computational modelling of dynamic loads of a container under viscous interaction with a flat wagon in sea transport

The article deals with the computational modelling of dynamic loads of a container under viscous interaction with a flat wagon transported by a train ferry. The calculation was made with the finite element method in CosmosWorks software. The study defined acceleration fields for the carrying structure of a container and a flat wagon. It was established that the maximum variance percent between the accelerations obtained by theoretical and computational modelling was 17.7 %. The research will contribute to higher efficiency of combined transportation along international transport corridors.

The research of the influence of viscous interaction between wagon and container on the dynamic load during transportation by rail ferry

This paper proposes the improved scheme of interaction of containers with the load-bearing structure of the wagon when transporting by rail ferry. In order to ensure the stability of the container balance in the event of fluctuations in the railway ferry, it is proposed to attach special structures to the support structure of the wagons. To reduce the dynamic loading of containers, a material with damping properties is installed on the internal surfaces of the superstructures. Mathematical modelling was performed to substantiate the proposed technical solution. It was found that the total amount of acceleration that acts on the container is 3.47 m/s2 (0.35 g), and on the load-bearing structure of the wagon 2.47 m/s2 (0.25 g), which is 38 % and 23 % less, respectively, for the acceleration values in the typical scheme of their interaction. The conducted research will contribute to improving the efficiency of combined transport through the international transport corridors.

Nonlinear Response of the Cross Polar Cap Potential to Solar Wind Density Under Northward Interplanetary Magnetic Field

AbstractIt is commonly believed that the magnitude and orientation of interplanetary magnetic field (IMF) together with the solar wind (SW) velocity have the most important impact on the cross polar cap potential (φpc), so that little attention has been given to the effect of SW density, especially under northward IMF conditions. Previous studies have shown that φpc increases with SW density as a response to the changes in magnetosheath force balance, while our study shows that φpc has more complicated responses to the SW density depending on the magnitude of IMF rather than a simple linear response as reported previously. The φpc may be insensitive to SW density increasing at moderate IMF Bz (cf. 8 nT) and at intense Bz (20 nT) under large‐density conditions. The different behavior of SW density in regulating φpc is mainly due to the competing effects originated from viscous interaction and magnetic reconnection. Further, the physical mechanisms are explored, including the driving sources of the viscous potential and affecting factors of reconnection potential. These results pave the way for better understanding of the SW density effects on solar wind‐magnetosphere‐ionosphere (SW‐M‐I) interactions.

Dynamics of a solid of nearly neutral buoyancy in cavity subjected to rotational vibrations

The behavior of a cylindrical body in a horizontal annulus with a longitudinal partition filled with a viscous fluid and subject to high-frequency rotational oscillations is experimentally investigated. The experiments are performed with light and heavy bodies, the density of which is only slightly different from the density of the liquid. The frequency and the amplitude of vibration vary in the experiments. With an increase in the vibration intensity, the repulsion from the boundary and suspension of the light body near the upper boundary of the layer (the heavy one—near the bottom) is found. The repulsion force acts on a solid near the boundary independently from its density. It is shown that vibrational suspension of the body in the gravity field is not associated with inertial oscillations of the body relative to the fluid but is determined by shear oscillations of the liquid itself and viscous interaction of the solid with the cavity boundary.

Additive rheology of complex granular flows

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows.

Laser-induced fluorescence velocimetry for a hypersonic leading-edge separation

Two-dimensional mapping of the velocity distribution for a hypersonic leading-edge separation flowfield generated by a “tick” shaped geometry is presented for the first time. Discrete measurements of two velocity components were acquired at a flow condition having a total specific enthalpy of 3.8 MJ/kg by imaging nitric oxide fluorescence over numerous runs of the hypersonic tunnel at the Australian Defence Force Academy (T-ADFA). The measured freestream velocity distribution exhibited some non-uniformity, which is hypothesized to originate from images acquired using a set of ultraviolet specific mirrors mounted on the shock tunnel deflecting under load during a run of the facility, slightly changing the laser sheet orientation. The flow separation point was measured to occur at 1.4 ± 0.2 mm from the model leading edge, based on the origin of the free shear layer emanating from the expansion surface. Reattachment of this free shear layer on the compression surface occurred at 59.0 ± 0.2 mm from the model vertex. Recirculating the flow bound by the separation and reattachment points contained supersonic reverse flow and areas of subsonic flow aligned with the location of three identified counter-rotating vortices. A comparison of the recirculation flow streamline plots with those computed using Navier–Stokes and direct simulation Monte Carlo (DSMC) codes showed differences in flow structures. At a flow time close to that produced by the facility, flow structures generated by the DSMC solution were seen to agree more favorably with the experiment than those generated by the Navier–Stokes solver due to its ability to better characterize separation by modeling the strong viscous interactions and rarefaction at the leading edge. The primary reason for this is that the no-slip condition used in the Navier–Stokes solution predicts a closer separation point to the leading edge and structures when compared to the DSMC solution, which affects surface shear stress and heat flux, leading to a difference in flow structures downstream of the separation.

Stress fluctuations and shear thickening in dense granular suspensions

We experimentally investigate the rheology and stress fluctuations of granules densely suspended in silicone oil. We find that both thickening strength and stress fluctuations significantly weaken with oil viscosity $\eta_0$. Comparison of our rheological results to the Wyart-Cates model for describing different dynamic jamming states suggests a transition from frictional contacts to lubrication interactions as $\eta_0$ increases. To clarify the contribution from viscous interactions to the rheology, we systematically measure stress fluctuations in various flow states. Reduction of stress fluctuations with $\eta_0$ indicates that a strong lubrication layer greatly inhibits force correlations among particles. Measuring stress fluctuations in the strong shear thickening regime, we observe a crossover from asymmetric Gamma to symmetric Gaussian distributions and associated with it a decrease of lateral (radial) correlation length $\xi$ with increasing shear rate.

Bile acid-retention by native and modified oat and barley β-glucan

Foods rich in cereal β-glucan are efficient dietary tools to help reduce serum cholesterol levels and hence the risk of cardiovascular diseases. However, β-glucan undergoes various reactions during food processing, which alter its viscous properties and interactions with components of the gastrointestinal tract. It has been proposed in the literature that oxidation and partial hydrolysis increase β-glucan’s bile acid-binding activity, and therefore its effectiveness in lowering cholesterol. Here, the passage kinetics of a bile salt mix across a dialysis membrane was studied with or without oat and barley β-glucan extracts, native or modified (partial hydrolysis and oxidations by sodium periodate or TEMPO (2,2,6,6-tetramethylpiperidine-1-oxyl)). Bile acid-retention turned out to be purely a function of viscosity, with the most viscous native extracts exhibiting the strongest retardation of bile acid permeation. Opposite of what was suggested in the literature, oxidation and molecular weight reduction do not seem to increase the bile acid-binding capability of β-glucan.

Determination of the strength of a flat wagon by elastic viscous interaction with tank containers

The article highlights the peculiarities of the mathematical modelling for dynamic load of the bearing structure of a flat wagon by elastic-viscous interaction with tank containers. It was established that the presence of viscous or elastic-viscous connections between fittings and fitting stops, taking into account the possible movements of tank containers in relation to the frame, provides the dynamic load of the bearing structure of the flat wagon within normal range. The conducted researches will provide efficiency increase of combined transportations and develop recommendations for designing modern constructions of railway rolling stock.

Design and Optimization Method for Hypersonic Quasi-Waverider

The waverider has an extensive application prospect in the design of hypersonic vehicles due to its excellent aerodynamic efficiency. However, it is known that the original cone-derived waverider is longitudinally unstable. To solve the problem, a design method for hypersonic quasi-waverider configuration is first proposed and then a genetic algorithm optimization framework is constructed to obtain optimum quasi-waveriders with different constraints. During the optimization, the aerodynamic performance is evaluated by an efficient aerodynamic model that considers the impacts of strong viscous interaction effects. Results from numerical simulations show that, for the optimum quasi-waveriders without constraints, good shock wave attachment along the leading edge is achieved, and the maximum lift-to-drag ratio () is even higher than that of the original waverider. Optimized quasi-waveriders are also generated based on the constraints of volumetric efficiency and stability. The first increases and then decreases with the increase in volumetric efficiency. In addition, an interesting phenomenon is found that the is reduced almost linearly with the increase in the degree of stability at each design condition. Furthermore, a linear relationship is also constructed between the variation of with respect to degree of stability and the viscous interaction parameter .

Deformation analysis of lipid membranes subjected to general forms of intra-membrane viscous flow and interactions with an elliptical-cross-section substrate

We study the morphology of lipid membranes subjected to intra-membrane viscous flows and interactions with elliptical cylinder substrates. From the non-linear theory of elastic surfaces, a linearized shape equation and admissible boundary conditions are formulated in elliptical coordinates via the Monge representation of a surface. In particular, the intra-membrane viscosity terms are linearized and mapped into elliptic coordinates in order to accommodate more general forms of viscous flow. The assimilated viscous flow is characterized by potential functions which satisfies the continuity condition. A complete solution in terms of Mathieu function is then obtained within the prescription of incremental deformations superposed on large. The results describe smooth morphological transitions over the domain of interest and, more importantly, predicts wrinkle formations in the presence of intra-membrane viscous flow in the surface. Lastly, the obtained solution accommodates the results from the circular cases in the limit of vanishing eccentricity and intra-membrane viscous flow.

Viscous Interaction Forces of Two Pulsating Spheres in a Fluid Near their Contact Point

Viscous Interaction Forces of Two Pulsating Spheres in a Fluid Near their Contact Point