Numerical investigation of plant tissue porosity and its influence on cellular level shrinkage during drying

Dried plant food products are increasing in demand in the consumer market, leading to continuing research to develop better products and processing techniques. Plant materials are porous structures, which undergo large deformations during drying. For any given food material, porosity and other cellular parameters have a direct influence on the level of shrinkage and deformation characteristics during drying, which involve complex mechanisms. In order to better understand such mechanisms and their interrelationships, numerical modelling can be used as a tool. In contrast to conventional grid-based modelling techniques, it is considered that meshfree methods may have a higher potential for modelling large deformations of multiphase problem domains. This work uses a meshfree based microscale plant tissue drying model, which was recently developed by the authors. Here, the effects of porosity have been newly accounted for in the model with the objective of studying porosity development during drying and its influence on shrinkage at the cellular level. For simplicity, only open pores are modelled and in order to investigate the influence of different cellular parameters, both apple and grape tissues were used in the study. The simulation results indicated that the porosity negatively influences shrinkage during drying and the porosity decreases as the moisture content reduces (when open pores are considered). Also, there is a clear difference in the deformations of cells, tissues and pores, which is mainly influenced by the cell wall contraction effects during drying.

Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy

This article aims to fill in the gap of the second-order accurate schemes for the time-fractional subdiffusion equation with unconditional stability. Two fully discrete schemes are first proposed for the time-fractional subdiffusion equation with space discretized by finite element and time discretized by the fractional linear multistep methods. These two methods are unconditionally stable with maximum global convergence order of $O(\tau+h^{r+1})$ in the $L^2$ norm, where $\tau$ and $h$ are the step sizes in time and space, respectively, and $r$ is the degree of the piecewise polynomial space. The average convergence rates for the two methods in time are also investigated, which shows that the average convergence rates of the two methods are $O(\tau^{1.5}+h^{r+1})$. Furthermore, two improved algorithms are constrcted, they are also unconditionally stable and convergent of order $O(\tau^2+h^{r+1})$. Numerical examples are provided to verify the theoretical analysis. The comparisons between the present algorithms and the existing ones are included, which show that our numerical algorithms exhibit better performances than the known ones.

Maximum principle and numerical method for the multi-term time–space Riesz–Caputo fractional differential equations

The maximum principle for the space and time–space fractional partial differential equations is still an open problem. In this paper, we consider a multi-term time–space Riesz–Caputo fractional differential equations over an open bounded domain. A maximum principle for the equation is proved. The uniqueness and continuous dependence of the solution are derived. Using a fractional predictor–corrector method combining the L1 and L2 discrete schemes, we present a numerical method for the specified equation. Two examples are given to illustrate the obtained results.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Numerical simulation of anomalous infiltration in porous media

Nonlinear time-fractional diffusion equations have been used to describe the liquid infiltration for both subdiffusion and superdiffusion in porous media. In this paper, some problems of anomalous infiltration with a variable-order timefractional derivative in porous media are considered. The time-fractional Boussinesq equation is also considered. Two computationally efficient implicit numerical schemes for the diffusion and wave-diffusion equations are proposed. Numerical examples are provided to show that the numerical methods are computationally efficient.

Experimental and numerical investigation of strain-rate dependent mechanical properties of single living cells

The objective of this project is to investigate the strain-rate dependent mechanical behaviour of single living cells using both experimental and numerical techniques. The results revealed that living cells behave as porohyperlastic materials and that both solid and fluid phases within the cells play important roles in their mechanical responses. The research reported in this thesis provides a better understanding of the mechanisms underlying the cellular responses to external mechanical loadings and of the process of mechanical signal transduction in living cells. It would help us to enhance knowledge of and insight into the role of mechanical forces in supporting tissue regeneration or degeneration.

Numerical investigation of case hardening of plant tissue during dying and its influence on the cellular level shrinkage

Dried plant food materials are one of the major contributors to the global food industry. Widening the fundamental understanding on different mechanisms of food material alterations during drying assists the development of novel dried food products and processing techniques. In this regard, case hardening is an important phenomenon, commonly observed during the drying processes of plant food materials, which significantly influences the product quality and process performance. In this work, a recent meshfree-based numerical model of the authors is further improved and used to simulate the influence of case hardening on shrinkage characteristics of plant tissues during drying. In order to model fluid and wall mechanisms in each cell, Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM) are used. The model is fundamentally more capable of simulating large deformation of multiphase materials, when compared with conventional grid-based modelling techniques such as Finite Element Methods (FEM) or Finite Difference Methods (FDM). Case hardening is implemented by maintaining distinct moisture levels in the different cell layers of a given tissue. In order to compare and investigate different factors influencing tissue deformations under case hardening, four different plant tissue varieties (apple, potato, carrot and grape) are studied. The simulation results indicate that the inner cells of any given tissue undergo limited shrinkage and cell wall wrinkling compared to the case hardened outer cell layers of the tissues. When comparing unique deformation characteristics of the different tissues, irrespective of the normalised moisture content, the cell size, cell fluid turgor pressure and cell wall characteristics influence the tissue response to case hardening.

Numerical simulation of railway track supporting system using finite-infinite and thin layer elements under impulsive loads

The present study deals with two dimensional, numerical simulation of railway track supporting system subjected to dynamic excitation force. Under plane strain condition, the coupled finite-infinite elements to represent the near and far field stress distribution and thin layer interface element was employed to model the interfacial behavior between sleepers and ballast. To account for the relative debonding, slipping and crushing that could take place in the contact area between the sleepers and ballast, modified Mohr-Coulomb criterion was adopted. Furthermore an attempt has been made to consider the elasto-plastic material non-linearity of the railway track supporting media by employing different constitutive models to represent steel, concrete and supporting materials. Based on the proposed physical and constitutive modeling a code has been developed for dynamic loads. The applicability of the developed F.E code has been demonstrated by analyzing a real railway supporting structure.

The synthesis, characterization, X-ray structure and magnetism of dinuclear-based bis[μ-(1,1,3,3-tetracyano-2-ethoxypropenido-κ2N,N′) (1,1,3,3-tetracyano-2-ethoxypropenido-κN)(2,2′-bipyridine)copper(II)] organized in alternating chains via semi-coordinating Cu–N distances

The monoanionic ligand 1,1,3,3 tetracyano-2 ethoxypropenide (tcnoet) is reported with its Cu(II)–bpy complex of formula [Cu2(µ-tcnoet)2(tcnoet)2(bpy)2]. The structure has been determined using X-ray diffraction and features an alternating chain with bridging tcnoet ligands. One ligand acts as a bidentate, dinucleating ligand with one short Cu–N and one medium Cu–N bond, whereas the other tcnoet is largely monodentate, albeit with a very weak interdimer Cu–N bond. Despite the arrangement in dinuclear units, further arranged into linear chains through the non-bridging tcnoet ligand, the compound shows no significant magnetic exchange, as deduced from magnetic susceptibility down to 4 K. Ligand-field, IR and EPR spectra in the solid state and in frozen solution are reported and are consistent with the overall structure.

Numerical modeling of railway track supporting system using finite–infinite and thin layer elements

The present contribution deals with the numerical modelling of railway track-supporting systems-using coupled finite-infinite elements-to represent the near and distant field stress distribution, and also employing a thin layer interface element to account for the interfacial behaviour between sleepers and ballast. To simulate the relative debonding, slipping and crushing at the contact area between sleepers and ballast, a modified Mohr-Coulomb criterion was adopted. Further more an attempt was made to consider the elasto plastic materials’ non-linearity of the railway track supporting media by employing different constitutive models to represent steel, concrete and other supporting materials. It is seen that during an incremental-iterative mode of load application, the yielding initially started from the edge of the sleepers and then flowed vertically downwards and spread towards the centre of the railway supporting system.

Characterization of the sulphate mineral coquimbite, a secondary iron sulphate from Javier Ortega mine, Lucanas Province, Peru – Using infrared, Raman spectroscopy and thermogravimetry

The mineral coquimbite has been analysed using a range of techniques including SEM with EDX, thermal analytical techniques and Raman and infrared spectroscopy. The mineral originated from the Javier Ortega mine, Lucanas Province, Peru. The chemical formula was determined as ðFe3þ 1:37; Al0:63ÞP2:00ðSO4Þ3 9H2O. Thermal analysis showed a total mass loss of 73.4% on heating to 1000 C. A mass loss of 30.43% at 641.4 C is attributed to the loss of SO3. Observed Raman and infrared bands were assigned to the stretching and bending vibrations of sulphate tetrahedra, aluminium oxide/hydroxide octahedra, water molecules and hydroxyl ions. The Raman spectrum shows well resolved bands at 2994, 3176, 3327, 3422 and 3580 cm 1 attributed to water stretching vibrations. Vibrational spectroscopy combined with thermal analysis provides insight into the structure of coquimbite.

Vibrational spectroscopic characterization of the sulphate-carbonate mineral burkeite: Implications for evaporites

Burkeite formation is important in saline evaporites and in pipe scales. Burkeite is an anhydrous sulphate-carbonate with an apparent variable anion ratio. Such a formula with two oxyanions lends itself to vibrational spectroscopy. Two symmetric sulphate stretching modes are observed, indicating at least at the molecular level the nonequivalence of the sulphate ions in the burkeite structure. The strong Raman band at 1065 cm−1 is assigned to the carbonate symmetric stretching vibration. The series of Raman bands at 622, 635, 645, and 704 cm−1 are assigned to the ν4 sulphate bending modes. The observation of multiple bands supports the concept of a reduction in symmetry of the sulphate anion from T d to C 3v or even C 2v.

Vibrational spectroscopic characterization of the arsenate mineral barahonaite: Implications for the molecular structure

The mineral barahonaite is in all probability a member of the smolianinovite group. The mineral is an arsenate mineral formed as a secondary mineral in the oxidized zone of sulphide deposits. We have studied the barahonaite mineral using a combination of Raman and infrared spectroscopy. The mineral is characterized by a series of Raman bands at 863 cm−1 with low wavenumber shoulders at 802 and 828 cm−1. These bands are assigned to the arsenate and hydrogen arsenate stretching vibrations. The infrared spectrum shows a broad spectral profile. Two Raman bands at 506 and 529 cm−1 are assigned to the triply degenerate arsenate bending vibration (F 2, ν4), and the Raman bands at 325, 360, and 399 cm−1 are attributed to the arsenate ν2 bending vibration. Raman and infrared bands in the 2500–3800 cm−1 spectral range are assigned to water and hydroxyl stretching vibrations. The application of Raman spectroscopy to study the structure of barahonaite is better than infrared spectroscopy, probably because of the much higher spatial resolution.

Quantitative characterization of kaolinite dispersibility in styrene–butadiene rubber composites by fractal dimension

A fractal method was introduced to quantitatively characterize the dispersibility of modified kaolinite (MK) and precipitated silica (PS) in styrene–butadiene rubber (SBR) matrix based on the lower magnification transmission electron microscopic images. The fractal dimension (FD) is greater, and the dispersion is worse. The fractal results showed that the dispersibility of MK in the latex blending sample is better than that in the mill blending samples. With the increase of kaolinite content, the FD increases from 1.713 to 1.800, and the dispersibility of kaolinite gradually decreases. There is a negative correlation between the dispersibility and loading content. With the decrease of MK and increase of PS, the FD significantly decreases from 1.735 to 1.496 and the dipersibility of kaolinite remarkably increases. The hybridization can improve the dispersibility of fillers in polymer matrix. The FD can be used to quantitatively characterize the aggregation and dispersion of kaolinite sheets in rubber matrix.

Structure evolution characterization of Anyang anthracites via H2O2 oxidization and HF acidification

The structural characteristics of the raw coal (AY), the H2O2 oxidized coals (AY–H2O2) and the HF acidized AY–H2O2 (AY–H2O2–HF) were investigated by SEM, X-ray diffraction, Raman and FTIR spectroscopy. The results indicate that the derivative coals show an obvious increase in the aromaticity, crystalline carbon content and hydroxyl content, especially the AY–H2O2–HF. The stacking layer number of crystalline carbon decreases and the aspect ratio (La/Lc) remarkably increases for AY–H2O2 and AY–H2O2–HF. The crystalline layers become much thinner. The particle size of AY–H2O2–HF in width significantly decreases from 1 μm to less than 100 nm. The combination of H2O2 oxidization and HF acidification is effective to reduce the size of the aromatic layers and to increase the reactivity of derivative coals. The process can help us obtain the superfine crystalline carbon materials like graphite structure.