Tetrel bonds between PySiX3 and some nitrogenated bases: Hybridization,substitution, and cooperativity

Ab initio calculations have been performed to study the influence of hybridization, substitution, and cooperativity on the tetrel bond in the complexes of PySiX₃ (Py = pyridine and X = halogen). The tetrel bond becomes stronger in the order of p-PySiF₃⋯NCH(sp) < p-PySiF₃⋯NHCH₂(sp²) < p-PySiF₃⋯NH₃(sp³). The electron-donating group in the electron donor strengthens the tetrel bond, and this effect is mainly achieved through electrostatic and polarization interactions. Tetrel bonding displays cooperative effects with triel bonding and chalcogen bonding, characterized by shorter binding distances and greater electron densities. The cooperative effects between triel/chalcogen bond and tetrel bond have been analyzed by molecular electrostatic potentials and charge transfer. Energy decomposition indicates that many-body effects are mainly caused by polarization energy. The geometries of Si⋯N interaction and its applications in crystal materials have been characterized and evidenced by a CSD research.     

Fabrication and characterization of Pb-free transparent dielectric layer for plasma display panel

Glasses within the Bi₂O₃–B₂O₃–BaO–ZnO system were examined as potential replacements for PbO-based glass frits with low firing temperatures. These frits are used in the transparent dielectric layer of plasma display panels (PDP). The glass transition temperature (T_g) of the prepared glasses varied between 450 and 460 °C. These glasses display dynamic dielectric properties, high transparency and thermal expansion as well as matching well with substrate glass. The thermal coefficient of expansion (TCE) was with the desired range of 81–86×10⁻⁷/K. Moreover, when the screen printed film was heat-treated at 570 °C for 30 min, optical transmittance (83%), root-mean square (rms) roughness (177.6 Å), dielectric constant (10.25) and withstand voltage (4.15 kV) satisfied the requirements necessary for transparent dielectric layers to be used in PDP applications.     

Research on low-temperature anodic bonding using induction heating

A novel low-temperature anodic bonding process using induction heating is presented in this paper. Anodic bonding between silicon and glass (Pyrex 7740) has been achieved at temperature below 300 °C and almost bubble-free interfaces have been obtained. A 1 kW 400 kHz power supply is used to induce heat in graphite susceptors (simultaneously as the high-voltage electrodes of anodic bonding), which conduct heat to the bonding pair and permanently join the pair in 5 min. The results of pull tests indicate a bonding strength of above 5.0 MPa for induction heating, which is greater than the strength for resistive heating at the same temperature. The fracture mainly occurs inside the glass or across the interface other than in the interface when the bonding temperature is over 200 °C. Finally, the interfaces are examined and analyzed by scanning electron microscopy (SEM) and the bonding mechanisms are discussed.     

Cationic P⋯N interaction in XH3P+⋯NCY complexes (X = H,F, CN,NH2, OH; Y = H,Li, F,Cl) and its cooperativity with hydrogen/lithium/halogen bond

The geometries, interaction energies and bonding properties of cationic pnicogen bond (CPB) interactions are studied in binary XH₃P⁺⋯NCY (X = H, F, CN, NH₂, OH; Y = H, Li, F, Cl) complexes by means of MP2/aug-cc-pVTZ calculations. Interaction energies of these binary complexes span a large range, from −16.36 kcal/mol in (NH₂)H₃P⁺⋯NCF to −71.36 kcal/mol in FH₃P⁺⋯NCLi complex. The spin–spin coupling constant across P⋯N interaction depends considerably on the nature of X and Y substituents. The characteristic of CPB interactions is analyzed in terms of parameters derived from quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) analyses. The charge transfer from the nitrogen base to the cationic acid stabilizes these pnicogen–bonded complexes. For a given XH₃P⁺, the net charge transfer value increases as the interaction energy of the complex becomes more negative, i.e., NCLi > NCCl > NCH > NCF. Moreover, mutual influence between the CPB and hydrogen/halogen/lithium bond is studied in the ternary XH₃P⁺⋯NCY⋯NCH complexes. The results indicate that the formation of a Y⋯N interaction tends to strengthen CPB in the ternary systems.     

DFT study on X−·(H2O)n=1-10 (X = OH,NO2, NO3, CO3) anionic water cluster

A theoretical study to understand the interaction between anion and the water molecules through the hydration (X⁻·(H₂O)_n (X = OH, NO₂, NO₃, CO₃), where n = 1–10), using the density functional theory method with B3LYP functional and 6-311++G(d,p) basis set has been carried out systematically. In these hydrated clusters we notice three different cases of bond arrangements, namely, symmetrical double hydrogen bond, single hydrogen bond and inter-water hydrogen bond. All the complexes are dominated by the OH⋯O hydrogen bond, in which the anion act as a proton acceptor, while the water molecule act as a proton donor. A linear correlation is obtained between the solvent stabilization energy and the size (n) of the hydrated cluster for all the anions. The weighted average interaction energy values, shows that the water molecules strongly bind with the OH⁻ anion. Besides, the solvation of the OH⁻ anion requires less number of water molecules when compared with the other anions. Energy decomposition analysis (EDA) shows the strong dominance of the electrostatic energy component within the interaction energy. The total NPA charges on the anions indicate an increase in the solvation due to hydration. From AIM analysis, excellent linear inverse correlation is observed for both the electron density and Laplacian of the electron density with respect to the hydrogen bond length. Natural bonding orbital analysis (NBO) predicts large charge transfer between the OH⁻ anion and the water molecules.     

Spin-valve planar Hall sensor for single bead detection

The planar Hall effect (PHE) sensor with a junction size of 3 μm × 3 μm for a single micro-bead detection has been fabricated successfully using a typical spin-valve thin film Ta(5)/NiFe(16)/Cu(1.2)/NiFe(2)/IrMn(15)/Ta(5) nm. The PHE sensor exhibits a sensitivity of about 7.2 μV Oe^?1 in the magnetic field range of ±7 Oe approximately. We have performed an experiment to illustrated the possibility of single micro-bead detection by using a PHE sensor. A single micro-bead of 2.8 μm diameter size is secluded from 0.1% dilute solution of the Dynabeads^® M-280 dropped on the sensor surface and is located on the sensor junction by using a micro magnetic needle. The comparison of the PHE voltage profiles in the field range from 0 to 20 Oe in the absence and presence of a single micro-bead identifies a single Dynabeads^® M-280, the maximal signal change as large as ΔV ～ 1.1 μV can be obtained at the field ～6.6 Oe. The results are well described in terms of the reversal of a basic single domain structure.     

Theoretical studies on kinetics,mechanism and thermochemistry of gas-phase reactions of HFE-449mec-f with OH radicals and Cl atom

A theoretical study on the mechanism and kinetics of the gas phase reactions of CF₃CHFCF₂OCH₂CF₃ (HFE-449mec-f) with the OH radicals and Cl atom have been performed using meta-hybrid modern density functional M06-2X using 6-31+G(d,p) basis set. Two conformers have been identified for CF₃CHFCF₂OCH₂CF₃ and the most stable one is considered for detailed study. Reaction profiles for OH-initiated hydrogen abstraction are modeled including the formation of pre-reactive and post-reactive complexes at entrance and exit channels. Our calculations reveal that hydrogen abstraction from the CH₂ group is thermodynamically and kinetically more facile than that from the CHF group. Using group-balanced isodesmic reactions, the standard enthalpies of formation for HFE-449mecf and radicals generated by hydrogen abstraction, are also reported. The calculated bond dissociation energies for CH bonds are in good agreement with experimental results. The rate constants of the two reactions are determined for the first time in a wide temperature range of 250–450 K. The calculated rate constant values are found to be 9.10 × 10⁻¹⁵ and 4.77 × 10⁻¹⁷ cm³ molecule⁻¹ s⁻¹ for reactions with OH radicals and Cl atom, respectively. At 298 K, the total calculated rate coefficient for reactions with OH radical is in good agreement with the experimental results. The atmospheric life time of HFE-449mec-f is estimated to be 0.287 years.     

Enhancement of second-order nonlinear optical response in boron nitride nanocone: Li-doped effect

The unusual properties of Li-doped boron nitride nanomaterials have been paid further attention due to their wide applications in many promising fields. Here, density functional theory (DFT) calculations have been carried out to investigate the second-order nonlinear optical (NLO) properties of boron nitride nanocone (BNNC) and its Li-doped BNNC derivatives. The natural bond orbital charge, electron location function, localized orbital locator and frontier molecular orbital analysis offer further insights into the electron density of the Li-doped BNNC derivatives. The electron density is effectively bounded by the Li atom and its neighboring B atoms. The Li-doped BNNC molecules exhibit large static first hyperpolarizabilities (β_tot) up to 1.19 × 10³ a.u. for Li@2N-BNNC, 5.05 × 10³ a.u. for Li@2B-BNNC, and 1.08 × 10³ a.u. for Li@BN-BNNC, which are significantly larger than that of the non-doped BNNC (1.07 × 10² a.u.). The further investigations show that there are clearly dependencies of the first hyperpolarizabilities on the transition energies and oscillator strengths. Moreover, time-dependent DFT results show that the charge transfer from BNNC to Li atom becomes more pronounced as doping the Li atom to BNNC. It is also found that the frequency-dependent effect on the first hyperpolarizabilities is weak, which may be beneficial to experimentalists for designing Li-doped BNNC molecules with large NLO responses.     

The effect of sinusoidal rolling ground motion on lifting biomechanics

The objective of this study was to quantify the effects of ground surface motion on the biomechanical responses of a person performing a lifting task. A boat motion simulator (BMS) was built to provide a sinusoidal ground motion (simultaneous vertical linear translation and a roll angular displacement) that simulates the deck motion on a small fishing boat. Sixteen participants performed lifting, lowering and static holding tasks under conditions of two levels of mass (5 and 10 kg) and five ground moving conditions. Each ground moving condition was specified by its ground angular displacement and instantaneous vertical acceleration: A): +6°, −0.54 m/s²; B): +3°, −0.27 m/s²; C): 0°, 0 m/s²; D): −3°, 0.27 m/s²; and E): −6°, 0.54 m/s². As they performed these tasks, trunk kinematics were captured using the lumbar motion monitor and trunk muscle activities were evaluated through surface electromyography. The results showed that peak sagittal plane angular acceleration was significantly higher in Condition A than in Conditions C, D and E (698°/s² vs. 612–617°/s²) while peak sagittal plane angular deceleration during lowering was significantly higher in moving conditions (conditions A and E) than in the stationary condition C (538–542°/s² vs. 487°/s²). The EMG results indicate that the boat motions tend to amplify the effects of the slant of the lifting surface and the external oblique musculature plays an important role in stabilizing the torso during these dynamic lifting tasks.     

Perchlorate-selective polymeric membrane electrode based on a cobaloxime as a suitable carrier

A cobaloxime ([chlorobis(dimethylglyoximeato)(triphenylphosphine)] cobalt (III), [Co(dmgH)₂pph₃Cl]) incorporated in a plasticized poly(vinyl chloride) membrane was used to develop a perchlorate-selective electrode. The influence of membrane composition on the electrode response was studied. The electrode exhibits a Nernstian response over the perchlorate concentration range 1.0 × 10⁻⁶ to 1 × 10⁻¹ mol l⁻¹ with a slope of −56.8 ± 0.7 mV per decade of concentration, a detection limit of 8.3 × 10⁻⁷, a wide working pH range (3–10) and a fast response time (<15 s). The electrode shows excellent selectivity towards perchlorate with respect to many common anions. The electrode was used to determine perchlorate in water and human urine.     

A micro shear stress sensor based on laterally aligned carbon nanotubes

This paper reports the development of a micro thermal shear stress sensor that utilizes multiwalled carbon nanotubes as the sensing element. The sensor was fabricated by laterally aligning randomly distributed nanotubes into a 360 μm long and 90 μm wide conductive trace between two triangular shaped micro electrodes through the use of a high frequency AC electric field. During operation, the aligned nanotubes are electrically heated to an elevated temperature and surface shear stress is measured indirectly by the amount of convective heat transfer from the heated nanotubes to the surrounding fluid flow.The nanotube alignment process was primarily controlled by three different phenomena: dielectrophoresis, joule heating, and Brownian motion. Numerical simulations, together with experimental verifications, indicated that a successful alignment could only be realized if: (1) the dielectrophoretic force was positive, (2) the electro-thermal force was also positive, and (3) the dielectrophoretic force was high enough to overcome Brownian motion. The aligned nanotube trace has a room-temperature resistance of 580 Ω, which corresponds to a conductivity of 2.7 × 10⁴ S/m. The absolute temperature coefficient of resistivity ranges from 0.01 to 0.04% °C⁻¹. This is about one order of magnitude smaller than the highly doped polysilicon sensing material used in the MEMS micro shear stress sensor. The shear stress sensitivity of the nanotube trace operated at a 3% overheat ratio is found to follow the theoretical sensor power ∝ (shear stress)^1/3 relationship, provided the shear stress level is higher than 0.34 mPa. This result confirms the feasibility of using aligned multi-walled carbon nanotubes as a thermal shear stress sensing material.     

Revealing halogen bonding interactions with anomeric systems: An ab initio quantum chemical studies

A computational study has been performed using MP2 and CCSD(T) methods on a series of O⋯X (X = Br, Cl and I) halogen bonds to evaluate the strength and characteristic of such highly directional noncovalent interactions. The study has been carried out on a series of dimeric complexes formed between interhalogen compounds (such as BrF, BrCl and BrI) and oxygen containing electron donor molecule. The existence and consequences of the anomeric effect of the electron donor molecule has also been investigated through an exploration of halogen bonding interactions in this halogen bonded complexes. The ab initio quantum chemical calculations have been employed to study both the nature and directionality of the halogen molecules toward the sp³ oxygen atom in anomeric systems. The presence of anomeric n_O → σ*_CN interaction involves a dominant role for the availability of the axial and equatorial lone pairs of donor O atom to participate with interhalogen compounds in the halogen-bonded complexes. The energy difference between the axial and equatorial conformers with interhalogen compounds reaches up to 4.60 kJ/mol, which however depends upon the interacting halogen atoms and its attaching atoms. The energy decomposition analysis further suggests that the total halogen bond interaction energies are mainly contributed by the attractive electrostatic and dispersion components. The role of substituents attached with the halogen atoms has also been evaluated in this study. With the increase of halogen atom size and the positive nature of σ-hole, the halogen atom interacted more with the electron donor atom and the electrostatic contribution to the total interaction energy enhances appreciably. Further, noncovalent interaction (NCI) studies have been carried out to locate the noncovalent halogen bonding interactions in real space.     

Electrochemical determination of ascorbic acid in fruits on a vanadium oxide polypropylene carbonate modified electrode

A novel vanadium oxide polypropylene carbonate modified glassy carbon electrode was developed and used for the measurement of ascorbic acid (AA). The electrode was prepared by casting a mixture of vanadium tri(isopropoxide) oxide (VO(OC₃H₇)₃) and poly(propylene carbonate) (PPC) onto the surface of a glassy carbon electrode. The electrochemical behavior of the VO(OC₃H₇)₃–PPC film modified glassy carbon electrode was investigated by cyclic voltammetry and amperometry. This modified electrode exhibited electrocatalytic response to the oxidation of ascorbic acid. Compared with a bare glassy carbon electrode, the modified electrode exhibits a 220 mV shift of the oxidation potential of ascorbic acid in the cathodic direction and a marked enhancement of the current response. The response current revealed a good linear relationship with the concentration of ascorbic acid in the range of 4 × 10⁻⁸ and 1 × 10⁻⁴ mol L⁻¹ and the detection limit of 1.5 × 10⁻⁸ mol L⁻¹ (S/N = 3) in the pH 8.06 Britton–Robinson solution. Quantitative recovery of the ascorbic acid in synthetic samples has been obtained and the interferences from different species have been studied. The method has been successfully applied to the determination of ascorbic acid in fruits. The concentrations of ascorbic acid measured by this method are in good agreement with the literature value. It is much promising for the modified films to be used as an electrochemical sensor for the detection of ascorbic acid.     

A mechanistic approach to explore novel HDAC1 inhibitor using pharmacophore modeling, 3D- QSAR analysis,molecular docking,density functional and molecular dynamics simulation study

Deregulated epigenetic activity of Histone deacetylase 1 (HDAC1) in tumor development and carcinogenesis pronounces it as promising therapeutic target for cancer treatment. HDAC1 has recently captured the attention of researchers owing to its decisive role in multiple types of cancer. In the present study a multistep framework combining ligand based 3D-QSAR, molecular docking and Molecular Dynamics (MD) simulation studies were performed to explore potential compound with good HDAC1 binding affinity. Four different pharmacophore hypotheses Hypo1 (AADR), Hypo2 (AAAH), Hypo3 (AAAR) and Hypo4 (ADDR) were obtained. The hypothesis Hypo1 (AADR) with two hydrogen bond acceptors (A), one hydrogen bond donor (D) and one aromatics ring (R) was selected to build 3D-QSAR model on the basis of statistical parameter. The pharmacophore hypothesis produced a statistically significant QSAR model, with co-efficient of correlation r² = 0.82 and cross validation correlation co-efficient q² = 0.70. External validation result displays high predictive power with r² (o) value of 0.88 and r² (m) value of 0.58 to carry out further in silico studies. Virtual screening result shows ZINC70450932 as the most promising lead where HDAC1 interacts with residues Asp99, His178, Tyr204, Phe205 and Leu271 forming seven hydrogen bonds. A high docking score (−11.17 kcal/mol) and lower docking energy −37.84 kcal/mol) displays the binding efficiency of the ligand. Binding free energy calculation was done using MM/GBSA to access affinity of ligands towards protein. Density Functional Theory was employed to explore electronic features of the ligands describing intramolcular charge transfer reaction. Molecular dynamics simulation studies at 50 ns display metal ion (Zn)-ligand interaction which is vital to inhibit the enzymatic activity of the protein.     

Tuning the push–pull configuration for efficient second-order nonlinear optical properties in some chalcone derivatives

Using the density functional theory methods, we effectively tune the second-order nonlinear optical (NLO) properties in some chalcone derivatives. Various unique push–pull configurations are used to efficiently enhance the intramolecular charge transfer process over the designed derivatives, which result in significantly larger amplitudes of the first hyperpolarizability as compared to their parent molecule. The ground state molecular geometries have been optimized using B3LYP/6-311G** level of theory. A variety of methods including B3LYP, CAM-B3LYP, PBE0, M06, BHandHLYP and MP2 are tested with 6-311G** basis set to calculate the first hyperpolarizability of parent system 1. The results of M06 are found closer to highly correlated MP2 method, which has been selected to calculate static and frequency dependent first hyperpolarizability amplitudes of all selected systems. At M06/6-311G** level of theory, the permanent electronic dipole moment (μ_tot), polarizability (α₀) and static first hyperpolarizability (β_tot) amplitudes for parent system 1 are found to be 5.139 Debye, 274 a. u. and 24.22 × 10⁻³⁰ esu, respectively. These amplitudes have been significantly enhanced in designed derivatives 2 and 3. More importantly, the (β_tot) amplitudes of systems 2 and 3 mount to 75.78 × 10⁻³⁰ and 128.51 × 10⁻³⁰ esu, respectively, which are about 3 times and 5 times larger than that of their parent system 1. Additionally, we have extended the structure-NLO property relationship to several newly synthesized chalcone derivatives. Interestingly, the amplitudes of dynamic frequency dependent hyperpolarizability μβ_ω (SHG) are also significantly larger having values of 366.72 × 10⁻⁴⁸, 856.32 × 10⁻⁴⁸ and 1913.46 × 10⁻⁴⁸ esu for systems 1–3, respectively, at 1400 nm of incident laser wavelength. The dispersion behavior over a wide range of change in wavelength has also been studied adopting a range of wavelength from 1907 to 544 nm. Thus, the present work realizes the potential of designed derivatives as efficient NLO-phores for modern NLO applications.     

Mechanical design and characterization of a resonant magnetic field microsensor with linear response and high resolution

A resonant magnetic field microsensor based on Microelectromechanical Systems (MEMS) technology including a piezoresistive detection system has been designed, fabricated, and characterized. The mechanical design for the microsensor includes a symmetrical resonant structure integrated into a seesaw rectangular loop (700 μm × 450 μm) of 5 μm thick silicon beams. An analytical model for estimating the first resonant frequency and deflections of the resonant structure by means of Rayleigh and Macaulay's methods is developed. The microsensor exploits the Lorentz force and presents a linear response in the weak magnetic field range (40–2000 μT). It has a resonant frequency of 22.99 kHz, a sensitivity of 1.94 V T^?1, a quality factor of 96.6 at atmospheric pressure, and a resolution close to 43 nT for a frequency difference of 1 Hz. In addition, the microsensor has a compact structure, requires simple signal processing, has low power consumption (16 mW), as well as an uncomplicated fabrication process. This microsensor could be useful in applications such as the automotive sector, the telecommunications industry, in consumer electronic products, and in some medical applications.     

Chromium(III)-selective sensor based on tri-o-thymotide in PVC matrix

Tri-o-thymotide (I) has been used as an electroactive material in PVC (poly(vinyl chloride)) matrix for fabrication of chromium(III)-selective sensor. The membrane containing tri-o-thymotide, sodium tetraphenyl borate (NaTPB), dibutyl phthalate (DBP) and PVC in the optimum ratio 5:1:75:100 (w/w) exhibits a working concentration range of 4.0 × 10⁻⁶ to 1.0 × 10⁻¹ M with a Nernstian slope of 20.0 ± 0.1 mV/decade of activity in the pH range of 2.8–5.1. The detection limit of this sensor is 2.0 × 10⁻⁷ M. The electrode exhibits a fast response time of 15 s, shows good selectivity towards Cr³⁺ over a number of mono-, bi- and trivalent cations and can also be used in partially non-aqueous medium (up to 15%, v/v) also. The assembly has been successfully used as an indicator electrode in the potentiometric titration of chromium(III) against EDTA and also to determine Cr(III) quantitatively in electroplating industry waste samples.     

Simultaneous determination of epinephrine and ascorbic acid at the electrochemical sensor of triazole SAM modified gold electrode

The electrochemical sensor of triazole (TA) self-assembled monolayer (SAM) modified gold electrode (TA SAM/Au) was fabricated. The electrochemical behaviors of epinephrine (EP) at TA SAM/Au have been studied. The TA SAM/Au shows an excellent electrocatalytic activity for the oxidation of EP and accelerates electron transfer rate. The diffusion coefficient is 1.135 × 10⁻⁶ cm² s⁻¹. Under the optimum experiment conditions (i.e. 0.1 mol L⁻¹, pH 4.4, sodium borate buffer, accumulation time: 180 s, accumulation potential: 0.6 V, scan rate: 0.1 Vs⁻¹), the cathodic peak current of EP versus its concentration has a good linear relation in the ranges of 1.0 × 10⁻⁷ to 1.0 × 10⁻⁵ mol L⁻¹ and 1.0 × 10⁻⁵ to 6.0 × 10⁻⁴ mol L⁻¹ by square wave adsorptive stripping voltammetry (SWASV), with the correlation coefficient of 0.9985 and 0.9996, respectively. Detection limit is down to 1.0 × 10⁻⁸ mol L⁻¹. The TA SAM/Au can be used for the determination of EP in practical injection. Meantime, the oxidative peak potentials of EP and ascorbic acid (AA) are well separated about 200 ± 10 mV at TA SAM/Au, the oxidation peak current increases approximately linearly with increasing concentration of both EP and AA in the concentration range of 2.0 × 10⁻⁵ to 1.6 × 10⁻⁴ mol L⁻¹. It can be used for simultaneous determination of EP and AA.     

Effect of temperature on humido-sensitive conducting polymer actuators

Temperature dependence of water vapor sorption and electro-active polymer actuating behavior of free-standing films made of poly(3,4-ethylenedioxythiophene) doped with poly(4-styrenesulfonate) (PEDOT/PSS) was investigated by means of sorption isotherm and electromechanical analyses. The non-porous PEDOT/PSS film, having a specific surface area of 0.13 m² g^?1, sorbed water vapor of 1080 cm³(STP) g^?1, corresponding to 87 wt%, at relative water vapor pressure of 0.95. A temperature rise from 25 °C to 40 °C lowered sorption degree, indicative of an exothermic process, where isosteric heat of sorption decreased with increasing water vapor sorption and the value reached 43.9 kJ mol^?1, being consistent with the heat of water condensation (44 kJ mol^?1). Upon application of 10 V, the film underwent contraction of 2.46% at 5 °C caused by desorption of water vapor due to Joule heating, which slightly decreased to 2.10% at 45 °C. The speed of contraction was one order of magnitude faster than that of expansion and less dependent on the temperature since water vapor sorbed in the film were forced to desorb by Joule heating. In contrast, the higher the temperature the faster the film expansion because diffusion coefficient increased as the temperature became higher.     

Computer-based analysis of explicit approximations to the implicit Colebrook–White equation in turbulent flow friction factor calculation

The implicit Colebrook–White equation has been widely used to estimate the friction factor for turbulent fluid-flow in rough-pipes. In this paper, the state-of-the-art review for the most currently available explicit alternatives to the Colebrook–White equation, is presented. An extensive comparison test was established on the 20 × 500 grid, for a wide range of relative roughness (ε/D) and Reynolds number (R) values (1 × 10^?6 ? ε/D ? 5 × 10^?2; 4 × 10³ ? R ? 10⁸), covering a large portion of turbulent flow zone in Moody’s diagram. Based on the comprehensive error analysis, the magnitude points in which the maximum absolute and the maximum relative error are occurred at the pair of ε/D and R values, are observed. A limiting case of the most of these approximations provided friction factor estimates that are characterized by a mean absolute error of 5 × 10^?4, a maximum absolute error of 4 × 10^?3 whereas, a mean relative error of 1.3% and a maximum relative error of 5.8%, over the entire range of ε/D and R values, respectively. For practical purposes, the complete results for the maximum and the mean relative errors versus the 20 sets of ε/D value, are also indicated in two comparative figures. The examination results for error properties of these approximations gives one an opportunity to practically evaluate the most accurate formula among of all the previous explicit models; and showing in this way its great flexibility for estimating turbulent flow friction factor. Comparative analysis for the mean relative error profile revealed, the classification for the best-fitted six equations examined was in a good agreement with those of the best model selection criterion claimed in the recent literature, for all performed simulations.