Non-ideal Fluid Research Articles

Fluctuating multicomponent lattice Boltzmann model.

Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.

Introducing Students to Rheological Classification of Foods, Cosmetics, and Pharmaceutical Excipients Using Common Viscous Materials

Rheological measurements are very important tools for the characterization of the flow and deformation of a material, as well as for optimization of the rheological parameters. The application and acceptance of pharmaceutical formulations, cosmetics, and foodstuffs depends upon their rheological characteristics, such as texture, consistency, or viscosity, which also influences their stability and bioavailability. This article describes a simple 2 h laboratory procedure for the rheological characterization of some foods, cosmetics, and pharmaceutical excipients using a digital Brookfield viscometer. The experiment was designed to introduce basic rheological concepts to undergraduate Health Science students, such as Pharmacy and Biochemistry students, allowing them to perform viscosity measurements of ideal and nonideal fluids and to classify the flow behavior based on the experimental flow curves of common viscous materials.

Effect of fluid-colloid interactions on the mobility of a thermophoretic microswimmer in non-ideal fluids.

Janus colloids propelled by light, e.g., thermophoretic particles, offer promising prospects as artificial microswimmers. However, their swimming behavior and its dependence on fluid properties and fluid-colloid interactions remain poorly understood. Here, we investigate the behavior of a thermophoretic Janus colloid in its own temperature gradient using numerical simulations. The dissipative particle dynamics method with energy conservation is used to investigate the behavior in non-ideal and ideal-gas like fluids for different fluid-colloid interactions, boundary conditions, and temperature-controlling strategies. The fluid-colloid interactions appear to have a strong effect on the colloid behavior, since they directly affect heat exchange between the colloid surface and the fluid. The simulation results show that a reduction of the heat exchange at the fluid-colloid interface leads to an enhancement of colloid's thermophoretic mobility. The colloid behavior is found to be different in non-ideal and ideal fluids, suggesting that fluid compressibility plays a significant role. The flow field around the colloid surface is found to be dominated by a source-dipole, in agreement with the recent theoretical and simulation predictions. Finally, different temperature-control strategies do not appear to have a strong effect on the colloid's swimming velocity.

Pattern formation in liquid-vapor systems under periodic potential and shear.

In this paper the phase behavior and pattern formation in a sheared nonideal fluid under a periodic potential is studied. An isothermal two-dimensional formulation of a lattice Boltzmann scheme for a liquid-vapor system with the van der Waals equation of state is presented and validated. Shear is applied by moving walls and the periodic potential varies along the flow direction. A region of the parameter space, where in the absence of flow a striped phase with oscillating density is stable, will be considered. At low shear rates the periodic patterns are preserved and slightly distorted by the flow. At high shear rates the striped phase loses its stability and traveling waves on the interface between the liquid and vapor regions are observed. These waves spread over the whole system with wavelength only depending on the length of the system. Velocity field patterns, characterized by a single vortex, will also be shown.

Bose–Einstein condensate dark matter phase transition from finite temperature symmetry breaking of Klein–Gordon fields

In this paper, the thermal evolution of scalar field dark matter (SFDM) particles at finite cosmological temperatures is studied. Starting with a real SF in a thermal bath and using the one-loop quantum corrections potential, we rewrite Klein–Gordon’s equation in its hydrodynamical representation and study the phase transition of this SF due to a Z2 symmetry breaking of its potential. A very general version of a nonlinear Schrödinger equation is obtained. When introducing Madelung’s representation, the continuity and momentum equations for a non-ideal SFDM fluid are formulated, and the cosmological scenario with the SFDM described in analogy to an imperfect fluid is then considered where dissipative contributions are obtained in a natural way. Additional terms appear in the results compared to those in the classical version commonly used to describe the ΛCDM model, i.e., the ideal fluid. The equations and parameters that characterize the physical properties of the system such as its energy, momentum and viscous flow are related to the temperature of the system, scale factor, Hubble’s expansion parameter and the matter energy density. Finally, some details on how galaxy halos and smaller structures might be able to form by condensation of this SF are given.

Theoretical analysis of effects of viscosity, surface tension, and magnetic field on the bubble evolution of Rayleigh-Taylor instability

The evolution of bubble in Rayleigh-Taylor (RT) instability for non-ideal hydromagnetic fluid is investigated theoretically in this study. In a plane perpendicular to the magnetic field, the general governing equation describing the bubble evolution is derived by considering the influences of viscousity, surface tension and magnetic field. The numerical and asymptotic solutions of the bubble velocity in two-dimensional planar geometry are obtained under different conditions and the effects of fluid viscosity, surface tension and magnetic field on the bubble growth are then analyzed in detail. It is found that the bubble velocity is reduced by viscosity and surface tension, which indicates that viscosity and surface tension can suppress the RT instability. It is also observed that the influence of magnetic field on the RT instability is caused by its nonlinear part, and whether the RT instability can be suppressed or enhanced depends on the direction of the nonlinear part of magnetic field.

The Geometry of Non-Ideal Fluids

Arnold showed that the Euler equations of an ideal fluid describe geodesies on the Lie algebra of incompressible vector fields. We generalize this to fluids with dissipation and Gaussian random forcing. The dynamics is determined by the structure constants of a Lie algebra, along with inner products defining kinetic energy, Ohmic dissipation and the covariance of the forces. This allows us to construct tractable toy models for fluid mechanics with a finite number of degrees of freedom. We solve one of them to show how symmetries can be broken spontaneously.In another direction, we derive a deterministic equation that describes the most likely path connecting two points in the phase space of a randomly forced system: this is a WKB approximation to the Fokker-Plank-Kramer equation, analogous to the instantons of quantum theory. Applied to hydrodynamics, we derive a PDE system for Navier-Stokes instantons.

MATHEMATICAL MODELING OF SUPERCRITICAL MULTICOMPONENT REACTIVE FLUIDS

We investigate a system of partial differential equations modeling supercritical multicomponent reactive fluids. These equations involve nonideal fluid thermodynamics, nonideal chemistry as well as multicomponent diffusion fluxes driven by chemical potential gradients. Only local symmetrization of the resulting system of partial differential equations may be achieved because of thermodynamic instabilities even though the entropy function is globally defined. Local symmetrized forms are explicitly evaluated in terms of the inverse of the chemical potential Hessian and local normal forms lead to global existence and asymptotic stability of equilibrium states as well as decay estimates. We also discuss the deficiency of the resulting system of partial differential equations at thermodynamically unstable states typically associated with nonideal fluids.

Modelling of the reactive absorption of CO2 using mono-ethanolamine

The post-combustion capture of CO2 by reactive absorption using amines is a widely studied technology for the mitigation of CO2 emissions, especially from the fossil fuel-fired power plants. Reactive absorption of CO2 is a well-studied process on lab-scale. For the efficient design of reactive absorption columns, a reliable and predictive rate-based process model is necessary. In this work, a detailed rate-based model, which considers multicomponent mass transfer, chemical reactions in the film and in the bulk phase, non-ideal phase behaviour, fluid dynamics and heat transfer, is presented. The model is validated using the published pilot-scale experimental results of the absorption of CO2 by aqueous mono-ethanolamine (MEA), where two different types of structured packings (Sulzer BX and Sulzer Mellapak™ 250.Y) were employed. The model predicts the experimental profiles of the temperature and the concentration of CO2 in the liquid phase with an accuracy of ±8%. Furthermore, based on the Hatta numbers, the necessity of the liquid film discretisation is analysed for a given operation window. The paper also presents the results of a sensitivity analysis of the most relevant parameters on the overall CO2 absorption for two representative operating points (one for each packing). The inlet flow rate of the gas and liquid streams, the composition of CO2 and MEA in lean solvent, the distribution coefficient, the liquid hold-up and the effective interfacial area were the most sensitive parameters that affected the overall CO2 absorption. The sensitivity analysis is useful to understand the influence of the input parameters on the performance of the absorption column and for the optimisation of the reactive absorption of CO2 using amines.

Interfacial roughening in nonideal fluids: Dynamic scaling in the weak- and strong-damping regime

Interfacial roughening denotes the nonequilibrium process by which an initially flat interface reaches its equilibrium state, characterized by the presence of thermally excited capillary waves. Roughening of fluid interfaces has been first analyzed by Flekkoy and Rothman [Phys. Rev. Lett. 75, 260 (1995)], where the dynamic scaling exponents in the weakly damped case in two dimensions were found to agree with the Kardar-Parisi-Zhang universality class. We extend this work by taking into account also the strong-damping regime and perform extensive fluctuating hydrodynamics simulations in two dimensions using the Lattice Boltzmann method. We show that the dynamic scaling behavior is different in the weakly and strongly damped case.

Simulation of viscous sintering using the lattice Boltzmann method

The viscous flow is one of the important mass transport mechanisms in sintering powder materials such as porous glass. The main underlying driving force here is the tendency of the system to minimize the overall surface free energy. In this work, we first address the fundamental problem of the coalescence of two suspending drops and provide an alternative derivation of Frenkel's formula by explicitly taking account of driving forces which arise from the curvature of the contact zone. The result thus obtained is compared with non-ideal (two phase) fluid lattice Boltzmann simulations. Furthermore, we use this simulation tool to address the more complex case of the sintering of a compact of viscous spherical particles. We observe a significantly faster densification dynamics than in experiments but obtain qualitative agreement upon rescaling the unit of time. We attribute this faster dynamics in simulations to the absence of intergranular friction and discuss a possible improvement of the model. We also propose, for the present LB model, a simple way of imposing shear flow to determine the time dependence of the effective viscosity during the sintering process. The method is benchmarked via a simple analytic case and first simulation results are presented for situations for which no analytic theory exists.

Bubble velocities in the nonlinear Rayleigh-Taylor and Richtmyer-Meshkov instabilities in non-ideal fluids

In a reference system moving with the bubble vertex we investigate the effects of fluid viscosity and surface tension on the bubble velocity in the nonlinear Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities, by extending the ideal fluid model [Goncharov V N, Phys. Rev. Lett. 88 134502 (2002)] to the non-ideal fluid case. First of all, the governing equation (i.e. self-consistent differential equations) describing the dynamic of the bubble front in RT and RM instabilities is obtained. Then, the numerical and asymptotic solutions of the bubble velocity in two-dimensional planar geometry and three-dimensional cylindrical geometry are obtained. Moreover, we quantitatively study the effects of fluid viscosity and surface tension on the RT and RM bubble velocities. It is found that in the fully nonlinear evolutions of RT and RM instabilities, the bubble velocity and amplitude in the non-ideal fluid are both less than those in its ideal fluid counterpart. That is to say, the effects of fluid viscosity and surface tension tend to stabilize the RT and RM instabilities.

Effects of surface tension on Rayleigh-Taylor instability

In this paper, Layzers model which has a simple velocity potential, and Zufirias model are extended to the case of non-ideal fluids, and the effects of surface tension on Rayleigh-Taylor instability are investigated. Firstly, the analytical expressions for the asymptotic bubble velocity and curvature are obtained in the two models. Secondly, the effects of surface tension on Rayleigh-Taylor instability are studied systematically. Finally, the two models are compared with each other and the comparisons with numerical simulation are made as well. The results indicate that the surface tension depresses the bubble velocity, but does not affect the bubble curvature. The Layzers model with the simple velocity potential gives a smaller bubble velocity than that predicted by the Layzers model with a complex velocity potential. But the bubble velocity predicted by the Layzers model with the simple velocity potential is larger than that obtained by Zufirias model. Both Layzers models lead to the same bubble velocity when the Atwood number is A = 1.

Critical dynamics of an isothermal compressible nonideal fluid

A pure fluid at its critical point shows a dramatic slow-down in its dynamics, due to a divergence of the order-parameter susceptibility and the coefficient of heat transport. Under isothermal conditions, however, sound waves provide the only possible relaxation mechanism for order-parameter fluctuations. Here we study the critical dynamics of an isothermal, compressible nonideal fluid via scaling arguments and computer simulations of the corresponding fluctuating hydrodynamics equations. We show that, below a critical dimension of 4, the order-parameter dynamics of an isothermal fluid effectively reduces to "model A," characterized by overdamped sound waves and a divergent bulk viscosity. In contrast, the shear viscosity remains finite above two dimensions. Possible applications of the model are discussed.

Pinch instability of a cylindrical couette flow in a nonuniform axial magnetic field

The paper addresses the linear stability to axisymmetric perturbations of an incompressible nonideal fluid between two rotating coaxial infinitely long cylinders in a nonuniform axial magnetic field. For conducting cylinders, the results for uniform and nonuniform magnetic fields are qualitatively identical. This is also observed for nonconducting cylinders in a magnetic field with a constant direction. Instability appears for nonconducting cylinders in a magnetic field with a varying direction, whose magnitude exceeds a certain critical value. This new instability also exists in the absence of rotation and, hence, is independent of its parameters. In addition, the critical magnetic field is independent of the magnetic Prandtl number, which facilitates experimental observation of the new instability.

Unified framework for a side-by-side comparison of different multicomponent algorithms: Lattice Boltzmann vs. phase field model

Lattice Boltzmann models (LBM) and phase field models (PFM) are two of the most widespread approaches for the numerical study of multicomponent fluid systems. Both methods have been successfully employed by several authors but, despite their popularity, still remains unclear how to properly compare them and how they perform on the same problem. Here we present a unified framework for the direct (one-to-one) comparison of the multicomponent LBM against the PFM. We provide analytical guidelines on how to compare the Shan–Chen (SC) lattice Boltzmann model for non-ideal multicomponent fluids with a corresponding free energy (FE) lattice Boltzmann model. Then, in order to properly compare the LBM vs. the PFM, we propose a new formulation for the free energy of the Cahn–Hilliard/Navier–Stokes equations. Finally, the LBM model is numerically compared with the corresponding phase field model solved by means of a pseudo-spectral algorithm. This work constitute a first attempt to set the basis for a quantitative comparison between different algorithms for multicomponent fluids. We limit our scope to the few of the most common variants of the two most widespread methodologies, namely the lattice Boltzmann model (SC and FE variants) and the phase field model.

Application of the Maxwell–Stefan Approach to Acrylonitrile Adsorption and Desorption in a Macroporous Polymer

This article reports the application of the Maxwell–Stefan approach for multicomponent liquid-phase diffusion in a macroporous polymer. The adsorption of acrylonitrile onto Dowex Optipore L-493 from water and its desorption from the sorbent in different water/acetone mixtures was modeled. The intraparticle diffusion is treated as diffusion in a nonideal bulk fluid since the pores of the sorbent are large and the molecules–pore wall interactions can therefore be neglected. The results of the simulations are in good agreement with the experimental data. The Maxwell–Stefan intraparticle diffusion coefficients are in the same range as the free liquid diffusion coefficients according to Fick. The calculation of the thermodynamic factors shows that, whereas for low acrylonitrile mole fractions in water, Fick’s diffusion can give good results, the nonideality of the system has to be taken into account for higher acrylonitrile concentrations.

Simulation of static critical phenomena in nonideal fluids with the lattice Boltzmann method

A fluctuating nonideal fluid at its critical point is simulated with the lattice Boltzmann method. It is demonstrated that the method, employing a Ginzburg-Landau free energy functional, correctly reproduces the static critical behavior associated with the Ising universality class. A finite-size scaling analysis is applied to determine the critical exponents related to the order parameter, compressibility and specific heat. A particular focus is put on finite-size effects and issues related to the global conservation of the order parameter.

The emergence of supramolecular forces from lattice kinetic models of non-ideal fluids: applications to the rheology of soft glassy materials

A systematic study for a single-specie lattice Boltzmann model with frustrated-short range attractive and mid/long-range repulsive-interactions is presented. The equilibrium analysis is performed along the guidelines proposed by [X. Shan, Phys. Rev. E 77, 066702 (2008)] and allows us to determine the surface tension density and the resulting disjoining pressure developing in a thin film when two interfaces overlap. Numerical simulations of confined flows are then performed with a multicomponent model and are successfully tested against the recent suggestion by Bocquet and coworkers on the existence of a cooperative length underlying the non-local rheology of highly confined soft-glassy materials [Goyon et al., Nature 454, 84-87 (2008); Soft Matter 6, 2668-2678 (2010)].

Mesoscopic simulation of non-ideal fluids with self-tuning of the equation of state

A dynamic optimization strategy is presented to generate customized equations of state (EOS) for the numerical simulation of non-ideal fluids at high density ratio. While stable branches of the analytical EOS are preserved, the spinodal region is self-tuned during the simulation, in order to compensate for numerical errors caused by discretization in phase space. The employed EOS permits the readily setting of the sound speeds for the gas and liquid phases, thus allowing stable simulation with high density (1 : 10 to 1 : 1000) and compressibility ratios (250 : 1–25000 : 1). The present technique is demonstrated for lattice Boltzmann simulation of (free-space) multiphase systems with flat and circular interfaces.