Are upwind techniques in multi-phase flow models necessary?

Two alternatives of primary variables are compared for two-phase flow in heterogeneous media by solving fully established benchmarks. The first combination utilizes pressure of the wetting fluid and saturation of the non-wetting fluid as primary variables, while the second employs capillary pressure of the wetting fluid and pressure of the non-wetting fluid. While the standard Galerkin finite element method (SGFEM) is known to fail in the physical reproduction of two-phase flow in heterogeneous media (unless employing a fully upwind correction), the second scheme with capillary pressure as a primary variable without applying an upwind technique produces correct physical fluid behaviour in heterogeneous media, as observed from experiments.     

An evaluation of a 3D free‐energy‐based lattice Boltzmann model for multiphase flows with large density ratio

In this paper, the 3D Navier–Stokes (N–S) equation and Cahn–Hilliard (C–H) equations were solved using a free‐energy‐based lattice Boltzmann (LB) model. In this model, a LB equation with a D3Q19 velocity model is used to recover continuity and N–S equations while another LB equation with D3Q7 velocity model for solving C–H equation (Int. J. Numer. Meth. Fluids, 2008; 56 :1653–1671) is applied to solve the 3D C–H equation. To avoid the excessive use of computational resources, a moving reference frame is adopted to allow long‐time simulation of a bubble rising. How to handle the inlet/outlet and moving‐wall boundary conditions are suggested. These boundary conditions are simple and easy for implementation. This model's performance on two‐phase flows was investigated and the mass conservation of this model was evaluated. The model is validated by its application to simulate the 3D air bubble rising in viscous liquid (density ratio is 1000). Good agreement was obtained between the present numerical results and experimental results when Re is small. However, for high‐Re cases, the mass conservation seems not so good as the low‐Re case. Copyright © 2009 John Wiley & Sons, Ltd.     

The characteristic‐based split (CBS) meshfree method for free surface flow problems in ALE formulation

A semi‐implicit characteristic‐based split (CBS) meshfree algorithm in the arbitrary Lagrangian Eulerian (ALE) framework is proposed for the numerical solution of incompressible free surface flow problem in the paper. The algorithm is the extension of general CBS method which was initially introduced in finite element framework, this is due to the fact that CBS method not only can enhance the stability, but also avoid LBB condition when equal order basis function is used to approximate velocity and pressure variables. Meanwhile, a simple way for node update and node speed calculation is developed which is used to capture the free surface exactly. The numerical solutions are compared with available analytical and numerical solutions, which shows that the proposed method has better ability to simulate the free surface incompressible flow problem. Copyright © 2009 John Wiley & Sons, Ltd.     

Simulation of two‐phase flow with moving immersed boundaries

A two‐dimensional multi‐phase model for immiscible binary fluid flow including moving immersed objects is presented. The fluid motion is described by the incompressible Navier–Stokes equation coupled with a phase‐field model based on van der Waals' free energy density and the Cahn–Hilliard equation. A new phase‐field boundary condition was implemented with minimization of the free energy in a direct way, to specifically improve the physical behavior of the contact line dynamics for moving immersed objects. Numerical stability and execution time were significantly improved by the use of the new boundary condition. Convergence toward the analytical solution was demonstrated for equilibrium contact angle, the Lucas–Washburn theory and Stefan's problem. The proposed model may be used for multi‐phase flow problems with moving boundaries of complex geometry, such as the penetration of fluid into a deformable, porous medium. Copyright © 2010 John Wiley & Sons, Ltd.     

Flow behavior and deposition study of pollen-shape carrier particles in an idealized inhalation path model

Pollen-shape (spiked sphere) hydroxyapatite (HA) particles for drug carrier application are studied. The particle shape and size effect on flow characteristics and deposition are assessed. The pollen-shape HA particles are synthesized to have comparable size as typical carrier particles with mean diameter of 30-50 m and effective density less than 0.3 g/cm 3 . The flow behaviors of HA and commonly used lactose (LA) carrier particles are characterized by the Carr's compressibility index (CI). The HA particle...     

Finite element analysis of thermally coupled nonlinear Darcy flows

We consider a coupled system describing nonlinear Darcy flows with temperature dependent viscosity and with viscous heating. We first establish existence, uniqueness, and regularity of the weak solution of the system of equations. Next, we decouple the coupled system by a fixed point algorithm and propose its finite element approximation. Finally, we present convergence analysis with an error estimate between continuous solution and its iterative finite element approximation.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Study of the quiescent and shear‐induced crystallization kinetics of intercalated PTT/MMT nanocomposites

An intercalated nanocomposite made of montmorillonite nanoclay, MMT, and poly(trimethylene terephthalate), PTT, was produced by twin screw extrusion and characterized by wide angle X‐ray diffraction, WAXD, and transmission electron microscopy, TEM. The quiescent isothermal and non‐isothermal and the flow‐induced crystallization of the nanocomposite were studied by differential scanning calorimetry, DSC, polarized light optical microscopy, PLOM, and rheometry. The quiescent results showed that the nanoclay acted as an efficient nucleating agent for the PTT, which result in an anticipation of the transition temperature between regimes II and III of crystallization. The fold interfacial free energy, σ_e, of the PTT in the nanocomposite during regime III was lower than in the pure state; that is, the pure PTT developed spherulites, whereas in the nanocomposite it produced a paracrystalline morphology. Under shear rate, the total times for crystallization in the nanocomposite were higher than in the pure PTT. In flow‐induced crystallization, a fibrillar nucleus must be formed as a result of chain orientation. In the nanocomposite, chain orientation only occurred after the percolated structure was broken. Therefore, the formation of a fibrillar nucleus in the nanocomposite took more time, which increased the total crystallization time. Inc. J Polym Sci Part B: Polym Phys 48: 113–127, 2010     

Averaging the pressure and flow rate of the carrier gas in a gas chromatographic column

Summary A systematic derivation of corresponding equations shows that averaging the pressure and the flow rate of the mobile phase in a gas chromatographic column over the column length and over the time that an unretained component resides in the column, requires the use of three different compressibility correction factors,j ₂ ¹ ,j ₃ ² , andj ₄ ³ . When multiplied by the adjusted retention volume,V _R-V_M, the Martin and James mobile phase compressibility correction factorj ₃ ² , only, produces the value of specific retention volume,V _g ^T , which is connected unambiguously with the thermodynamic phase distribution coefficient,K, of the sorbate.     

Sources of Error in Sorption and Density Measurements

In sorption measurements, volumetric or gravimetric procedures are commonly used to determine the amount adsorbed. At low pressures, thermomolecular flow and pressure differences according to Knudsen's law disturb measurements. In volumetry, calibration of the dead space is required; in gravimetry, the influence of buoyancy has to be taken into account. In both cases, adsorption of the calibrating gas, usually helium, may disturb the measurements [1]. From the calibration measurements, the density of the sample can in principle be calculated. However, it has been observed in many experiments that its value depends on the calibrating gas. This revised version was published online in July 2006 with corrections to the Cover Date.     

A ‘tree’ for generation and identification of the colour symmetry point groups

A flow chart (inverted ‘tree’) for generating and identifying the 58 magnetic and 18 polychromatic point groups using a classification for the 32 generating crystallographic point groups is suggested. The idea of colour generator is explored for generating the colour symmetry point groups. The advantages in presenting the identification of colour groups through a tree are discussed.