Melt Shape Research Articles

Investigations into 4D printed PLA/graphite composite with thermal induced shape memory effect

PurposeThe paper aims to fabricate shape memory composites using polylactic acid (PLA) matrix and graphite. Shape memory polymers are a promising family of materials for biomedical applications because of their favourable mechanical properties, fast reactions and good biocompatibility. For most SMPs, however, achieving controllable sequential shape change is challenging.Design/methodology/approachIn the present work, 4D printing technology is used to fabricate shape memory composites using polylactic acid (PLA) matrix and graphite. A comparative study of pure PLA and graphite’s different weight % composition has been done.FindingsBy carefully managing the deformation state, PLA with graphite shape memory composites produced controllable sequential deformation with an amazing shape memory effect. Surface morphology, thermal properties, melt flow index and shape recovery tests have all been carried out to assess the qualities of manufactured samples.Originality/valueThis is a one-of-a-kind to fabricate shape memory composites using graphite and a PLA matrix. Thus, this research attempts to deliver the possible use of PLA/graphite composites fabricated using 4D printing in robotics and biomedical devices.Graphical

A novel hybridity model for (Cu-Al2O3-H2O) hybrid nanofluid flow with melting heat transfer, shape factor, and irreversibility analysis: A development on Blasius and Sakiadis problems

The mass-based hybrid nanofluid model is applied for the flow over the flat plate with melting heat transfer phenomenon by considering Blasius and Sakiadis problems. Instead of the volumetric concentration of the first and second nanoparticles, the masses of the base fluid and nanoparticles are taken into account. This model is used for the first time to develop the Blasius and Sakiadis problem along with the irreversibility analysis. The nanoparticles of various shapes are also taken for investigation. Appropriate similarity transformations are applied to turn the partial differential equations into ordinary differential equations. To numerically solve the transformed boundary layer equations, the shooting technique with the Runge Kutta–Felhberg scheme was employed. Copper and alumina nanoparticles of two different sorts have been incorporated into the base fluid. The influence of controlling physical factors on the velocity profile, thermal profile, coefficient of skin friction, and Nusselt number for both the Sakiadis and Blasius flows are graphically investigated. In addition, the fluctuation in the entropy generation as well as Bejan number has been illustrated through graphs. In-depth discussion is given regarding the traits of physical and engineering interest.

Pressure drop non-linearities in material extrusion additive manufacturing: A novel approach for pressure monitoring and numerical modeling

Fused Filament Fabrication is an additive manufacturing technique in which molten thermoplastic polymers are extruded through a nozzle. Therefore, the interplay between the viscoelastic nature of the polymer melt, temperature, printing conditions and nozzle shape may lead to inconsistent extrusion. To improve the extrusion control and optimize the print-head performance, a better understanding of the flow process of the polymer melt both in the nozzle and the liquefier is needed. However, several challenges need to be overcome due to the complexity of gathering experimental data on the melt pressure in the nozzle and the lack of numerical models able to capture the full rheology of the molten polymer. This research introduces an innovative approach for monitoring the pressure within a material extrusion 3D printer’s nozzle. This method involves utilizing a pin in direct contact with the molten material, which then transmits the applied force from the material to an externally mounted load cell. The setup provides reliable, repeatable pressure data in steady-state conditions for two nozzle geometries and at different extrusion flows and temperatures. Moreover, the Giesekus model enabled capturing the viscoelastic rheometric features of the melt, and the numerical predictions have been compared with the experimental data. Results show that the numerical model accurately describes the flow conditions in the nozzle and allows the estimation of the behavior of the melt in the liquefier zone, the area of the print-head where the filament is molten. It could be concluded that the backflow, which is the backward flow of the molten polymer in the gap between the filament and the liquefier towards the cold end, caused significant non-linearities in the total pressure drop measured in the feeders, which were related to normal forces induced by shear in that region.

Fuzzy modeling and characterization of mechanical and biological properties of a selective laser melting shape: A comprehensive study

The bone scaffold is a porous structure that possesses suitable biological and mechanical properties similar to those of natural bone, thereby providing a suitable substrate for bone growth. The scaffold plays a temporary role in the bone repair process and is composed of degradable material that gradually degrades over time to enable new bone growth and replacement. The scaffolds are implanted using bone morphogenetics of transplanted bone-protein (BMP-7) and implanted subcutaneously to assess biological properties and tissue growth. This study demonstrates the ability to design and fabricate a titanium scaffold with a porous architecture using the Selective Laser Melting (SLM) method, employing two different geometries. The scaffolds' mechanical properties are assessed via a compression test, and the results are utilized for finite element analysis (FEA), predicting the designed metallic scaffold's optimal geometric shape and porosity percentage. The biological response of the scaffolds is evaluated via simulated body fluid (SBF) and phosphate buffer saline (PBS) analyses. The findings indicate that the 8-sided scaffold has superior mechanical and biological features compared to the circular and 6-sided geometries. To predict the scaffold's specifications before conducting the experiment, a fuzzy modeling system is used to model the effect of inputs such as weight percentage, elastic modulus, porosity, and Poisson ratio on the compressive strength output variable.

A high-temperature and high-pressure cell for in situ visualization of reaction processes by neutron imaging

This study developed a high-temperature and high-pressure (HTHP) cell for in situ neutron imaging of hydrothermal reactions. The cell’s maximum temperature and pressure were 500 °C and 50 MPa, respectively, and its vessel for observing reactions comprised SUS316 stainless steel. Neutron transmission images were obtained to observe the behavior of sub- and supercritical water and the decomposition of two plastics (polypropylene and polyethylene) at HTHP. The images showed that water’s density and phase changed with temperature and pressure, affecting neutron transmission (and thus image brightness). The plastics began to melt and change shape at 150–200 °C, and they decomposed at 500 °C and 20 MPa. This study provides a basis for future research using the HTHP cell to examine various reactions such as the decomposition of biomass samples, the reforming of heavy oil, and the synthesis of nano-materials using sub- and supercritical water.

Generalization of Young-Laplace, Kelvin, and Gibbs-Thomson equations for arbitrarily curved surfaces

The Young-Laplace, Kelvin, and Gibbs-Thomson equations form a cornerstone of colloidal and surface sciences and have found successful applications in many subfields of physics, chemistry, and biology. The Gibbs-Thomson effect, for example, predicts that small crystals are in equilibrium with their liquid melt at a lower temperature than large crystals and the positive interfacial energy increases the energy required to form small particles with a high curvature interface. In cases of liquids contained within porous media (confined geometry), the effect indicates decreasing the freezing/melting temperatures and the increment of the temperature is inversely proportional to the pore size. These phenomena can be reformulated for Gaussian maps of macromolecules and can be asked the following question: can one use the equations for predicting the melting temperature and shape of polymer chains in confined geometries? The answer is no, mainly because macromolecules form highly curved surfaces (Gaussian maps), and the equations hold only for simple geometries (sphere, plane, or cylinder). Here, we present general Young-Laplace, Kelvin, and Gibbs-Thomson equations for arbitrarily curved surfaces and apply them to predict temperature distribution on a few protein surfaces. Also, after increased interest toward liquid/liquid phase separation in biology, we derive generic Ostwald ripening and show that for shape-changing condensates, instead of a monotonic growing mechanism, a variety of processes are possible. Due to the generality of equations, we clarify that at appropriate internal/external pressure conditions systems, bounded by surfaces, may adopt any shape and thermal stability is strongly influenced by the geometries of confined spaces.

Ionic Mixture of Binary Sugar Alcohols and a Polymer: Composition Optimization for Long-Term Thermal Energy Storage

A new cold crystallizing material (NaPP) is analyzed for long-term thermal energy storage (TES). NaPP comprises a mixture of erythritol and mannitol as the binary phase change material (PCM) in the scaffold of polyvinyl alcohol (PVA) cross-linked with sodium citrate (SC). The material demonstrates a unique behavior of stable supercooling and vitrification during cooling and cold crystallization during subsequent heating, which enables a reliable long-term storage of the melting enthalpy and a controllable heat release. The use of several components in the material composition, however, impedes optimization of the thermal properties for the storage. As such, differential scanning calorimetry (DSC) was applied to expose the effect of the material components on the thermal properties, and the mixture experimental methodology (MEM) was used to model and optimize these properties. Successful modeling yielded a linear response for the thermal performance, which was significantly affected by the content of SC. Increasing the amount of SC (from 0 to 18 wt %) elevated the ionic strength of the system, which caused reduction in the amount of active PCM (confirmed by X-ray diffraction and DSC) and coarsening of the surface morphology (revealed by optical and scanning electron microscopies). This was also manifested as gradual disappearance of cold crystallization which limits the use of the material to compositions with the glass-transition temperature below −15 °C. MEM identified the optimal composition as 88.9 wt % PCM and 11.1 wt % SC, which showed a melting enthalpy of 194 J/g at 105 °C. Yet, the composition comprising 80 wt % PCM, 10 wt % PVA, and 10 wt % SC showed both high melting enthalpy (176 J/g) and shape stability facilitating larger scale applications. These compositions demonstrated a temperature increase of 10–20 °C during cold crystallization of a 10 g sample, confirming the suitability of the optimization model and the operation of the new material for long-term TES.

Influence of functional carbon nanotube and multi‐cyclic shape memory performance on thermally triggered polyurethane nanocomposites

AbstractIn this study, thermally triggered shape memory thermoplastic polyurethane‐multiwall carbon nanotube (TPU/MWCNTs) nanocomposites with varying nanofiller content (0–5 wt%) were prepared. Melt flow, morphology, and shape memory properties of TPU/MWCNTs nanocomposites were investigated. We attempt to clarify the reinforcement effect of CNTs on the shape memory behavior of TPU/MWCNTs nanocomposites. Moreover, the influence of acid treatment on surface morphology, thermal stability, and dispersion state of MWCNTs has been evaluated. Pristine MWCNTs were treated with highly concentrated nitric acid (68%) and introduced by solution mixing to TPU as an efficient reinforcement phase. The thermogravimetric analysis revealed thermal stability improvement of acid treatment MWCNTs. Field emission‐scanning electron microscopy images confirmed the homogenous distribution of oxidized MWCNTs in the matrix and some aggregated structures at 5 wt% nanofiller. Higher melt flow rate values were observed for composites loaded with 0.5–1 wt% ox‐MWCNTs compared with 2–5 wt% because of their better dispersion in TPU. The experimental results show a higher shape recovery ratio of TPU/ox‐MWCNTs nanocomposites than pure polyurethane (over 20%). A good shape recovery in the 90%–100% range could be obtained during a shape recovery test when ox‐MWCNTs content of 0.5–2 wt% is proposed to synthesize TPU/ox‐MWCNTs nanocomposites.

Photothermal driven polymorph pattern in semicrystalline polymers towards programmable shape morphing

Shape programming polymer materials from planar sheets to three-dimensional (3D) geometries is appealing in many advanced devices. Different design strategies provide guidance for optimized materials selection and potential applications development. Herein, we report a simple yet effective approach that allows programable shape morphing in commercialized semicrystalline polymer by photothermal driven polymorph pattern. Two regions with different polymorphs show greatly distinct melting temperatures (Tm), moduli, and shape recovery abilities at a specified temperature. The resulting 3D geometries can be controlled by the applied strain and the spatial distribution of polymorphs. Due to the remarkable moduli difference, 2D sheets with well-designed polymorph patterns can transform into concave-convex structures used for “mortise-tenon” joints, which can be assembled into load-bearing devices. The materials with polymorph patterns are reprogrammable, due to the reversible nature of melting/crystallization process. Our strategy can be generalized to other semicrystalline polymers with polymorphism and can also expand unconstrained shape programming of morphing materials.

Surface Properties and Architectures of Male Moth Trichoid Sensilla Investigated Using Atomic Force Microscopy

The surfaces of trichoid sensilla on male moth antennae have been sculpted over evolutionary time to capture pheromone odorant molecules emitted by the females of their species and transport the molecules in milliseconds into the binding protein milieu of the sensillum lumen. The capture of pheromone molecules likely has been optimized by the topographies and spacings of the numerous ridges and pores on these sensilla. A monolayer of free lipids in the outer epicuticle covers the sensillar surfaces and must also be involved in optimal pheromone odorant capture and transport. Using electro-conductive atomic force microscopy probes, we found that electrical surface potentials of the pores, ridges and flat planar areas between ridges varied in consistent ways, suggesting that there is a heterogeneity in the distribution of surface lipid mixtures amongst these structures that could help facilitate the capture and transport of pheromone molecules down through the pores. We also performed experiments using peak force atomic force microscopy in which we heated the sensilla to determine whether there is a temperature-related change of state of some of the surface lipid exudates such as the prominent domes covering many of the pores. We found that these exudates were unaffected by heating and did not melt or change shape significantly under high heat. Additionally, we measured and compared the topographies of the trichoid sensilla of five species of moths, including the distributions, spacings, heights and diameters of ridges, pores and pore exudates.

Melting and Heat Transfer Characteristics of Urea Water Solution According to a Heating Module’s Operating Conditions in a Frozen Urea Tank

The urea-selective catalytic reduction (SCR) system, a nitrogen oxide reduction device for diesel vehicles, is a catalytic system that uses urea water solution (UWS) as a reducing agent. This system has a relatively wide range of operating temperatures. However, the freezing point of the reducing urea solution used in this system is −11 °C. When the ambient temperature dips below this freezing point in winter, the solution may freeze. Therefore, it is important to understand the melting characteristics of frozen UWS in relation to the operating conditions of the heating device to supply the minimum amount of aqueous solution required by the system in the initial stage of normal operation and startup of the urea–SCR system. In this study, we artificially froze a liquid solution by placing it along with a heating module in an acrylic chamber to simulate a urea solution tank. Two types of heating modules (P120 and P160) consisting of two heating elements and heat transfer bodies were used to melt the frozen solution. The melting characteristics of the frozen solution were observed, for example, changes in the temperature distribution around the heating module and the cross-sectional melting shape with the passage of time since the start of the power supply to the heating module. The shape of melting around the heating module differed depending on the level of UWS relative to the heater inside the urea tank. In case 1, it melted in a wide shape with an open top, and in case 2, it melted in a closed shape. This shape change was attributed to the formation of internal gaseous space due to volume reduction during melting and the heat transfer characteristics of the fluid and solid substances.

Species discrimination and hybrid detection in terrestrial orchids using Bar-HRM: A case of the Calanthe group

The Calanthe group of terrestrial orchid species comprises three genera as Calanthe R.Br., Phaius Lour. and Cephalantheropsis Guillaumin that have similar morphological characteristics. Orchid species taxonomy is generally investigated based on the features of the flowers. This is a difficult task and requires an expert taxonomist, while it is often impossible to identify species if the specimens have none or incomplete flowers. Nowadays, standardized short DNA, so-called DNA barcoding, is widely used for species identification. Here, the DNA barcode, internal transcribed spacer-1 (ITS1) in the nuclear DNA or trnL in the chloroplast DNA, combined with high resolution melting (HRM) analysis was used to identify 13 orchid species in the Calanthe alliance and also to determine hybrid species. Results showed that the melting temperature (Tm) and melting curve obtained by HRM using mini-ITS1 significantly differed among Calanthe alliance species, with an accuracy of 92% compared to HRM using mini-trnL. HRM using mini-ITS1 provided a good marker for hybrid determination with two peaks from parental species. To determine the hybrids, HRM using mini-trnL was necessary for assigning the maternal parent; however, in some cases the melting shapes obtained from HRM using mini-trnL of parental species were different. Results suggested that HRM using mini-ITS1 gave good species differentiation and hybrid detection for species of the Calanthe alliance, while HRM using mini-trnL was exploited for assessing the maternal parent of hybrid species.

Significant Performance Improvement of Thermoplastic Polyurethane Composites by Multiple Effects of Monodispersed Graphene: Micro‐Crosslinking, Isolation, and Induced Crystallization

AbstractThermoplastic polyurethane composites (TPCs) in kilogram scale reinforced with monodispersed functionalized graphene (FGr) are prepared by melt‐blending on industrial extruder and their properties are studied in this work. It shows that the saturation content of monodispersed FGr in TPCs is ≈0.5 wt%, beyond which part of it will agglomerate. The multiple effects of monodispersed FGr—micro‐crosslinking, isolation, and induced crystallization—have great impact on the properties of TPCs. With the content increase of FGr, the melt rheological properties, crystallization properties, mechanical properties, and shape memory properties of TPCs show regular changes. More importantly, the tensile fracture behaviors of TPCs are dramatically changed by FGr. Some microfibers with high strength are formed and lay astride the cracks to prevent crack propagation during the damage process. Therefore, the tensile strength of TPC with 0.5 wt% FGr is maximumly improved, showing an increase of 139% compared to neat thermoplastic polyurethane. Its shape fixed ratio and shape recovery ratio are respectively raised to 96% and 94%, showing a good shape memory performance.

Scaling laws for the geometry of an impact-induced magma ocean

Growing protoplanets experience a number of impacts during the accretion stage. A large impactor hits the surface of a protoplanet and produces impact-induced melt, where the impactor's iron emulsifies and experiences metal-silicate equilibration with the mantle of the protoplanet while it descends towards the base of the melt. This process repeatedly occurs and determines the chemical compositions of both mantle and core. The partitioning is controlled by parameters such as the equilibration pressure and temperature, which are often assumed to be proportional to the pressure and temperature at the base of the melt. The pressure and temperature depend on both the depth and shape of the impact-induced melt region. A spatially confined melt region, namely a melt pool, can have a larger equilibrium pressure than a radially uniform (global) magma ocean even if their melt volumes are the same. Here, we develop scaling laws for (1) the distribution of impact-induced heat within the mantle and (2) shape of the impact-induced melt based on more than 100 smoothed particle hydrodynamic (SPH) simulations. We use Legendre polynomials to describe these scaling laws and determine their coefficients by linear regression, minimizing the error between our model and SPH simulations. The input parameters are the impact angle θ (0∘,30∘,60∘, and 90∘), total mass MT (1MMars−53MMars, where MMars is the mass of Mars), impact velocity vimp (vesc−2vesc, where vesc is the mutual escape velocity), and impactor-to-total mass ratio γ (0.03−0.5). We find that the equilibrium pressure at the base of a melt pool can be higher (up to ≈80%) than those of radially-uniform global magma ocean models. This could have a significant impact on element partitioning. These melt scaling laws are publicly available on GitHub (https://github.com/mikinakajima/MeltScalingLaw).

Numerical Analysis of Melt Flow and Interface Deflection during the Growth of Directional Solidified Multi-Crystalline Silicon Ingots of Three Different Dimension

In this article, we have investigated the impact of furnace geometry on the melt flow while growing ingot of three different sizes. The heat flux within the three different hot zones is observed and the variation in heat dissipation during the growth is discussed. The evolution of melt/crystal interface has been analysed at 25%, 50% and 75% of solidification fraction for 7, 40 and 330 kg ingots. The influence of radial temperature gradient on the variation of melt flow velocity above the melt/crystal interface and free surface of melt has been analysed during the growth of all the three ingots. It is found that the smaller size ingots such as 7 kg and 40 kg show higher radial temperature gradient compared to 330 kg ingot particularly in the peripheral region. Simulation result shows that the furnace geometry significantly influences the thermal field, velocity of convective melt flow and shape of the melt/crystal interface during the growth process.

Unraveling the Effect of Citric Acid on Microstructure, Rheology, and Structural Recovery of Thermoplastic Potato Starch

AbstractThe main objective of the present work is to explore the role of citric acid (CA) on microstructural changes and their impact on the melt rheological behavior, mechanical performance, and shape recovery of thermoplastic starch (TPS). The results of frequency sweep test show a pronounced nonterminal storage modulus (G’) at lower frequencies (high melt elasticity) for TPS, which is found to be greatly reduced in favor of improving the processability through the addition of CA. This could be explained in terms of reduced disentanglements of amylopectin molecules, as a crucial parameter responsible for the 3D‐type interconnected microstructure of TPS, through catalyzing effect of CA on hydrolysis. The results of the temperature sweep test (cooling mode) show a pronounced liquid‐to‐solid transition at ∼136℃ for CA‐modified TPS. This transition could be attributed to the temperature‐driven significant strengthening of the formation of single helical amylose crystalline structure and/or the hydrogen bonds between hydrolyzed amylopectin chains at temperatures below 136℃. The results are found to be consistent with the results obtained from the tensile and DMTA experiments. As expected, the shape recovery of the CA‐modified TPS sample is lower than that of unmodified TPS because of the lower elastic stored energy (stiffness) in the presence of CA, which can be largely compensated by incorporating appropriate nanoparticles.

발전소 고압배전계통 계기용변압기 Fuse 손상 메커니즘 및 대책

Power Fuses that are installed to protect for Voltage Transformer had been burnt out by operating environments, the characteristic of fuse and aging in power plants. To analyzes the root causes of fuse failures, this study reviews the appropriateness of the fuse selection according to the VT rating and capacity, the effects of inrush current that may occur during VT power up and the possibility of resonance due to poor VT excitation characteristics. In addition, the internal condition and the blown-off melt shape of the burned-out fuse were confirmed by the industrial X-ray, the electron microscope, and the material analysis.

Using mini-barcodes coupled with high resolution melting (minibar-HRM) method for species discrimination across Pangasianodon gigas, Pangasianodon hypophthalmus and Pangasius larnaudii

Pangasianodon gigas (giant catfish) is well-recognized as a critically endangered species due to overhunting and habitat degradation. Giant catfish aquaculture has expanded to meet the ever-increasing demands with augmented prices. Contamination or substitution of P. gigas products with other related species e.g. Pangasianodon hypophthalmus and Pangasius larnaudii because of their similar morphology but lower cost requires investigation. A method was established to differentiate species by mini-barcodes or microsatellites conjugated with high resolution melting analysis (minibar-HRM or microsatellite-HRM) using mitochondrial genes cytochrome c oxidase subunit I (COI), cytochrome b (Cytb), the nuclear recombination activator gene 1 (Rag1) and two microsatellite loci (Pg-9 and Pg-13). Results revealed that primer sets for the mitochondrial genes PanCytb1 and PanCytb2 showed a significant difference in melting shapes and melting temperature (Tm) between the three species. For nuclear genes, a single locus was not sufficient to discriminate between the three species, and at least two loci such as PanRag1 + Pg9 or PanRag1 + Pg13 were required. The sufficient amount of DNA for species discrimination using minibar-HRM with PanCytb1 and PanCytb2 was suggested as at least 5 pg. This method can also be used for adulteration determination of the P. gigas substitution with P. hypophthalmus and P. larnaudii at greater than 5% adulteration. Findings demonstrated that mini-barcode or microsatellite-HRM offered optimal performance for species discrimination of P. gigas, P. hypophthalmus and P. larnaudii. This approach can be adopted for hybrid detection using PanRag1 + Pg9 or PanRag1 + Pg13-HRM and PanCytb1 or PanCytb2 for matrilineal detection to benefit aquaculture research and quality control on a commercial scale.

Differentiation of Siam weed (Chromolaena odorata (L.) R.M. King & H. Rob.) and morphologically related species in Asteraceae by ITS barcode coupled with high resolution melting analysis (HRM)

Siam weed (Chromolaena odorata (L.) R.M. King & H. Rob.) is a commercially viable plant that has various pharmacological properties including hemostasis and wound healing. Three other plant species as Praxelis (Praxelis clematidea R.M. King & H. Rob.), Goat weed (Ageratum conyzoides L.) and Crofton weed (Ageratina adenophora (Spreng.) R.M. King) in the same family have similar morphological characteristics. Misidentification of processed materials can occur in the absence of a skilled taxonomist. These four plants can often be found in close proximity, leading to erroneous sample collection and misleading results. DNA identification through molecular techniques is an accurate method for correctly identifying and differentiating Siam weed to control the quality of product development. Two primers (ITS1A and ITS1B) were designed based on the barcode (Bar) locus of the internal transcribed spacer (ITS) region. High resolution melting (HRM) analysis (Bar-HRM) was performed to acquire melting shapes and melting temperatures (Tm) to discern the four plant species. Bar-HRM using ITS1A and ITS1B showed differences in melting shapes among the four species. The method employing ITS1A distinguished the four species with higher accuracy than ITS1B. The Tm values of each species obtained from Bar-HRM using ITS1A ranged from 82.54 °C to 86.26 °C. Bar-HRM using ITS served as a rapid and reliable tool for species differentiation among Siam weed, Praxelis, Goat weed and Crofton weed.

Solving the Problem of Silicon Dioxide Melting Based on Deviation Model

In order to reveal the dissolution behavior of iron tailings in blast furnace slag, we studied the main component of silica in iron tailings. First, edge contour features need to be established to represent the melting process of silica. We choose shape, perimeter, area and generalized radius as objects. By independently analyzing the influence of these four indexes on the melting rate, the area and shape were selected as the characteristic parameters of the edge contour of the silica particles. Then, the actual melting rate of the silica is estimated by the edge contour feature index. Finally, we can calculate the melting rate of the first second of three time periods of 0.00010312mm3/s, 0.0002399mm3/s, 0.0000538mm3/s.