Mass Change Measurements Research Articles

A method of determining nanoparticle size distribution in iron ammonia synthesis catalyst by measuring mass changes during the nitriding process

A new method for determination of nanoparticle size distribution, on the basis of measurements of nanomaterial conversion degree as a function of the chemical potential of gas reagent, was presented. The method was applied for determination of nanocrystallite size distribution in a pre-reduced iron catalyst for ammonia synthesis being an example of a nanomaterial. Samples were reduced with hydrogen at 500°C and then nitrided at 300°C in gaseous ammonia-hydrogen mixtures of different nitriding potentials. Conversion degree measurements, viz., measurements of mass changes of the catalyst were performed in a differential reactor equipped with systems that enable thermogravimetric measurements and analysis of gas phase chemical composition. Based on the performed measurements, a relationship binding the conversion degree with size distribution was proposed. The resulting size distribution of nanocrystallites was compared to distributions determined by known techniques based on XRD or on measurements of the nitriding reaction rate. The size distribution determined using the new method has a higher resolution, revealing more details of the sample morphology.

Serial weighting of micro-objects with resonant microchanneled cantilevers

Atomic force microscopy (AFM) cantilevers have proven to be very effective mass sensors. The attachment of a small mass to a vibrating cantilever produces a resonance frequency shift that can be monitored, providing the ability to measure mass changes down to a few molecules resolution. Nevertheless, the lack of a practical method to handle the catch and release process required for dynamic weighting of microobjects strongly hindered the application of the technology beyond proof of concept measurements. Here, a method is proposed in which FluidFM hollow cantilevers are exploited to overcome the standard limitations of AFM-based mass sensors, providing high throughput single object weighting with picogram accuracy. The extension of the dynamic models of AFM cantilevers to hollow cantilevers was discussed and the effectiveness of mass weighting in air was validated on test samples.

Corrosion Behavior of Austenitic Stainless Steel in Supercritical CO2 Containing O2 and H2O

The corrosion behavior of 347H stainless steel was investigated in supercritical CO2 (sCO2) containing H2O and O2 simulating heat exchanger conditions that would exist in direct sCO2 power cycles. Thermodynamic properties of oxygenated sCO2 aqueous systems related to the corrosion phenomena was determined using NIST developed software REFPROP. The exposure tests of the corrosion samples were performed at a pressure of 80 bar and two temperatures, 50 °C and 248 °C up to 1500 hours. The samples were exposed to oxygenated H2O-containing CO2, and oxygenated sCO2-containing H2O. The corrosion rate of the alloys was determined by mass change measurements. The surface microstructure and composition of the corrosion films were investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM) equipped with energy dispersive X-ray spectroscopy, and X-ray photoelectron spectroscopy (XPS). The XRD results for the corrosion products on the sample surfaces formed in the oxygenated CO2-containg H2O and water-containing CO2 and O2 at 248°C revealed the presence of Fe2O3 and Fe3O4,-rich phase, respectively. The XPS results revealed that the samples had thicker films after exposure to 0.01 O2/ 0.04 H2O ratio in CO2 at 248°C than at 50°C. The outer film layer contained Fe and O and the inner layer Cr and O at 248°C. Mostly Cr and O were found at 50°C.

Biodegradability of poly(lactic-co-glycolic acid) after femtosecond laser irradiation.

Biodegradation is a key property for biodegradable polymer-based tissue scaffolds because it can provide suitable space for cell growth as well as tailored sustainability depending on their role. Ultrashort pulsed lasers have been widely used for the precise processing of optically transparent materials, including biodegradable polymers. Here, we demonstrated the change in the biodegradation of a poly(lactic-co-glycolic acid) (PLGA) following irradiation with femtosecond laser pulses at different wavelengths. Microscopic observation as well as water absorption and mass change measurement revealed that the biodegradation of the PLGA varied significantly depending on the laser wavelength. There was a significant acceleration of the degradation rate upon 400 nm-laser irradiation, whereas 800 nm-laser irradiation did not induce a comparable degree of change. The X-ray photoelectron spectroscopy analysis indicated that laser pulses at the shorter wavelength dissociated the chemical bonds effectively, resulting in a higher degradation rate at an early stage of degradation.

Cellular Assays with a Molecular Endpoint Measured by SAMDI Mass Spectrometry.

Cell-based, high-throughput screening (HTS) assays are increasingly important tools used in drug discovery, but frequently rely on readouts of gene expression or phenotypic changes and require development of specialized, labeled reporters. Here a cell-based, label-free assay compatible with HTS is introduced that can report quantitatively on enzyme activities by measuring mass changes of substrates with matrix-assisted laser desorption/ionization mass spectrometry. The assay uses self-assembled monolayers to culture cells on arrays presenting substrates, which serve as reporters for a desired enzyme activity. Each spot of cells is treated with a compound, cultured and lysed, enabling endogenous enzymes to act on the immobilized peptide substrate. It is demonstrated that the assay can measure protein tyrosine phosphatase (PTP) activity from as few as five cells and a screen is described that identifies a compound that reduces PTP activity in cell lysates. This approach offers a valuable addition to the methods available for cell-based screening.

Effect of the extent of pre-reduction of γ-Fe2O3 by H2 on the synthesis of Fe3C powder from CH4

The present study aims to investigate effect of the extent of pre-reduction of γ-Fe2O3 (maghemite) on the synthesis of Fe3C (cementite). Initially, pre-reduced powders with oxygen contents of 12.36, 3.26 and 0.59wt.% were obtained at 800K in H2 atmosphere for 2.5, 5 and 10min, respectively. Carburization behaviors of these pre-reduced powders were then explored using undiluted CH4 at 800K. Mass change measurements, XRD and SEM analyses were used to characterize the samples. It was found that single Fe3C phase was obtained from the pre-reduced powders containing 3.26 and 0.59wt.% oxygen for carburization periods of 15 and 30min. The kinetic data for the carburization under pure CH4 indicates that there are essentially two successive distinct regimes: reduction of the remaining oxides and Fe3C formation. When the pre-reduced powder with oxygen contents of 3.26 and 0.59wt.% are used, CH4 pyrolysis rate suffices for the reduction of the remaining oxides and carburization. The pre-reduced powder with the highest oxygen (12.36wt.% oxygen) did not yield Fe3C, but iron and iron oxides, because the extent of the reduction by CH4 is found to be too small for such high oxygen content. It was postulated that the reduction product H2O vapor hinders the formation of Fe3C. The carburization process was discussed in terms of reaction pathways using equilibrium thermodynamic analysis and reaction kinetics.

Trimethylaluminum as the Metal Precursor for the Atomic Layer Etching of Al2O3 Using Sequential, Self-Limiting Thermal Reactions

Trimethylaluminum (TMA, Al(CH3)3) was used as the metal precursor, together with HF, for the atomic layer etching (ALE) of Al2O3 using sequential, self-limiting thermal reactions. Al2O3 ALE using TMA demonstrates that other metal precursors, in addition to Sn(acac)2, can be employed for Al2O3 ALE. The use of TMA for Al2O3 ALE is especially interesting because TMA can also be used for Al2O3 atomic layer deposition (ALD). Quartz crystal microbalance (QCM) experiments monitored Al2O3 ALE at temperatures from 250 to 325 °C. The Al2O3 ALE was linear versus the number of HF and TMA reaction cycles. The QCM studies showed that the sequential HF and TMA reactions were self-limiting versus reactant exposure. The Al2O3 etching rates increased at higher temperatures. The QCM analysis measured mass change per cycle (MCPC) values that varied from −4.2 ng/(cm2 cycle) at 250 °C to −23.3 ng/(cm2 cycle) at 325 °C. These MCPCs correspond to Al2O3 etch rates from 0.14 Å/cycle at 250 °C to 0.75 Å/cycle at 325 °C. X-ray reflectivity and spectroscopic ellipsometry analyses confirmed the linear removal of Al2O3 and etching rates. Fourier transform infrared spectroscopy measurements monitored Al2O3 ALE by observing the loss of infrared absorbance from Al–O stretching vibrations. Surface intermediates were also identified after the HF and TMA exposures. Al2O3 ALE with TMA is believed to occur by the reaction Al2O3 + 4Al(CH3)3 + 6HF → 6AlF(CH3)2 + 3H2O. The proposed mechanism involves fluorination and ligand-exchange reactions. The HF exposure fluorinates the Al2O3 and forms an AlF3 surface layer and H2O as a volatile reaction product. During the ligand-exchange transmetalation reaction, TMA accepts F from the AlF3 surface layer and donates CH3 to produce volatile AlF(CH3)2 reaction products. The QCM measurements were consistent with an AlF3 surface layer thickness of 3.0 Å on Al2O3 after the HF exposures. The larger etch rates at higher temperatures were attributed to the removal of a larger fraction of the AlF3 surface layer by TMA exposures at higher temperatures.

Durability and mechanical properties of C–S–H/nitrobenzoic acid composite systems

The influence of nitrobenzoic acid on the nanostructure of calcium-silicate-hydrate (C–S–H) systems has been recently investigated by the authors. This study focuses on the assessment of durability and mechanical performance of the C–S–H/nitrobenzoic acid composite systems. In this context different nitrobenzoic acid isomers in various concentrations were studied. The C–S–H-based preparations were compacted into porous bodies. Their dimensional stability and the leaching of calcium ions in aqueous salt solutions containing Mg2+, Li+, Cl− or SO42− ions were evaluated. The resistance of the compacted samples to the diffusion of isopropyl alcohol was also obtained by the mass-change measurements. The microindentation technique was used to measure the creep modulus and the hardness of the samples. Evidence was obtained that nitrobenzoic acid has the potential to significantly improve the durability and mechanical properties of the C–S–H systems. This improvement, however, only occurred in the systems with the lower concentration of nitrobenzoic acid. The systems with higher concentration of nitrobenzoic acid had reduced durability and mechanical performance due to the limited interaction of the organic and inorganic phases in these systems.

Deposition in the inner and outer corners of the JET divertor with carbon wall and metallic ITER-like wall

Rotating collectors and quartz microbalances (QMBs) are used in JET to provide time-dependent measurements of erosion and deposition. Rotation of collector discs behind apertures allows recording of the long term evolution of deposition. QMBs measure mass change via the frequency deviations of vibrating quartz crystals. These diagnostics are used to investigate erosion/deposition during JET-C carbon operation and JET-ILW (ITER-like wall) beryllium/tungsten operation. A simple geometrical model utilising experimental data is used to model the time-dependent collector deposition profiles, demonstrating good qualitative agreement with experimental results. Overall, the JET-ILW collector deposition is reduced by an order of magnitude relative to JET-C, with beryllium replacing carbon as the dominant deposit. However, contrary to JET-C, in JET-ILW there is more deposition on the outer collector than the inner. This reversal of deposition asymmetry is investigated using an analysis of QMB data and is attributed to the different chemical properties of carbon and beryllium.

Fracture and thermal aging of resin‐filled silicone elastomers

ABSTRACTThe role of nano‐sized resin fillers on the fracture and viscoelastic behavior of silicones was examined in the context of thermal aging. Systems with different resin volume fractions and resin glass transition temperatures were compared. X‐ray scattering patterns were collected over a wide range of q‐values in order to provide insight into the physical structure of the silicone elastomers. Additionally, tensile, dynamic mechanical, and fracture tests were performed. Temperature shift factors obtained from the dynamic mechanical data were used to obtain master plots of the fracture toughness as a function of reduced crack velocity. The elastic modulus for each of the materials increased as a function of thermal aging time, and the high‐temperature fracture behavior for each of the systems was reduced to values characteristic of unfilled systems after 14 days of aging at 200 °C. In order to obtain an accurate representation of the viscoelastic response of the materials in the megahertz frequency regime, quartz crystal resonators were used to measure mass changes and rheological properties after thermal aging. The results are consistent with a simple picture of dynamic heterogeneity, where high toughness requires that regions with different dynamic properties exist within the sample. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 263–273

Characterisation of Oxide Coatings Produced on Aluminium by PEO at Different Frequencies of Pulsed Current

The Plasma Electrolytic Oxidation (PEO) is a surface modification process that allows producing protective oxide coatings on light metal alloys. These coatings are characterized by high microhardness and wear resistance. Changes of electrical conditions of alternate current during process, such as duration and frequency of anodic and cathodic pulses, influence on layer growth rate, its microstructure and final properties. In this study aluminium samples were oxidized at different electrical parameters in sodium silicate electrolyte. The growth rates of oxide layers were determined by mass change and thickness measurements. The microstructure of the obtained coatings was investigated by using scanning electron microscope. Additionally, phase compositions of coatings was determined by X-ray diffraction on top surfaces of layers. Generally, shorter duration and higher frequency of anodic pulses provides more uniform structure at lower growth rate. Nevertheless, there are certain ranges of electrical parameters that provide decent uniformity of oxide coatings.

Antitumor effect of recombinant human endostatin combined with cisplatin on rats with transplanted Lewis lung cancer.

To observe the antitumor effect and mechanism of recombinant human endostatin (Endostar) injection in tumor combined with intraperitoneal injection of cisplatin on subcutaneous transplanted Lewis lung cancer in rats. A total of 30 C57 rats were selected, and the monoplast suspension of Lewis lung cancer was injected into the left axilla to prepare the subcutaneous transplanted tumor models in the axilla of right upper limb. The models were randomly divided into Groups A, B, and C. Medication was conducted when the tumor grew to 400mm(3). Group A was the control group without any interventional treatment. Group B was injected with Endostar 5mgkg(-1)d(-1) for 10d. Group C was given the injection of Endostar 5mgkg(-1)d(-1) combined with intraperitoneal injection of cisplatin 5mgkg(-1)d(-1) for 10d. All the rats in three groups were executed the day after the 10 d medication and the tumor was taken off for measurement of volume and mass changes and calculation of antitumor rate, after which the vascular endothelial growth factor (VEGF) concentration in rats' plasma was determined by ELISA. The tumor tissues were cut for the preparation of conventional biopsies. After hematoxylin-eosin staining, the pathologic histology was examined to observe the structures of tumor tissues, VEGF score and microvessel density (MVD) in each group. The volume and mass of tumor in Groups B and C were significantly lower than Group A (P<0.05) while the tumor volume and mass in Group C were significantly lower than Group B (P<0.05). The antitumor rate in Group C was significantly higher than Group B (P<0.05), but the tumor VEGF score, MVD and plasma VEGF level in Group C were significantly lower than Groups A and B (P<0.05). In Group B, the tumor VEGF score, MVD and plasma VEGF level were significantly lower than Group A (P<0.05). The microscopic image of Group C showed that its number of active tumor cells and the blood capillary around tumor was significantly smaller than that of Groups A and B, and meanwhile atrophy and liquefactive necrosis were seen in local tumor. Endostar injection combined with intraperitoneal injection of cisplatin is effective in reducing tumor VEGF score and MVD of transplanted tumor tissues in rats with Lewis lung cancer to obstruct the nutrient supply of tumor cells and kill tumor cells, so that the inhibition of tumor cell proliferation and metastasis can be achieved with a remarkable effect.

Mechanistic analysis of PLGA/HPMC-based in-situ forming implants for periodontitis treatment

In-situ forming implant formulations based on poly(lactic-co-glycolic acid) (PLGA), acetyltributyl citrate (ATBC), minocycline HCl, N-methyl pyrrolidone (NMP) and optionally hydroxypropyl methylcellulose (HPMC) were prepared and thoroughly characterized in vitro. This includes electron paramagnetic resonance (EPR), nuclear magnetic resonance (1H NMR), mass change and drug release measurements under different conditions, optical microscopy, size exclusion chromatography (SEC) as well as antibacterial activity tests using gingival crevicular fluid samples from periodontal pockets of periodontitis patients. Based on these results, deeper insight into the physico-chemical phenomena involved in implant formation and the control of drug release could be gained. For instance, the effects of adding HPMC to the formulations, resulting in improved implant adherence and reduced swelling, could be explained. Importantly, the in-situ formed implants effectively hindered the growth of bacteria present in the patients’ periodontal pockets. Interestingly, the systems were more effectively hindering the growth of pathogenic bacterial strains (e.g., Fusobacterium nucleatum) than that of strains with a lower pathogenic potential (e.g., Streptococcus salivarius). In vivo, such a preferential action against the pathogenic bacteria can be expected to give a chance to the healthy flora to re-colonize the periodontal pockets.

Effect of GIA models with 3D composite mantle viscosity on GRACE mass balance estimates for Antarctica

Seismic data indicate that there are large viscosity variations in the mantle beneath Antarctica. Consideration of such variations would affect predictions of models of Glacial Isostatic Adjustment (GIA), which are used to correct satellite measurements of ice mass change. However, most GIA models used for that purpose have assumed the mantle to be uniformly stratified in terms of viscosity. The goal of this study is to estimate the effect of lateral variations in viscosity on Antarctic mass balance estimates derived from the Gravity Recovery and Climate Experiment (GRACE) data. To this end, recently-developed global GIA models based on lateral variations in mantle temperature are tuned to fit constraints in the northern hemisphere and then compared to GPS-derived uplift rates in Antarctica.We find that these models can provide a better fit to GPS uplift rates in Antarctica than existing GIA models with a radially-varying (1D) rheology. When 3D viscosity models in combination with specific ice loading histories are used to correct GRACE measurements, mass loss in Antarctica is smaller than previously found for the same ice loading histories and their preferred 1D viscosity profiles. The variation in mass balance estimates arising from using different plausible realizations of 3D viscosity amounts to 20 Gt/yr for the ICE-5G ice model and 16 Gt/yr for the W12a ice model; these values are larger than the GRACE measurement error, but smaller than the variation arising from unknown ice history. While there exist 1D Earth models that can reproduce the total mass balance estimates derived using 3D Earth models, the spatial pattern of gravity rates can be significantly affected by 3D viscosity in a way that cannot be reproduced by GIA models with 1D viscosity. As an example, models with 1D viscosity always predict maximum gravity rates in the Ross Sea for the ICE-5G ice model, however, for one of the three preferred 3D models the maximum (for the same ice model) is found near the Weddell Sea. This demonstrates that 3D variations in viscosity affect the sensitivity of present-day uplift and gravity rates to changes in the timing of the ice history. In particular, low viscosities (<1019 Pas) found in West Antarctica make the mantle very sensitive to recent changes in ice thickness.

Long Term Investigation on Sulphate Resistance of Concrete Containing Laterite Aggregate

Utilization of laterite rock at 20% as partial aggregate replacement in concrete production is seen as one of the alternative to reduce the high dependency of concrete industry on granite aggregate supply and preserve this natural resource for future generation. This paper reports the durability performance of concrete containing laterite aggregate upon sulphate attack. A reference mix, plain concrete consisting 100% granite aggregate and another one mix containing 20% laterite aggregate as partial coarse aggregate replacement were used. All specimens were prepared in cubes of (100×100×100mm) and subjected to water curing for 28 days. After that, the specimens were immersed in Magnesium Sulphate solution for a period of 50 weeks. The durability of the concrete mixes was determined through measurement of mass change and residual compressive strength. The compressive strength test was conducted following the procedures in BSEN 12390 – 3. Upon exposure in sulphate environment, reaction between sulphate ions and portlandite which formed gypsum contributes to concrete expansion and disintegration causing strength reduction in both specimens. Owing to the small difference in total mass loss and residual compressive strength between the two mixes, it is concluded that the sulphate resistance of laterite concrete is comparable to plain concrete.

High‐Temperature Na2SO4 Deposit‐Assisted Corrosion of Silicon Carbide – I: Temperature and Time Dependence

Time and temperature dependence of Na2SO4‐induced hot corrosion were studied for sintered‐α (Hexoloy) as well as CVD‐SiC at temperatures between 900°C and 1100°C and at times from 0.75 to 96 h. The extent of corrosion was quantified using mass change measurements, removal of corrosion products using sequential water, HCl, and HF dissolution steps followed by ICP‐OES analysis, and by optical profilometry of corroded materials to characterize pitting on the sample surface. In addition, SEM, EDS, and XRD were used to better understand the morphology, distribution, and phase composition of corrosion products. It was found that hot corrosion of Hexoloy was more severe than that of high‐purity CVD‐SiC. Hot corrosion is initially rapid until a continuous silica layer is formed underneath the mixed silicate layer. Once a continuous silica layer was formed the temperature dependence of the corrosion rate was consistent with diffusion of oxygen through the silica layer.

Passive measurement of progressive mass change via bifurcation sensing with a multistable micromechanical system

Mass sensing using the onset and crossing of a dynamic bifurcation of a micromechanical system has been shown to reduce the mass threshold which may be detected and exhibited improved robustness to damping and noise compared to traditional tracking of resonant frequency shift. Previous investigations demonstrated that mass measurement over time via actively controlled strategies or explored passively operated threshold-type methods to indicate a pre-determined mass was adsorbed. Recently, an alternative idea integrating aspect of frequency shift- and bifurcation-based mass sensors and methods was proposed, providing initial illustration of a noteworthy ability to passively quantify progressive mass adsorption due to sequentially activated bifurcations. To advance the state of the art, this research provides a thorough investigation of this new sensing concept in terms of its dynamic characteristics and devises guidelines for effective, reliable operations. The conceptual foundation of the sensing method and an experimentally validated sensor model are reviewed. The results of numerous simulated operational trials and parametric investigations are detailed to reach important conclusions on sensor operations and versatility, and to uncover the influences of key operational conditions upon detection metrics. Finally, suitable microscale sensor architectures and fabrications are described to exemplify the flexibility of successfully realizing the mass sensing strategy.

Resistance of concrete and mortar against combined attack of chloride and sodium sulphate

Marine environments are typically aggressive to concrete structures, since sea water contains high concentrations of chlorides and sulphates. To improve predictions of concrete durability within such environments, it is important to understand the attack mechanisms of these ions in combination.In this research, the reciprocal influence of Cl− and SO42− was investigated for four mixtures, namely with Ordinary Portland Cement, High Sulphate Resistant cement, and with Blast-Furnace Slag (50% and 70% cement replacement). Chloride penetration depths and diffusion coefficients were measured to investigate the influence of SO42− on Cl− attack. Besides, length and mass change measurements were performed to examine the influence of Cl− on SO42− attack. Since the formation of ettringite, gypsum and Friedel’s salt plays an important role, XRD-analyses were done additionally.It can be concluded that chloride penetration increases when the sulphate content increases at short immersion periods, except for HSR concrete. Concerning the sulphate attack, the presence of chlorides has a mitigating effect.

Incipient subsurface heterogeneity and its effect on overland flow generation – insight from a modeling study of the first experiment at the Biosphere 2 Landscape Evolution Observatory

Abstract. Evolution of landscape heterogeneity is controlled by coupled Earth system dynamics, and the resulting process complexity is a major hurdle to cross towards a unified theory of catchment hydrology. The Biosphere 2 Landscape Evolution Observatory (LEO), a 334.5 m2 artificial hillslope built with homogeneous soil, may have evolved into heterogeneous soil during the first experiment driven by an intense rainfall event. The experiment produced predominantly seepage face water outflow, but also generated overland flow, causing superficial erosion and the formation of a small channel. In this paper, we explore the hypothesis of incipient heterogeneity development in LEO and its effect on overland flow generation by comparing the modeling results from a three-dimensional physically based hydrological model with measurements of total mass change and seepage face flow. Our null hypothesis is that the soil is hydraulically homogeneous, while the alternative hypothesis is that LEO developed downstream heterogeneity from transport of fine sediments driven by saturated subsurface flow. The heterogeneous case is modeled by assigning saturated hydraulic conductivity at the LEO seepage face (Ksat,sf) different from that of the rest (Ksat). A range of values for Ksat, Ksat,sf, soil porosity, and pore size distribution is used to account for uncertainties in estimating these parameters, resulting in more than 20 000 simulations. It is found that the best runs under the heterogeneous soil hypothesis produce smaller errors than those under the null hypothesis, and that the heterogeneous runs yield a higher probability of best model performance than the homogeneous runs. These results support the alternative hypothesis of localized incipient heterogeneity of the LEO soil, which facilitated generation of overland flow. This modeling study of the first LEO experiment suggests an important role of coupled water and sediment transport processes in the evolution of subsurface heterogeneity and on overland flow generation, highlighting the need of a coupled modeling system that integrates across disciplinary processes.

Analysis of D2-law in case of Leidenfrost drop evaporation

An experimental method to measure the heat transfer between a hot surface and a drop under Leidenfrost regime is reported. The phenomenon concerns large water drops with initial mass of ∼1g that evaporate under ambient pressure. The test facility allows measurement of the instantaneous mass change of the evaporating drop located on surface at constant temperature. Both thermal and video cameras register the size of a drop for further calculation of its bottom area. On the basis of the energy balance, the evaporative heat flux is calculated. Its power dependence on the drop orthogonal projection area on the heating surface is found. In the linear range of D2-law, an analytical solution of the energy balance is given and its validity is discussed. The improvement in accuracy by the second order polynomial approximation for drop area is suggested and consequently D2-law in the form of quadratic function. But in this case, the numerical calculation is necessary. The main factors of measurement uncertainty are also discussed. It is pointed out that the electronic scales accuracy and the resolution of camera are the most important factors affecting the accuracy.