Direct solution of Navier–Stokes equations by radial basis functions

The pressure–velocity formulation of the Navier–Stokes (N–S) equation is solved using the radial basis functions (RBF) collocation method. The non-linear collocated equations are solved using the Levenberg–Marquardt method. The primary novelty of this approach is that the N–S equation is solved directly, instead of using an iterative algorithm for the primitive variables. Two flow situations are considered: Couette flow with and without pressure gradient, and 2D laminar flow in a duct with and without flow obstruction. The approach is validated by comparing the Couette flow results with the analytical solution and the 2D results with those obtained using the well-validated CFD-ACE™ commercial package.     

Patient-specific model of lung deformation using spatially dependent constitutive parameters

Breathing-induced spatially dependent lung deformation is predicted using patient-specific elastic properties with the contact–impact analysis model. The lung geometry is derived from 4D CT scan data of real patients. The spatially varying Young’s modulus for the patient is obtained from a previous study that used inverse deformation of the lung. The compact–impact analysis is implemented using the finite element method. The predicted lung deformation is compared with the results based on linear elasticity. The results are consistent with physiology, indicating large deformations near the diaphragm and smaller values at remote locations on the lobe. The effect of non-linearity of elastic property is most significant at the remote locations where the diaphragm-induced deformation is significantly attenuated.     

Mathematical modelling of tongue deformation during swallow in patients with head and neck cancer

ABSTRACT

Cancer localized to the tongue is often characterized by increased stiffness in the affected region. This stiffness affects swallow in a manner that is difficult to quantify in patients. A biomechanical model was developed to simulate the spatio-temporal deformation of the tongue during the pharyngeal phase of swallow in patients with cancer of the tongue base. The model involves finite element analysis (FEA) of a three-dimensional (3D) model of the tongue reconstructed from magnetic resonance images (MRI). The tongue tissue is assumed to be hyper-elastic. In order to examine the effects of tissue change (increased stiffness) due to the presence of cancer localized to the tongue base, various sections of the 3D geometry are modified to exhibit different elastic properties. Three cases are considered, representing the normal tongue, a tongue with early-stage cancer, and tongue with late-stage cancer. Early- and late-stage cancers are differentiated by the degree of stiffness within the base of tongue tissue. Analysis of the model suggests that healthy tongue has a maximum deformation of 9.38 mm, whereas tongues having mild cancer and severe cancer have a maximum deformation of 8.65 and 6.17 mm, respectively. Biomechanical modelling is a useful tool to explain and estimate swallowing abnormalities associated with tongue cancer and post-treatment characteristics.     

Modeling of aerosol spray characteristics for synthesis of sensor thin film from solution

A model is developed of aerosol spray for synthesis of sensor film from solution. The synthesis technique considered involves atomization of a solution of mixed salts in methanol, spraying of solution droplets, droplet deposition on a heated substrate, evaporation and chemical reaction to produce mixed oxides, and subsequent film growth. The precise control of oxide nanoparticle size distribution and inter-particle spacing in the film is crucial to achieving high sensitivity. These in turn largely depend on the droplet characteristics prior to impingement on the substrate. This paper focuses on the development of a model to describe the atomization and spray processes prior to the film growth. Specifically, a mathematical model is developed utilizing computational fluid dynamics solution of the equations governing the transport of atomized droplets from the nozzle to the substrate in order to predict droplet characteristics in flight. The predictions include spatial distribution of droplet size and concentration, and the effect on these characteristics of swirling inlet flow at the spray nozzle.     

Numerical calculation of turbulent corner flows

Numerical predictions are presented of the hydrodynamic characteristics of developing and fully-developed turbulent flow in a square duct. The turbulent stresses in the plane of the cross-section, gradients of which cause the familiar secondary flows, are approximated by gradients in the axial mean velocity. Two distinct approximations are investigated, one of which specifies some of the model ‘constants’ as functions of the gradient of the length scale to account for wall effects. The stresses in the axial momentum equation are calculated from an eddy viscosity deduced from the K-W model of turbulence, K being the turbulence energy and W, a measure of the time-mean-square-vorticity fluctuations. The approximation incorporating wall effects generally performs better than the other when compared with fully-developed flow-data. This same approximation also compares favourably with data for developing flow and predictions based on K-? models in the literature.     

A hybrid rheological model for particulate suspension in zeolite crystal growth

A hybrid constitutive model is developed to represent the thixotropic behavior of particulate suspension during zeolite crystallization from solution. This model is valid over the complete solid fraction range typical for such a process. It employs two internal variables, agglomeration and contiguity, to describe the degree to which the gel particles form short- and long-range networks. The contiguity is used to weigh the effects of hydrodynamic to chain-like network deformation on the suspension viscosity. Heterogeneous nucleation and surface reaction-controlled crystal growth are assumed to describe the evolution of microstructure and solid fraction of gel and crystals. Such a model successfully captures the thixotropic behavior of zeolite particulate suspension by comparison of the predictions with a set of experimental data.