Supercritical Antisolvent Process Applied to the Pharmaceutical Industry

Pharmaceutical preparations are the final product of a technological process that gives the drugs the characteristics appropriate for easy administration, proper dosage, and enhancement of the therapeutic efficacy. The design of pharmaceutical preparations in nanoparticulate form has emerged as a new strategy for drug delivery (Pasquali, Bettini, and Giordano, 2006 Pasquali , I. , R. Bettini , and F. Giordano . 2006 . Solid-state chemistry and particle engineering with supercritical fluids in pharmaceutics . Eur. J. Pharm. Sci. 27 : 299 – 310 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Particle size (PS) and particle size distribution (PSD) are critical parameters that determine the rate of dissolution of the drug in the biological fluids and, hence, have a significant effect on the bioavailability of those drugs that have poor solubility in water, for which the dissolution is the rate-limiting step in the absorption process (Perrut, Jung, and Leboeuf, 2005 Perrut , M. , J. Jung , and F. Leboeuf . 2005 . Enhancement of dissolution rate of poorly-soluble active ingredients by supercritical fluid processes: Part I: Micronization of neat particles . Int. J. Pharm. 288 : 3 – 10 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]; Van Nijlen et al., 2003 Van Nijlen , T., G. Van Den Mooter , R. Kinget , P. Augustijns , N. Blaton , and K. Brennan . 2003 . Improvement of the dissolution rate of artemisinin by means of supercritical fluid technology and solid dispersions . Int. J. Pharm. 254 : 173 – 181 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). Supercritical antisolvent (SAS) processes have been widely used to precipitate active pharmaceutical ingredients (APIs) (Chattopadhyay and Gupta, 2001 Chattopadhyay , P. , and R. B. Gupta . 2001 . Production of antibiotic nanoparticles using supercritical CO₂ as antisolvent with enhanced mass transfer . Ind. Eng. Chem. Res. 40 : 3530 – 3539 .[Crossref], [Web of Science ®] , [Google Scholar]; Rehman et al., 2001 Rehman , M. , B. Y. Shekunov , P. York , and P. Colthorpe . 2001 . Solubility and precipitation of nicotinic acid in supercritical carbon dioxide . J. Pharm. Sci. 90 : 1570 – 1582 .[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) with a high level of purity, suitable dimensional characteristics, narrow PSD, and spherical morphologies. The SAS process is based on the particular properties of the supercritical fluids (SCFs). These fluids have diffusivities two orders of magnitude larger than those of liquids, resulting in a faster mass transfer rate SCF properties (solvent power and selectivity) can be also adjusted continuously by altering the experimental conditions (temperature and pressure). As a consequence, SCFs can be removed from the process by a simple change from the supercritical to room conditions, which avoids difficult post-treatments of waste liquid streams. Carbon dioxide (CO₂) at supercritical conditions, among all possible SCFs, is largely used because of its relatively low critical temperature (31.1°C) and pressure (73.8 bar), low toxicity, and low cost. In this article, we show some results about processed antibiotics (ampicillin and amoxicillin), two of the world's most widely prescribed antibiotics, when they are dissolved in 1-methyl-2-pyrrolidone (NMP) and carbon dioxide is used as antisolvent.     

Designing an optimal water quality monitoring network for river systems using constrained discrete optimization via simulation

The problem of designing a water quality monitoring network for river systems is to find the optimal location of a finite number of monitoring devices that minimizes the expected detection time of a contaminant spill event while guaranteeing good detection reliability. When uncertainties in spill and rain events are considered, both the expected detection time and detection reliability need to be estimated by stochastic simulation. This problem is formulated as a stochastic discrete optimization via simulation (OvS) problem on the expected detection time with a stochastic constraint on detection reliability; and it is solved with an OvS algorithm combined with a recently proposed method called penalty function with memory (PFM). The performance of the algorithm is tested on the Altamaha River and compared with that of a genetic algorithm due to Telci, Nam, Guan and Aral (2009) Telci, I. T., K. Nam, J. Guan, and M.M. Aral, 2009. “Optimal Water Quality Monitoring Network Design for River Systems.” Journal of Environmental Management, 90 (3–4): 2987–2998. doi: 10.1016/j.jenvman.2009.04.011[Crossref], [PubMed], [Web of Science ®] , [Google Scholar].     

Interactions and Collisions of Bubbles in Thermocapillary Motion: A 3D Study

Two- and three-dimensional simulations (created using volume of fluid-fluent) concerning the rise and interactions of two/multiple thermocapillary bubbles arranged horizontally and perpendicular to a hot surface are investigated and presented in this paper. The results indicate that thermocapillary bubble agglomeration can occur in zero gravity. Furthermore, the temperature gradient and bubble diameter were found to have a major impact on the collision between bubbles. The results of Nas and Tryggvason (1993 Nas, S., and G. Tryggvason. 1993. Computational investigation of the thermal migration of bubbles and drops. 175 Fluid Mechanics Phenomena In Microgravity 71–83. [Google Scholar]) in their three-dimensional numerical study reported that no such collisions could occur in zero gravity and that bubbles repel each other due to the cold liquid carried between particles during migration. Their results contrast with both the present results and those recorded onboard the Chinese 22nd recoverable satellite experiment by Kang et al. (2008 Kang, Q., H. L. Cui, L. Hu, and L. Duan. 2008. On-board experimental study of bubble thermocapillary migration in a recoverable satellite. Microgravity Science And Technology 20:67–71.[Crossref], [Web of Science ®] , [Google Scholar]), who observed a total of 19 coalescences between the air bubbles injected in the direction of the temperature gradient of the stagnant heated liquid.     

Feasibility study to investigate caking in washing powder formulations using a Freeman FT4 powder rheometer

ABSTRACT

Because of legislation and environmental concerns, washing powder manufacturers have phased out phosphate builders in favor of substitutes such as sodium carbonate. This has meant that the new formulations have a greater tendency toward unwanted agglomeration (caking), based on moisture uptake and migration. This study examines the feasibility of using a Freeman FT4 powder rheometer to examine the effect of moisture migration, using the basic flow energy value to compare formulations of sodium carbonate content 27–37% and sodium sulfate content 10–20% by mass after 7 d exposure to 80% relative humidity at 20°C. The results showed that 31 and 33% sodium carbonate formulations were the most resistant to caking, with 27 and 37% being the most susceptible under the test conditions. Using the method of Brockbank et al. (2015 Brockbank, K., B. Armstrong, Y. Chandorkar, and T. Freeman. 2015. Understanding powder caking as a consequence of a range of mechanisms by means of powder rheometry. Particulate Science and Technology 33:102–08.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), the FT4 was also used to detect the presence of a hard crust; under the test conditions, no hard crust was found. However, the presence of soft caking was detected in the force–height profile, showing a less abrupt transition.     

Corrigendum of ‘A deterministic model for a repairable item inventory system with a finite repair rate’

The main purpose of this corrigendum is to indicate and rectify the same mistakes made by Schrady (1967 Schrady, D. A. 1967. “A Deterministic Inventory Model for Repairable Items.” Naval Research Logistics Quarterly 14: 391–398.[Crossref] , [Google Scholar]), Nahmias and Rivera (1979 Nahmias, S., and H. Rivera. 1979. “A Deterministic Model for a Repairable Item Inventory System with a Finite Repair Rate.” International Journal of Production Research 17: 215–221.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]), and Teunter (2004 Teunter, R. H. 2004. “Lot-Sizing for Inventory Systems with Product Recovery.” Computers and Industrial Engineering 46: 431–441.[Crossref], [Web of Science ®] , [Google Scholar]) in the course of solving their respective models in order that subsequent researchers will not follow the same. To this end, we derive the corresponding correct global-optimal formulae for the substitution-policy model (1,?n), with infinite or finite recovery (or called repair) rate, using differential calculus, as well as providing a closed-form expression to identify the optimal positive integral value of n recovery set-ups. In addition, we also rectify the formulae and solution procedure for numerically solving the constrained non-linear programme.     

Non-Newtonian Fluids in Spout-Fluid Beds: Mass Transfer Coefficient at Low Reynolds Numbers

Following on from the work of Anabtawi et al. (2003) Anabtawi, M. Z., Hilal, N. and Al Muftah, A. E. 2003. Volumetric mass transfer coefficient in non-Newtonian fluids in spouted-fluid beds: Part I. Chem. Eng. Technol., 26: 759–764.  [Google Scholar], this study examined how the volumetric liquid-phase mass transfer coefficient, k _L a, of oxygen in air in three-phase spout-fluid beds was affected by varying the system parameters of bed height, bed diameter, gas velocity, and liquid velocity. The liquid used was 0.1% CMC solution, displaying a pseudo-plastic rheology, with 1.75 mm glass spheres as packing. The values of the Sherwood number were lower than in previous studies (Anabtawi et al., 2003 Anabtawi, M. Z., Hilal, N. and Al Muftah, A. E. 2003. Volumetric mass transfer coefficient in non-Newtonian fluids in spouted-fluid beds: Part I. Chem. Eng. Technol., 26: 759–764.  [Google Scholar]), in the range 9,000–186,000. Gas velocity had a similar effect on k _L a as in a bubble column, with results also giving good agreement with previous work on two-phase and three-phase spouted bed systems. The correlation obtained for the effect of liquid velocity on k _L a compared well with that of Schumpe et al. (1989) Schumpe, A., Deckwer, W. and Nigam, K. D. P. 1989. Gas-liquid mass transfer in three- phase fluidized beds with viscous pseudoplastic liquids. Can. J. Chem. Eng., 67: 873–877. [Crossref] , [Google Scholar]. An increase in the height of packing increased k _L a to the power of 0.319, with an increase in column diameter also causing an increase in k _L a, which is in agreement with the results of Akita and Yoshida (1973) Akita, K. and Yoshida, F. 1973. Gas hold-up and volumetric mass transfer coefficient in bubble columns. Ind. Eng. Chem. Process Des. Dev., 12: 76–80. [Crossref] , [Google Scholar].     

Creeping Flow of Viscoelastic Fluid Through a Packed Bed: Effect of Particle Shape and Porosity

Experiments were conducted to elucidate the effect of particle shape and porosity on frictional pressure drop for the flow of viscoelastic fluids through a packed bed under creeping flow regime. Extensive pressure drop-flow rate data were generated using different packing materials such as cylinders of different aspect ratios, square plates, triangles, and spheres covering a wide range of sphericity, 0.546 ≤ φ ≤ 1. Effect of bed porosity has been determined using uniform-size spheres of different diameters (4.38 mm, 5.76 mm, and 6.78 mm), covering column to particle diameter ratio in the range of 13.96–21.62; while porosity varies in the range of 0.345–0.375. The experimental results indicate that the modified Ergun correlation, proposed by Sobti and Wanchoo (2014 Sobti, A., and R. K. Wanchoo. 2014. Creeping flow of viscoelastic fluid through a packed bed. Industrial & Engineering Chemistry Research 53:14508–14518.[Crossref], [Web of Science ®] , [Google Scholar]), can adequately be applied for the nonspherical particles, provided the equivalent volume mean diameter (D_eq) together with sphericity (φ) is used instead of the diameter of the spherical particle (D_p), i.e., D_p = D_eqφ. Further, an attempt has been made to suitably define a packing structure parameter, [(1 ? ?)/(? φ)], which could well capture the balancing effect between porosity and sphericity.     

Minimising makespan heuristics for scheduling a single batch machine processing machine with non-identical job sizes

In this paper, the problem of minimising maximum completion time on a single batch processing machine is studied. A batch processing is performed on a machine which can simultaneously process several jobs as a batch. The processing time of a batch is determined by the longest processing time of jobs in the batch. The batch processing machine problem is encountered in many manufacturing systems such as burn-in operations in the semiconductor industry and heat treatment operations in the metalworking industries. Heuristics are developed by iterative decomposition of a mixed integer programming model, modified from the successive knapsack problem by Ghazvini and Dupont (1998 Ghazvini, F.J. and Dupont, L. 1998. Minimising mean flow times criteria on a single batch processing machine with non-identical jobs sizes. International Journal of Production Economics, 55: 273–280. [Crossref], [Web of Science ®] , [Google Scholar], Minimising mean flow times criteria on a single batch processing machine with non-identical jobs sizes. International Journal of Production Economics 55: 273–280) and the waste of batch clustering algorithm by Chen, Du, and Huang (2011 Chen, H., Du, B. and Huang, G.Q. 2011. Scheduling a batch processing machine with non-identical job sizes: a clustering perspective. International Journal of Production Research, 49(19): 5755–5778. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], Scheduling a batch processing machine with non-identical job sizes: a clustering perspective. International Journal of Production Research 49 (19): 5755–5778). Experimental results show that the suggested heuristics produce high-quality solutions comparable to those of previous heuristics in a reasonable computation time.     

Lagrangian relaxation based heuristic for an integrated production and maintenance planning problem

In this paper, an approach is developed to solve the joint production planning and maintenance problem. Moreover, some propositions and mathematical properties were suggested and applied in the proposed heuristic to solve this integrated problem. It is based on Lagrangian relaxation (Fisher, M.L., 1981 Fisher, M.L. 1981. Lagrangian relaxation method for solving integer programming problem. Management Science, 27(1): 1–18. [Crossref], [Web of Science ®] , [Google Scholar]. Lagrangian relaxation method for solving integer programming problem. Management Science, 27 (1), 1–18) of the capacity constraints and sub-gradient optimisation. At every step of the sub-gradient method, a smoothing procedure is applied to the solution of the Lagrangian problem to ensure the feasibility of solution and to improve it. Computational experiments are carried out to show the results obtained by our approaches and are compared to those of a commercial solver.     

Comparative Assessment of Two Constitutive Models for Superelastic Shape-Memory Wires Against Experimental Measurements

Two constitutive models representative of two well-known modeling techniques for superelastic shape-memory wires are reviewed. The first model has been proposed by Kim and Aberayatne in the framework of finite thermo-elasticity with non-convex energy [1 S.-J. Kim and R. Abeyaratne, On the effect of the heat generated during a stress-induced thermoelastic phase transformation, Continuum Mech. Thermodyn., vol. 7, pp. 311–332, 1995.[Crossref], [Web of Science ®] , [Google Scholar]]. In the present article this model has been modified in order to take into account the difference between elastic moduli of austenite and martensite and to introduce the isothermal approximation proposed in [1 S.-J. Kim and R. Abeyaratne, On the effect of the heat generated during a stress-induced thermoelastic phase transformation, Continuum Mech. Thermodyn., vol. 7, pp. 311–332, 1995.[Crossref], [Web of Science ®] , [Google Scholar]]. The second model has been developed by Auricchio et al. within the theory of irreversible thermodynamics with internal variables [2 F. Auricchio, D. Fugazza, and R. DesRoches, Rate-dependent thermo-mechanical modelling of superelastic shape-memory alloys for seismic applications, J. Intell. Mater. Syst. Struct., vol. 19, pp. 47–61, 2008.[Crossref], [Web of Science ®] , [Google Scholar]]. Both models are temperature and strain rate dependent and they take into account thermal effects. The focus in this article is on investigating how the two models compare with experimental data obtained from testing superelastic NiTi wires used in the design of a prototypal anti-seismic device [3 M. Indirli and M.G. Castellano, Shape memory alloy devices for the structural improvement of masonry heritage structures, Int. J. Archit. Heritage, vol. 2, no. 2, pp. 93–119, 2008.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 4 A. Chiozzi, M. Merlin, R. Rizzoni, and A. Tralli, Experimental comparison for two one-dimensional constitutive models for shape memory alloy wires used in anti-seismic applications. In: European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), e-Book Full Papers, pp. 4672–4682, 2012. [Google Scholar]]. After model calibration and numerical implementation, numerical simulations based on the two models are compared with data obtained from uniaxial tensile tests performed at two different temperatures and various strain rates.     

Hydrodynamic Study of Gas–Solid Internally Circulating Fluidized Bed Using Multiphase CFD Model

In the present work, hydrodynamic study of gas and solid flow in an internally circulating fluidized bed (ICFB) was carried out using the CFD multiphase model. Two- (2D) and three-dimensional (3D) computational meshes were used to represent physical ICFB geometries of 0.186-m and 0.3-m diameter columns. The model approach uses the two-fluid Eulerian model with kinetic theory of granular flow options to account particle–particle and particle–wall interactions. The model also uses various drag laws to account the gas–solid phase interactions. The 2D simulation results by various drag laws show that the Arastoopour and Gibilaro drag models predict the fluidization dynamics in terms of flow patterns, void fractions, and axial velocity fields in close agreement with the Ahuja et al. (2008 Ahuja, G. N., and A. W. Patwardhan. 2008. CFD and experimental studies of solids hold-up distribution and circulation patterns in gas–solid fluidized beds. Chemical Engineering Journal 143:147–160.[Crossref], [Web of Science ®] , [Google Scholar]) experimental data. Three dimensional simulations were also carried out for a large-scale ICFB. The effects of superficial gas velocity and the presence of draft tube on solid holdup distribution, solid recirculation pattern, and gas bypassing dynamics for the 3D ICFB were investigated extensively. The mechanism governing the solid circulation and the pressure losses in an ICFB has been explained based on gas and solid dynamics obtained from these simulations. Predicted total granular temperature distributions in 3D ICFB draft tube and the annular zone are qualitatively in agreement with the experimental data. The total granular temperature tends to increase with the increase in solids concentration in the dilute region (? < 0.1) and decrease with an increase of solids concentration in the dense region (? > 0.1).     

Virtual hybrid-FDM system to enhance surface finish

Many rapid prototyping systems which produce prototypes by layer-by-layer material deposition are now commercially available. The layer-by-layer deposition process leads to a stepped surface known as staircase. Staircase formation is a geometric constraint of the layered manufacturing, which can not be eliminated. The presence of staircase on the surface of a prototype detracts from the surface finish and hence restricts functionality of prototypes. It is realized that there is a need to make modifications in RP (rapid prototyping) systems so that prototypes with better surface finish can be produced without incurring high production costs. A virtual hybrid fused deposition modelling system (hybrid-FDM) is proposed in the present work that uses both layer-by-layer deposition and machining. In this system, CAD model is sliced adaptively using limited centre line average (Ra) value as a criterion (Pandey et al. 2003a Pandey, P.M., Reddy, N.V. and Dhande, S.G. 2003a. A real time adaptive slicing for fused deposition modelling. Int. J. Machine Tools and Manufacture, 43: 61–71.  [Google Scholar]). Hot cutter machining/ploughing (HCM) (Pandey et al. 2003b Pandey, P.M., Reddy, N.V. and Dhande, S.G. 2003b. Improvement of surface finish by staircase machining in fused deposition modelling. Journal of Material Processing Technology, 132: 323–331. [Crossref], [Web of Science ®] , [Google Scholar]) is recommended to machine the build edges (staircase) of ABS material. Numerically controlled x?y traversing mechanism is proposed as an attachment to move hot cutters along the periphery of slices to machine build edges. In this paper, geometrical designs of cutters are proposed. A process planning system to decide the number of layers to be deposited and then machined in order to access intricate features of a part is implemented. The developed system simulates surface roughness, before and after hot cutter machining. An experimental study is carried out by machining the build edges of an axisymmetric FDM part on lathe machine to form a basis for a hybrid-FDM system.     

Base Pressure Measurements under a Scale Model Stockpile: Effects of Offset Reclaim Channels and Predictive Model Developments

It has been shown (McBride, 2006 McBride , W. 2006 . Base pressure measurements under a scale model stockpile . Part. Sci. Technol. 24 : 59 – 71 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) that under a scale model stockpile a central pressure dip, or ‘M’ pressure, is formed during both the filling and refilling processes of a stockpile containing a central reclaim channel. This article presents the results from further experiments with a noncentral reclaim channel and clearly illustrates that a central pressure dip exists under a conical stockpile with an offset reclaim channel. Additional data were recorded regarding lateral load transfer within the stockpile on initiation of flow, although more experimental work is required to fully understand this aspect. A method for predicting conical stockpile base pressures is presented along with an overpressure theory to account for the vertical load instability induced by the onset of material discharge.     

Electro-Mechanical Impedance (EMI)-Based Incipient Crack Monitoring and Critical Crack Identification of Beam Structures

Fatigue-induced damage is often progressive and gradual in nature. Fatigue is often deteriorated by corrosion in ageing structures, creating maintenance problems, and even causing catastrophic failure. This ushers the development of structural health monitoring (SHM) and nondestructive evaluation (NDE) systems. Recent advent of smart materials applicable in SHM alleviates the shortcomings of the conventional techniques. Autonomous, real-time, remote monitoring becomes possible with the use of smart piezoelectric transducers. For instance, the electro-mechanical impedance (EMI) technique, employing piezoelectric transducers as collocated actuators and sensors, is known for its ability in damage detection and characterization. This article presents a series of lab-scale experimental tests and analysis to investigate the feasibility of fatigue crack detection and characterization employing the EMI technique. This study extends the work by Lim and Soh [1 Y. Y. Lim and C. K. Soh . Smart Materials and Structures 20 : 125001 ( 2011 ).[Crossref], [Web of Science ®] , [Google Scholar]] to incorporate the phases involving crack initiation and critical crack. It is suggested that the EMI technique is effective in characterizing fatigue induced cracking, even in its incipient stage. Micro-crack invisible to the naked eyes can be detected by the technique especially when employing the higher frequency range of 100–200 kHz. A quick and handy qualitative-based critical crack identification method is also suggested by visually inspecting the admittance frequency spectrum.     

Magnetic-saturation zone model for two semipermeable cracks in magneto-electro-elastic medium

Extension of the PS model (Gao et al. [1 H. Gao, T. Y. Zhang, and P. Tong, “Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic,” J. Mech. Phy. Solids, vol. 45, pp. 491–510, 1997.[Crossref], [Web of Science ®] , [Google Scholar]]) in piezoelectric materials and the SEMPS model (Fan and Zhao [2 C. Y. Fan and M. H. Zhao, “Nonlinear fracture of 2-D magnetoelectroelastic media: analytical and numerical solutions,” Int. J. Solids Struct., vol. 48, pp. 2383–2392, 2011.[Crossref], [Web of Science ®] , [Google Scholar]]) in MEE materials, is proposed for two semi-permeable cracks in a MEE medium. It is assumed that the magnetic yielding occurs at the continuation of the cracks due to the prescribed loads. We have model these crack continuations as the zones with cohesive saturation limit magnetic induction. Stroh's formalism and complex variable techniques are used to formulate the problem. Closed form analytical expressions are derived for various fracture parameters. A numerical case study is presented for BaTiO₃ ? CoFe₂O₄ ceramic cracked plate.     

An objective function to address production sequencing with minimal tooling replacements

A strategy is presented to obtain production sequences resulting in minimal tooling replacements. An objective function is employed to distribute the tool wear as evenly as possible throughout the sequence. This objective function is an extension of Miltenburg's earlier work (1989 Miltenburg, J. 1989. Level schedules for mixed-model assembly lines in just-in-time production systems. Manage. Sci., 35: 192–207. [Crossref], [Web of Science ®] , [Google Scholar]) concerned with obtaining production sequences while evenly distributing the satisfaction of demand. Smaller problems are solved to optimality, while larger problems are solved as close as possible to optimality. The production sequences are simulated to estimate required tooling replacements. The methodology presented here consistently results in fewer tooling replacements when compared with earlier published work (McMullen et al. 2002 McMullen, PR, Clark, M, Bell, J and Albritton, D. 2002. A correlation and heuristic approach to production sequences with uniformity of tool wear. Comp.?&;?Op. Res., 30: 435–454.  [Google Scholar], McMullen 2003 McMullen, PR. 2003. Sequencing for minimal tooling replacements via a variety of objective functions. Int. J. Prod. Res., 41: 2183–2199. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]).     

A new model for the viscosity of highly concentrated multi-sized particulate Bingham slurries

Bench scale tests were carried out to investigate the rheological properties of multi-sized particulate Bingham slurries at high solid concentrations ranging from 50% to 70% by weight. In addition, rheological data from Biswas et al. (2000 Biswas, A., B. K. Gandhi, S. N. Singh, and V. Seshari. 2000. Characteristics of coal ash and their role in hydraulic design of ash disposal pipelines. Indian Journal of Engineering and Materials Sciences 7:1–7.[Web of Science ®] , [Google Scholar]) and Chandel et al. (2009, 2010) have also been considered. Based on these extensive amount of rheological data, an empirical model is proposed for viscosity as a function of solid volume fraction (?), maximum solid volume fraction (?_m), median particle diameter (d₅₀), and coefficient of uniformity (C_u) using optimization and nonlinear least-square curve-fitting technique. The proposed model shows good agreement with the experimental data considered in the present study and is found to be much better than the previously developed models in predicting the viscosity of multi-sized particulate Bingham slurries at high solid concentrations.     

Hyperelastic analysis based on a polygonal finite element method

In this contribution, we present a novel polygonal finite element method applied to hyperelastic analysis. For generating polygonal meshes in a bounded period of time, we use the adaptive Delaunay tessellation (ADT) proposed by Constantinu et al. [1 A. Constantinu, P. Steinmann, T. Bobach, G. Farin, and G. Umlauf, The adaptive Delaunay tessellation: A neighborhood covering meshing technique., Comput. Mech., vol. 42, no. 5, pp. 655–669, 2008.[Crossref], [Web of Science ®] , [Google Scholar]]. ADT is an unstructured hybrid tessellation of a scattered point set that minimally covers the proximal space around each point. In this work, we have extended the ADT to nonconvex domains using concepts from constrained Delaunay triangulation (CDT). The proposed method is thus based on a constrained adaptive Delaunay tessellation (CADT) for the discretization of domains into polygonal regions. We involve the metric coordinate (Malsch) method for obtaining the interpolation over convex and nonconvex domains. For the numerical integration of the Galerkin weak form, we resort to classical Gaussian quadrature based on triangles. Numerical examples of two-dimensional hyperelasticity are considered to demonstrate the advantages of the polygonal finite element method.     

A note on ‘A bivariate optimal replacement policy for a repairable system’

An error appearing in equation (3) of Y.L. Zhang (J. Appl. Prob., 1994, 31, 1123–1127) has been pointed out by S.H. Sheu (Eur. J. Oper. Res., 1999, 112, 503–516) and the correct expressions (25)–(27) given accordingly on pp. 510–511. However, the derivation of the key expression (27), the long-run expected loss rate, was not presented. The purpose of this note is threefold. First, since a monotone process (e.g. an arithmetic, geometric, or arithmetic–geometric process) approach, as discussed by K.N.F. Leung (Eng. Optimiz., 2001, 33, 473–484), is considered to be relevant, realistic, and appropriate to the modelling of a deteriorating system maintenance problem, it is worth explicitly developing this expression, which is of benefit to the subsequent studies. Secondly, equation (3) in Zhang (1994) Zhang, Y. L. 1994. A bivariate optimal replacement policy for a repairable system. J. Appl. Prob., 31: 1123–1127. [Crossref], [Web of Science ®] , [Google Scholar] is shown to be fundamentally correct and so it can be viewed as an alternative method of formulating similar bivariate cases. Thirdly, although equations (4) and (5) in Zhang (1994) Zhang, Y. L. 1994. A bivariate optimal replacement policy for a repairable system. J. Appl. Prob., 31: 1123–1127. [Crossref], [Web of Science ®] , [Google Scholar] have been logically and correctly derived, both can be readily reduced to their simplest forms which are derived here.