A Numerical Method of Moments for Solute Transport in Nonstationary Flow Fields

A Lagrangian perturbation approach has been applied to develop the method of moments for predicting mean and variance of solute flux through a three-dimensional nonstationary flow field. The flow nonstationarity may stem from medium nonstationarity, finite domain boundaries, and/or fluid pumping and injecting. The solute flux is described as a space–time process where time refers to the solute flux breakthrough and space refers to the transverse displacement distribution at the control plane. The analytically derived moment equations for solute transport in a nonstationary flow field are too complicated to solve analytically, a numerical finite difference method is implemented to obtain the solutions. This approach combines the stochastic model with the flexibility of the numerical method to boundary and initial conditions. This method is also compared with the numerical Monte Carlo method. The calculation results indicate the two methods match very well when the variance of log-conductivity is small, but the method of moment is more efficient in computation.     

Chemically induced swelling of hydrogels

We consider a continuum model for chemically induced volume transitions in hydrogels. Consistent with experimental observations, the model allows for a sharp interface separating swelled and collapsed phases of the underlying polymer network. The polymer chains are treated as a solute with an associated diffusion potential and their concentration is assumed to be discontinuous across the interface. In addition to the standard bulk and interfacial equations imposing force balance and solute balance, the model involves a supplemental interfacial equation imposing configurational force balance. We present a hybrid eXtended-Finite-Element/Level-Set Method for obtaining approximate solutions to the governing equations of the model. As an application, we consider the swelling of a spherical specimen whose boundary is traction-free and is in contact with a reservoir of uniform chemical potential. Our numerical results exhibit good qualitative comparison with experimental observations and predict characteristic swelling times that are proportional to the square of the specimen radius. Our results also suggest several possible synthetic pathways that might be pursued to engineer hydrogels with optimal response times.     

Analysis of flow-structure coupling in a mechanical model of the vocal folds and the subglottal system

An analysis is made of the nonlinear interactions between flow in the subglottal vocal tract and glottis, sound waves in the subglottal system and a mechanical model of the vocal folds. The mean flow through the system is produced by a nominally steady contraction of the lungs, and mechanical experiments frequently involve a ‘lung cavity’ coupled to an experimental subglottal tube of arbitrary or ill-defined effective length L, on the basis that the actual value of L has little or no influence on excitation of the vocal folds. A simple, self-exciting single-mass mathematical model of the vocal folds is used to investigate the sound generated within the subglottal domain and the unsteady volume flux from the glottis for experiments where it is required to suppress feedback of sound from the supraglottal vocal tract. In experiments where the assumed absorption of sound within the sponge-like interior of the lungs is small, the influence of changes in L can be very significant: when the subglottal tube behaves as an open-ended resonator (when L is as large as half the acoustic wavelength) there is predicted to be a mild increase in volume flux magnitude and a small change in waveform. However, the strong appearance of second harmonics of the acoustic field is predicted at intermediate lengths, when L is roughly one quarter of the acoustic wavelength. In cases of large lung damping, however, only modest changes in the volume flux are predicted to occur with variations in L.     

爆炸冲击波对肺损伤的数值模拟

采用数值模拟方法,分析了人体胸部在自由空间爆炸场中受冲击波作用的力学过程。利用Mimics 软件对CT图像进行处理,建立人体胸部三维模型。根据人体胸部各生物组织的特性,选择合理的材料模 型和参数,并利用LS-DYNA有限元程序中流固耦合方法,计算分析冲击波作用于人体胸部肺的受力过程。 通过计算获得冲击波入射超压峰值和正压持续时间,参照Bowen损伤曲线评估出肺处于Dc 与D1损伤状态 之间。观察肺部应力变化过程,获得肺部表面的正应力变化规律和损伤最严重的区域。分析剪切应力变化规 律,了解肺受切应力作用损伤的可能性。     

Reactive Solute Transport in a Nonstationary,Fractured Porous Medium: A Dual-Porosity Approach

A numerical method of moment is developed for solute flux through a nonstationary, fractured porous medium. Solute flux is described as a space-time process where time refers to the solute flux breakthrough and space refers to the transverse displacement distribution at a control plane. A first-order mass diffusion model is applied to describe interregional mass diffusion between fracture (advection) and matrix (nonadvection) regions. The chemical is under linear equilibrium sorption in both fracture and matrix regions. Hydraulic conductivity in the fracture region is assumed to be a spatial random variable. In this study, the general framework of Zhang et al.(2000) is adopted for solute flux in a nonstationary flow field. A time retention function related to physical and chemical sorption in the dual-porosity medium is developed and coupled with solute advection along random trajectories. The mean and variance of total solute flux are expressed in terms of the probability density function of the parcel travel time and transverse displacement. The influences of various factors on solute transport are investigated. These factors include the interregional mass diffusion rate between fracture and matrix regions, chemical sorption coefficients in both regions, water contents in both regions, and location of the solute source. In comparison with solute transport in a one-region medium, breakthrough curves of the mean and variance of the total solute flux in a two-region medium have lower peaks and longer tails. As compared with the classical stochastic studies on solute transport in fractured media, the numerical method of moment provides an approach for applying the stochastic method to study solute transport in more complicated fractured media.     

The numerical analysis of water and solute movement in scale heterogeneous profiles

A computer based numerical method is presented for the analysis of water and solute movement in unsaturated heterogeneous porous materials. Such a method is necessary since, for those field studies where solute movement is of concern, the soil profiles under consideration are invariably heterogeneous. The numerical analysis is based on a general one-dimensional finite difference soil water flow model which includes a numerical technique combining the concepts of scale heterogeneity with an interpolative soil water hysteresis model. An explicit finite difference solute movement subroutine is incorporated into the unsaturated flow model to describe the transport of nonreactive solutes. A velocity dependent longitudinal dispersion coefficient is used in the solution of the hydrodynamic dispersion equation. The resulting hysteretic scale heterogeneous solute movement model permits the study of solute dynamics during infiltrating and redistribution in realistically complex spatially varying soil profiles. Results are presented for the leaching of both coarse grading to fine and fine grading to coarse sand profiles. Both vertical and horizontal profiles are studied using either a constant flux or a constant concentration input boundary condition. The four cases studied demonstrate the versatility of the numerical method and emphasise the substantial differences in transport behavior that can arise between heterogeneous and homogeneous profiles.Now with BHP Petroleum Pty. Ltd., GPO Box 1911R, Melbourne, Vic. 3001, Australia.     

铝合金板材塑性性能的研究

铝合金在汽车工业中的广泛应用对于降低汽车重量、减少燃油消耗和汽车尾气的排放量具有十分重要的意义，但其室温塑性成形性能却受到了锯齿形屈服行为的影响，从而制约了铝合金进一步的推广应用。本文基于合金材料塑性变形过程中位错和溶质原子间相互作用的分析，建立了一个可用于描述锯齿形屈服现象的唯象本构模型。该模型将溶质原子对位错运动的钉扎效应和位错挣脱后的脱钉效应置于一个统一的框架内进行考虑，而这两个效应的相互竞争将决定材料宏观变形行为的发展演化。基于该模型的数值模拟结果和实验测试结果取得了良好的一致性，从而验证了理论和模型的有效性。     

Sorption of inorganic nanoparticles in woven cellulose fabrics

Titanium dioxide was deposited from aqueous suspension onto cellulosic surfaces.Titania was sourced from Degussa (P25TM,70:30 anatase:rutile).Dry uptake of particles was shown to be rapid and dominant with one-third of the deposition occurring in less than 30 s and over one-half in the first minute.Isotherms were recorded to compare the rate of titanium deposition on dry and pre-wetted cotton.In the dry case uptake reached a maximum in 30 min whereas in the pre-wetted case the uptake was seen to continue beyond 180 min.A broad trend of higher deposition occurring at lower pH was seen,corresponding to the region where surface charges were opposite and thus attractive.Dry pickup was less significant at high pH.The response to varying ionic strength was complex and was attributed to the combined effect of charge screening,particle aggregation and consequent particle entrapment or occlusion.Titania deposition into the interstices of woven cotton sheets resulted in the formation of inorganic,nanoparticulate skeletons which could be isolated by controlled combustion of the cellulose and thus cotton was suggested to have potential for the templated synthesis of high surface area semiconductor materials.     

On Recent Progress in Modelling and Simulations of Multi-scale Transfer of Mass,Momentum and Particles in Bio-medical Applications

We present a short overview of some of our most recent work that combines the mathematical modeling, advanced computer simulations and state-of-the-art experimental techniques of physical transport phenomena in various bio-medical applications. In the first example, we tackle predictions of complex blood flow patterns in the patient-specific vascular system (carotid artery bifurcation) and transfer of the so-called “bad” cholesterol (low-density lipoprotein, LDL) within the multi-layered artery wall. This two-way coupling between the blood flow and corresponding mass transfer of LDL within the artery wall is essential for predictions of regions where atherosclerosis can develop. It is demonstrated that a recently developed mathematical model, which takes into account the complex multi-layer arterial-wall structure, produced LDL profiles within the artery wall in good agreement with in-vivo experiments in rabbits, and it can be used for predictions of locations where the initial stage of development of atherosclerosis may take place. The second example includes a combination of pulsating blood flow and medical drug delivery and deposition controlled by external magnetic field gradients in the patient specific carotid artery bifurcation. The results of numerical simulations are compared with own PIV (Particle Image Velocimetry) and MRI (Magnetic Resonance Imaging) in the PDMS (silicon-based organic polymer) phantom. A very good agreement between simulations and experiments is obtained for different stages of the pulsating cycle. Application of the magnetic drug targeting resulted in an increase of up to ten fold in the efficiency of local deposition of the medical drug at desired locations. Finally, the LES (Large Eddy Simulation) of the aerosol distribution within the human respiratory system that includes up to eight bronchial generations is performed. A very good agreement between simulations and MRV (Magnetic Resonance Velocimetry) measurements is obtained. Magnetic steering of aerosols towards the left or right part of lungs proved to be possible, which can open new strategies for medical treatment of respiratory diseases.     

A lattice Boltzmann method for solute transport

A lattice Boltzmann method is developed for solute transport. Proper expressions for the local equilibrium distribution functions enable the method to be formulated on rectangular lattice with the same simple procedure as that on a square lattice. This provides an additional advantage over a lattice Boltzmann method on a square lattice for problems characterized by dominant phenomenon in one direction and relatively weak in another such as solute transport in shear flow over a narrow channel, where the problems can efficiently be approached with fine and coarse meshes, respectively, resulting in more efficient algorithm. The stability conditions are also described. The proposed method on a square lattice is naturally recovered when a square lattice is used. It is verified by solving four tests and compared with the analytical/exact solutions. They are in good agreement, demonstrating that the method is simple, accurate and robust for solute transport. Copyright © 2008 John Wiley & Sons, Ltd.     

A hierarchical model for rate-dependent polycrystals

A hierarchical model of a polycrystalline aggregate of rigid viscoplastic grains is formulated, and a robust and efficient computational algorithm for its solution is proposed. The polycrystalline aggregate is modeled as a binary tree. The leaves of the binary tree represent grains, and higher tree nodes represent increasingly larger sub-aggregates of grains. The root of the tree represents the entire polycrystalline aggregate. Velocity and traction continuity are enforced across the interface between the children of each non-leaf node in the binary tree. The hierarchical model explicitly models intergranular interactions but is nevertheless comparable in computational effort to the mean field models of polycrystal plasticity. Simulations of tensile, compressive, torsional, and plane strain deformation of copper lead to predictions in good agreement with experiments, and highlight the interconnection between grain deformations and intergranular constraints. It is inferred from the results that a hybrid mean field/hierarchical model represents a computationally efficient methodology to simulate polycrystal deformation while accounting for intergranular interactions.     

Inhaled gas distribution in the lungs

A new mathematical method is considered for determination of the distribution of specific respiratory volumes from the experimental curves of nitrogen washing from the lungs upon oxygen respiration. On the basis of the specific respiratory volume distribution obtained, the distribution of inhaled gas in the lungs may be evaluated. The method developed here is a variant of an approximate reduction of a Laplace transform. Accuracy of the method was verified with mathematical lung models.     

Microstructure morphology transitions at mesoscopic epitaxial surfaces

Spiral surface growth is well understood in the limit where motion of the spiral ridge is controlled by the local supersaturation of adatoms in its surrounding. In liquid epitaxial growth, however, spirals can form governed by both, transport of heat as well as solute. We propose for the first time a two-scale model of epitaxial growth which takes into account all of these transport processes. This new model assumes a separation of length scales for the transport of heat compared to that of the solutal field. It allows for the first time numerical simulations of extended surface regions by at the same time taking into account microstructure evolution and microstructure interaction. We apply this model successfully to extend the scaling relation for the step spacing given by the BCF theory [Phil. Trans. R. Soc. London, Ser. A 243, 299 (1951)] to microstructure evolution governed by heat and solute diffusion. Further applications to understand the mechanisms and consequences of spiral interaction at epitaxial surfaces, in particular the resulting morphology transitions, are discussed.     

A Solute Transport in Stratified Media

Two-dimensional and steady solute transport in a stratified porous formation is analysed under assumption that the effect of pore-scale dispersion is negligible. The longitudinal dispersion produced as a result of the vertical variation of hydraulic conductivity is analysed by averaging the variability of a solute flux concentration and conductivity. The evolution of the solute flux concentration is expressed with respect to the correlated variable, that is the travel (arrival) time at a fixed location and the averaging procedure is constructed to satisfy the boundary condition where the inlet concentration is a known function of time. In such a statement, a velocity-averaged solute flux concentration is described by a conventional dispersion model (CDM) with a dispersion coefficient which is a function of the arrival time. It is demonstrated that such CDM satisfies the assumption that hydraulic conductivity of the layers is gamma distributed with the parameter of distribution which is chosen to represent a reasonable value of the field scale solute dispersion. The overall behaviour of the model is illustrated by several examples of two-dimensional mass transport.     

Deposition of non-spherical microparticles in the human upper respiratory tract

We investigated the deposition pattern of microparticles with different particle diameters, shape factors, and initial flow conditions in a realistic human upper respiratory tract model. We identified a close relationship between the deposition fraction and the particle shape factor. The deposition fraction of the particles decreased sharply with increasing particle shape factor because of the decreasing drag force. We also found that the deposition varied at different positions in the upper respiratory tract. At low shape factors, the highest fraction of particles deposited at the mouth and pharynx. However, with increasing shape factor, the deposition fraction in the trachea and lungs increased. Moreover, for a given shape factor, larger particles deposited at the mouth and pharynx, which indicates that the deposition fraction of microparticles in the human upper respiratory tract is affected first and foremost by particle inertia as well as by the drag force.     

A DEPTH-INTEGRATED 2D COASTAL AND ESTUARINE MODEL WITH CONFORMAL BOUNDARY-FITTED MESH GENERATION

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications.     

Exact Averaging of Stochastic Equations for Transport in Random Velocity Field

We present new examples of exactly averaged multi-dimensional equation of transport of a conservative solute in a time-dependent random flow velocity field. The functional approach and a technique for decoupling the correlations are used. In general, the averaged equation is non-local. We study the special cases where the averaged equation can be localized and reduced to a differential equation of finite-order, where the problem of evolution of the initial plume (Cauchy problem) can be solved exactly. We present in detail the results of the analyses of two cases of exactly averaged problems for Gaussian and telegraph random velocity with an identical exponential correlation function, which are informative and convenient models for continuous and discontinuous random functions. The problems in which the field has sources of solute and boundaries are also examined. We study the behavior of different initial plumes for all times (evolutions and convergence) and show the manner in which they approach the same asymptotic limit for two stochastic distributions of flow-velocity. A comparison between exact solutions and solutions derived by the method of perturbation is also discussed.     

多孔颗粒固定床层中颗粒内部溶质大分子受力的分析

利用以Brinkman方程为基础的有效介质方法和一般的点阵模型,研究固定床层中多孔颗粒内部溶质大分子的传递,在考虑颗粒内部空隙度和整个床层空隙度双重影响下,得到球形溶质大分子在多孔介质内部的受力公式,进而研究其在多孔颗粒固定床层中的传递现象。     

An inverse hyper-spherical harmonics-based formulation for reconstructing 3D volumetric lung deformations

A method to estimate the deformation operator for the 3D volumetric lung dynamics of human subjects is described in this paper. For known values of air flow and volumetric displacement, the deformation operator and subsequently the elastic properties of the lung are estimated in terms of a Green's function. A Hyper-Spherical Harmonic (HSH) transformation is employed to compute the deformation operator. The hyper-spherical coordinate transformation method discussed in this paper facilitates accounting for the heterogeneity of the deformation operator using a finite number of frequency coefficients. Spirometry measurements are used to provide values for the airflow inside the lung. Using a 3D optical flow-based method, the 3D volumetric displacement of the left and right lungs, which represents the local anatomy and deformation of a human subject, was estimated from 4D-CT dataset. Results from an implementation of the method show the estimation of the deformation operator for the left and right lungs of a human subject with non-small cell lung cancer. Validation of the proposed method shows that we can estimate the Young's modulus of each voxel within a 2% error level.