The Effect of surfactant on the drag and wall correction factor of a drop in a bounded medium

In the present article, the analytical solution for creeping motion of a drop/bubble characterized by insoluble surfactant is examined at the instant it passes the center of a spherical container filled with Newtonian fluid at low Reynolds number. The presence of surfactant characterizes the interfacial region by an axisymmetric interfacial tension gradient and coefficient of surface dilatational viscosity. Under the assumption of the small capillary number, the deformation of spherical phase interface is not taken into account. The computations not only yield information on drag force and wall correction factor, but also on interfacial velocity and flow field for different values of surface tension gradient and surface dilatational viscosity. In the limiting cases, the analytical solutions describing the drag force and wall correction factor for a drop in a bounded medium reduces to expressions previously stated by other authors in literature. The results reveal the strong influence of the surface dilatational viscosity and surface tension gradient on the motion of drop/bubble. Increasing the surface tension gradient and surface dilatational viscosity, results in linear variation of drag force. When the surface tension gradient increases, the drag force for unbounded medium increases more as compared to the bounded medium hence wall correction factor decreases with increase in surface tension gradient whereas it increases with increase in surface dilatational viscosity.

Evaluation of Three Lattice Boltzmann Models for Particulate Flows

A comparative study is conducted to evaluate three types of lattice Boltzmann equation (LBE) models for fluid flows with finite-sized particles, including the lattice Bhatnagar-Gross-Krook (BGK) model, the model proposed by Ladd [Ladd AJC, J. Fluid Mech., 271, 285-310 (1994); Ladd AJC, J. Fluid Mech., 271, 311-339 (1994)], and the multiple-relaxation-time (MRT) model. The sedimentation of a circular particle in a two-dimensional infinite channel under gravity is used as the first test problem. The numerical results of the three LBE schemes are compared with the theoretical results and existing data. It is found that all of the three LBE schemes yield reasonable results in general, although the BGK scheme and Ladd’s scheme give some deviations in some cases. Our results also show that the MRT scheme can achieve a better numerical stability than the other two schemes. Regarding the computational efficiency, it is found that the BGK scheme is the most superior one, while the other two schemes are nearly identical. We also observe that the MRT scheme can unequivocally reduce the viscosity dependence of the wall correction factor in the simulations, which reveals the superior robustness of the MRT scheme. The superiority of the MRT scheme over the other two schemes is also confirmed by the simulation of the sedimentation of an elliptical particle.

Evaluation of Wall Correction Factor of INER's Air-Kerma Primary Standard Chamber and Dose Variation by Source Displacement for HDR192Ir Brachytherapy

The aim of the present study was to estimate the wall effect of the self-made spherical graphite-walled cavity chamber with the Monte Carlo method for establishing the air-kerma primary standard of high-dose-rate (HDR)192Ir brachytherapy sources at the Institute of Nuclear Energy Research (INER, Taiwan). The Monte Carlo method established in this paper was also employed to respectively simulate wall correction factors of the192Ir air-kerma standard chambers used at the National Institute of Standards and Technology (NIST, USA) and the National Physical Laboratory (NPL, UK) for comparisons and verification. The chamber wall correction calculation results will be incorporated into INER's HDR192Ir primary standard in the future. For the brachytherapy treatment in the esophagus or in the bronchi, the position of the isotope may have displacement in the cavity. Thus the delivered dose would differ from the prescribed dose in the treatment plan. We also tried assessing dose distribution due to the position displacement of HDR192Ir brachytherapy source in a phantom with a central cavity by the Monte Carlo method. The calculated results could offer a clinical reference for the brachytherapy within the human organs with cavity.

Dynamic shape and wall correction factors of cylindrical particles falling vertically in a Newtonian liquid

Results of numerical calculations of dynamic shape and wall correction factors for the flow of a Newtonian fluid over a vertically oriented cylindrical particle in a cylindrical tube are reported. Mathematical model of the flow was solved using the finite element method by means of the COMSOL Multiphysics software. Dependences of the shape factor on the cylinder aspect ratio and of the wall correction factor, F W, on the ratio of the cylindrical particle diameter to the tube diameter, and on the aspect ratio were obtained. Numerical dependences were approximated by simple relationships suitable for dynamic shape and wall correction factors prediction.

Wall effects on terminal falling velocity of spherical particles moving in a Carreau model fluid

Experimental verification of our previous numerical simulation of wall effects on the terminal falling velocity of spherical particles moving slowly along the axis of a cylindrical vessel filled with a Carreau model fluid is presented. Dependences of the wall correction factor F W on the sphere to tube ratio d/D and on the dimensionless Carreau model parameters m, Λ, and η r were obtained using a finite element method. Calculated data of the wall correction factor were compared with the results of our new falling sphere experiments. The experiments were carried out in six types of cylindrical Perspex columns (16 mm, 21 mm, 26 mm, 34 mm, 40 mm, and 90 mm in diameter) filled with aqueous solutions of polymers exhibiting different degrees of shear thinning and elasticity. Seventeen types of spherical particles (1–8 mm in diameter) made of glass, ceramics, steel, lead, and tungsten carbide were used for the drop tests. Measurements of the liquid flow curves, primary normal stress differences, oscillatory, creep and recovery, stress relaxation, and stress growth tests were carried out on the rheometer Haake MARS (Thermo Scientific). A good agreement between numerically and experimentally obtained F W data was found.