A two-phase thermomechanical theory for granular suspensions

2016 ◽  
Vol 808 ◽  
pp. 410-440 ◽  
Author(s):  
D. Monsorno ◽  
C. Varsakelis ◽  
M. V. Papalexandris
Keyword(s):  
Volume Fraction ◽  
Constant Density ◽  
Two Phase ◽  
Important Special Case ◽  
Carrier Fluid ◽  
Thermomechanical Theory ◽  
Rate Dependent ◽  
Granular Suspensions ◽  
Developed Pressure ◽  
Viscous Stresses

In this paper, a two-phase thermomechanical theory for granular suspensions is presented. Our approach is based on a mixture-theoretic formalism and is coupled with a nonlinear representation for the granular viscous stresses so as to capture the complex non-Newtonian behaviour of the suspensions of interest. This representation has a number of interesting properties: it is thermodynamically consistent, it is non-singular and vanishes at equilibrium and it predicts non-zero granular bulk viscosity and shear-rate-dependent normal viscous stresses. Another feature of the theory is that the resulting model incorporates a rate equation for the evolution of the volume fraction of the granular phase. As a result, the velocity fields of both the granular material and the carrier fluid are divergent even for constant-density flows. Further, in this article we present the incompressible limit of our model which is derived via low-Mach-number asymptotics. The reduced equations for the important special case of constant-density flows are also presented and discussed. Finally, we apply the proposed model to two test cases, namely, steady shear flow of a homogeneous suspension and fully developed pressure-driven channel flow, and compare its predictions with available experimental and numerical results.

Application of Mixing Length Theory to Wavy Turbulent Liquid—Gas Interface

1981 ◽  
Vol 103 (3) ◽  
pp. 492-500 ◽  
Author(s):  
S. Levy ◽  
J. M. Healzer
Keyword(s):  
Liquid Film ◽  
Transition Layer ◽  
Volume Fraction ◽  
Density Ratio ◽  
Constant Density ◽  
Mixing Length ◽  
Two Phase ◽  
Liquid Entrainment ◽  
Wide Range ◽  
Mixing Length Theory

A fully developed and adiabatic two-phase annular model with liquid entrainment is derived for flow in a pipe with negligible gravity effects. The model is based upon application of the single phase mixing length theory to a wavy liquid-gas interface. The model subdivides the flow cross section into three regions: a liquid film, a gas core of constant density, and a transition wavy layer between them. The combination of a constant velocity and a density varying exponentially with distance from the wall is employed in the transition layer. This approach plus appropriate logarithmic velocity distributions in the liquid film and gas core make it possible to specify the two-phase pressure drop, volume fraction, wave velocity, and thickness of the liquid film and transition layer. The liquid entrainment is obtained in terms of the exponent of the density profile in the transition layer, and interface stability considerations are used to express this entrainment parameter semiempirically in terms of an apparent Weber number and density ratio. Comparisons of the model are made with air-water and steam-water test data, and the results generally are satisfactory over a wide range of conditions and for all the important characteristics of this flow pattern.

scholarly journals Rheology of dense granular suspensions

2018 ◽  
Vol 852 ◽  
Author(s):  
Élisabeth Guazzelli ◽  
Olivier Pouliquen
Keyword(s):  
Colloidal Particles ◽  
Volume Fraction ◽  
Phase System ◽  
Concentrated Suspensions ◽  
Two Phase ◽  
Transient Flows ◽  
Colloidal Spheres ◽  
Dense Suspensions ◽  
Granular Suspensions ◽  
Maximum Volume Fraction

Suspensions are composed of mixtures of particles and fluid and are omnipresent in natural phenomena and in industrial processes. The present paper addresses the rheology of concentrated suspensions of non-colloidal particles. While hydrodynamic interactions or lubrication forces between the particles are important in the dilute regime, they become of lesser significance when the concentration is increased, and direct particle contacts become dominant in the rheological response of concentrated suspensions, particularly those close to the maximum volume fraction where the suspension ceases to flow. The rheology of these dense suspensions can be approached via a diversity of approaches that the paper introduces successively. The mixture of particles and fluid can be seen as a fluid with effective rheological properties but also as a two-phase system wherein the fluid and particles can experience relative motion. Rheometry can be undertaken at an imposed volume fraction but also at imposed values of particle normal stress, which is particularly suited to yield examination of the rheology close to the jamming transition. The response of suspensions to unsteady or transient flows provides access to different features of the suspension rheology. Finally, beyond the problem of suspension of rigid, non-colloidal spheres in a Newtonian fluid, there are a great variety of complex mixtures of particles and fluid that remain relatively unexplored.

Effect of Precipitate Morphology on the Gradient-Dependent Behaviour of Two-Phase Single Crystals

1999 ◽  
Vol 578 ◽  
Author(s):  
E. P. Busso ◽  
F. T. Meissonnier ◽  
N. P. O'Dowd
Keyword(s):  
Volume Fraction ◽  
Large Strain ◽  
Deformation Gradient ◽  
Slip Rate ◽  
Strengthening Mechanism ◽  
Precipitate Size ◽  
Two Phase ◽  
Precipitate Morphology ◽  
Fully Implicit ◽  
Rate Dependent

AbstractIn this work a recently proposed gradient and rate-dependent crystallographic formulation is used to investigate the macroscopic behaviour of a precipitated single crystal. It relies on strain gradient concepts to account for the additional strengthening mechanism caused by presence of interfacial and geometrically necessary dislocations (GNDs). The total slip resistance is assumed to be due to a mixed population of mobile and sessile forest obstacles arising from both statistically stored dislocations (SSDs) and GNDs. The non-local crystallographic theory is implemented numerically into the finite element method. It requires the calculation of the slip rate gradients at the element level to determine the evolutionary behaviour of the GND densities, and a fully implicit numerical algorithm within a large strain kinematics framework and non-isothermal conditions. The effects of the relevant microstructural features (precipitate size, morphology and volume fraction) and deformation gradient-related length scales on the macroscopic behaviour is investigated and compared with experimental results.

scholarly journals Numerical Study on an Interface Compression Method for the Volume of Fluid Approach

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 80
Author(s):  
Yuria Okagaki ◽  
Taisuke Yonomoto ◽  
Masahiro Ishigaki ◽  
Yoshiyasu Hirose
Keyword(s):  
Linear Theory ◽  
Volume Fraction ◽  
Numerical Study ◽  
Volume Of Fluid ◽  
Interfacial Wave ◽  
Validation Process ◽  
Two Phase ◽  
Numerical Diffusion ◽  
Mesh Resolution ◽  
Water Reactors

Many thermohydraulic issues about the safety of light water reactors are related to complicated two-phase flow phenomena. In these phenomena, computational fluid dynamics (CFD) analysis using the volume of fluid (VOF) method causes numerical diffusion generated by the first-order upwind scheme used in the convection term of the volume fraction equation. Thus, in this study, we focused on an interface compression (IC) method for such a VOF approach; this technique prevents numerical diffusion issues and maintains boundedness and conservation with negative diffusion. First, on a sufficiently high mesh resolution and without the IC method, the validation process was considered by comparing the amplitude growth of the interfacial wave between a two-dimensional gas sheet and a quiescent liquid using the linear theory. The disturbance growth rates were consistent with the linear theory, and the validation process was considered appropriate. Then, this validation process confirmed the effects of the IC method on numerical diffusion, and we derived the optimum value of the IC coefficient, which is the parameter that controls the numerical diffusion.

scholarly journals Effects of Polydispersity on the Phase Behavior of Additive Hard Spheres in Solution

Molecules ◽  
2021 ◽  
Vol 26 (6) ◽  
pp. 1543
Author(s):  
Luka Sturtewagen ◽  
Erik van der Linden
Keyword(s):  
Phase Behavior ◽  
Critical Point ◽  
Volume Fraction ◽  
Hard Spheres ◽  
Second Virial Coefficient ◽  
Two Phase ◽  
Different Types ◽  
Asymmetric Partitioning ◽  
Average Size ◽  
Liquid Liquid Phase Separation

The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid–liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.

Experimental Model of Temperature-Driven Nanofluid

2006 ◽  
Vol 129 (6) ◽  
pp. 697-704 ◽  
Author(s):  
A. G. Agwu Nnanna
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Small Volume ◽  
Volume Fraction ◽  
Convective Heat Transfer Coefficient ◽  
Isothermal Condition ◽  
Carrier Fluid ◽  
Small Volume Fraction ◽  
The Impact

This paper presents a systematic experimental method of studying the heat transfer behavior of buoyancy-driven nanofluids. The presence of nanoparticles in buoyancy-driven flows affects the thermophysical properties of the fluid and consequently alters the rate of heat transfer. The focus of this paper is to estimate the range of volume fractions that results in maximum thermal enhancement and the impact of volume fraction on Nusselt number. The test cell for the nanofluid is a two-dimensional rectangular enclosure with differentially heated vertical walls and adiabatic horizontal walls filled with 27 nm Al2O3–H2O nanofluid. Simulations were performed to measure the transient and steady-state thermal response of nanofluid to imposed isothermal condition. The volume fraction is varied between 0% and 8%. It is observed that the trend of the temporal and spatial evolution of temperature profile for the nanofluid mimics that of the carrier fluid. Hence, the behaviors of both fluids are similar. Results shows that for small volume fraction, 0.2⩽ϕ⩽2% the presence of the nanoparticles does not impede the free convective heat transfer, rather it augments the rate of heat transfer. However, for large volume fraction ϕ>2%, the convective heat transfer coefficient declines due to reduction in the Rayleigh number caused by increase in kinematic viscosity. Also, an empirical correlation for Nuϕ as a function of ϕ and Ra has been developed, and it is observed that the nanoparticle enhances heat transfer rate even at a small volume fraction.

Micromechanical analysis of effective mechanical properties of graphene/ZrO2-hybrid poly (methyl methacrylate) nanocomposites

2021 ◽  
pp. 251659842110388
Author(s):  
Ankit Rathi ◽  
S. I. Kundalwal
Keyword(s):  
Methyl Methacrylate ◽  
Elastic Properties ◽  
Mechanical Performance ◽  
Volume Fraction ◽  
Element Model ◽  
Two Phase ◽  
Effective Elastic Properties ◽  
Poly Methyl Methacrylate ◽  
Three Phase ◽  
Effective Mechanical Properties

In this study, the tensile properties of two-phase and three-phase graphene/ZrO2-hybrid poly (methyl methacrylate) (PMMA) nanocomposites are investigated by developing finite element model using ANSYS. Primarily, the effective elastic properties of two- and three-phase graphene/ZrO2-hybrid PMMA nanocomposites (GRPCs) are estimated by developing mechanics of material (MOM) model. Results indicated that the effective elastic properties of GRPCs increase with an increase in the volume fraction of graphene. Also, the stiffness of GRPCs is increased by 78.12% with increasing in the volume fraction of graphene from 0.1 to 0.5 Vf. The incorporation of an additional ZrO2 interphase significantly improved the mechanical performance of resulting GRPCs.

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