Search Results (24)

This study introduces a modified computational scheme for handling linear and nonlinear fractal time-dependent partial differential equations. The method is constructed using three different stages that provide third-order accuracy in the fractal time variable. The stability of the approach is examined using scalar fractal models and Fourier analysis, while convergence is established for coupled convection–diffusion systems. The numerical algorithm is applied to analyze the mixed convective flow of a Carreau–Yasuda non-Newtonian fluid over stationary and oscillating plates under the influence of viscous dissipation and magnetic field effects. For spatial discretization, the incompressible continuity equation is handled by a first-order difference scheme, whereas higher-order compact schemes are implemented for the momentum, thermal, and concentration equations. The numerical findings show that increasing the Weissenberg number and magnetic field inclination reduces the velocity distribution. An accuracy assessment against existing numerical techniques demonstrates that the present method yields smaller computational errors, particularly when central difference schemes are used in space. In addition, a surrogate machine learning model is developed to predict the skin friction coefficient and local Nusselt number using Reynolds, Weissenberg, Prandtl, and Eckert numbers as input features. The predictive capability of the model is validated through Parity plots, bar charts for sensitivity analysis, scatter visualization, and Taylor Diagrams, confirming strong agreement with the numerical results. Full article

To investigate the influence of a second-phase mineral on the rheology of mantle peridotite, we conducted high-temperature deformation experiments on dry olivine–clinopyroxene (Ol-Cpx) aggregates. Cylindrical samples were manufactured using hot-isostatic pressing techniques, with Ol as the matrix phase and Cpx added at volume fractions of f_Cpx = 0.1, 0.3, and 0.5. Deformation experiments were performed in a Paterson gas-medium apparatus at a confining pressure of ~300 MPa, temperatures ranging from 1423 to 1523 K, and strain rates of ~5 × 10⁻⁶ s⁻¹, ~1 × 10⁻⁵ s⁻¹, ~2 × 10⁻⁵ s⁻¹, and ~5 × 10⁻⁵ s⁻¹. The stress exponents (n = 3.4–4.3) for two-phase aggregates are comparable to those reported for both pure Ol and pure Cpx, indicating that dislocation creep remains the dominant deformation mechanism. Increasing Cpx content does not induce a transition of dominant mechanism but leads to a slight decrease in activation energy, consistent with predictions from two-phase rheological models and reflecting the increasing contribution of Cpx to bulk deformation. Normalized flow stresses fall between the Ol and Cpx end-members within the Taylor–Sachs bounds, indicating moderate strain partitioning between phases. Aggregates with f_Cpx = 0.5 show slightly reduced strength and lower effective stress exponents. This is attributed to enhanced dynamic recrystallization, which triggers grain-size reduction and thereby increases the contribution of diffusion-assisted deformation, even though dislocation creep remains the dominant mechanism. These results suggest that under dry conditions, Cpx primarily modulates the rheology of olivine-rich aggregates through microstructural evolution and strain partitioning rather than by altering the dominant deformation mechanism. Full article

S235 low-carbon steel was boronized between 1123 K and 1273 K using a commercial powder mixture (Durborid) to study the formation and growth behavior of boride layers. The type of interface and thickness of the resulting layers were determined with scanning electron microscopy (SEM). The technique of X-ray diffraction (XRD) confirmed the formation of a predominantly single-phase Fe₂B layer under most processing conditions. To assess the diffusion behavior, the kinetic model with a Taylor series expansion was implemented to calculate the B diffusion coefficients in the Fe₂B layer under a transient diffusion regime. The B activation energy in Fe₂B was determined to be 157 kJ/mol, which aligns well with values derived from the literature. Full article

Hyaluronic acid (or hyaluronan) is a polysaccharide with therapeutic applications in dentistry due to its lubricating, anti-inflammatory, and antibacterial properties. This study evaluates the diffusion, conductivity, and viscosity of the sodium salt of HyH (that is, NaHy) with different molecular weights (124 kDa, 245 kDa, and 1800 kDa) in artificial saliva at pH 2.3, 4, 5, 6.8, and 8. Using the Taylor dispersion technique at 298.15 K, diffusion coefficients were determined and analyzed based on Fick’s second law equation. Results showed that NaHy diffusion was higher at acidic pH, particularly at pH 2.3, and decreased at pH 8, likely due to structural compaction in acidic conditions and expansion in alkaline media. The higher molecular weight of this polysaccharide exhibited greater diffusion and conductivity, suggesting an extended conformation that enhances mobility. These findings indicate that both pH and molecular weight significantly influence NaHy transport properties. Optimizing these parameters may enhance HA’s bioavailability and effectiveness in topical oral applications, improving its therapeutic potential in treating periodontal and oral conditions. Full article

A non-polynomial spline is a technique that utilizes information from symmetric functions to solve mathematical or physical models numerically. This paper introduces a novel non-polynomial spline construct incorporating a rational function term to develop an efficient numerical scheme for solving time-fractional differential equations. The proposed method is specifically applied to the time-fractional KdV–Burgers (TFKdV) equation. and time-fractional differential equations are crucial in physics as they provide a more accurate description of various complex processes, such as anomalous diffusion and wave propagation, by capturing memory effects and non-local interactions. Using Taylor expansion and truncation error analysis, the convergence order of the numerical scheme is derived. Stability is analyzed through the Fourier stability criterion, confirming its conditional stability. The accuracy and efficiency of the rational non-polynomial spline (RNPS) method are validated by comparing numerical results from a test example with analytical and previous solutions, using norm errors. Results are presented in $2D$ and $3D$ graphical formats, accompanied by tables highlighting performance metrics. Furthermore, the influences of time and the fractional derivative are examined through graphical analysis. Overall, the RNPS method has demonstrated to be a reliable and effective approach for solving time-fractional differential equations. Full article

The main objective of this work was to analyze the transport by diffusion of salts containing some metal ions (that is, CoCl₂, CrCl₃, HgCl₂, and PbCl₂), at 25.0 °C, in two different aqueous solutions with varying pH levels, namely, sodium chloride and hydrochloric chloride, by using Nernst–Hartley model equations. To analyze the applicability of this model, experimental data for two aqueous systems (CoCl₂ + NaCl) and (CoCl₂ + HCl), were obtained by using the Taylor technique and compared with the predicted values. The Nernst–Hartley model equations were used in this study to estimate the mutual diffusion coefficients of the eight ternary systems, which included (CoCl₂ + NaCl), (HgCl₂ + NaCl), (PbCl₂ + NaCl), (CrCl₃ + NaCl), and (CoCl₂ + HCl), (HgCl₂ + HCl), (PbCl₂ + HCl), and (CrCl₃ + HCl). By using the limiting equations of Nernst–Hartley coefficients, we were able to understand the composition dependence of the mutual diffusion coefficients of these mixed electrolyte solutions and the electrostatic mechanism for the strongly coupled diffusion of these components. Full article

This scientific study employs the Taylor dispersion technique for diffusion measurements to investigate the interaction between sulfamerazine (NaSMR) and macromolecular cyclodextrins (β-CD and HP-β-CD). The results reveal that the presence of β-CD influences the diffusion of the solution component, NaSMR, indicating a counterflow of this drug due to solute interaction. However, diffusion data indicate no inclusion of NaSMR within the sterically hindered HP-β-CD cavity. Additionally, toxicity tests were conducted, including pollen germination (Actinidia deliciosa) and growth curve assays in BY-2 cells. The pollen germination tests demonstrate a reduction in sulfamerazine toxicity, suggesting potential applications for this antimicrobial agent with diminished adverse effects. This comprehensive investigation contributes to a deeper understanding of sulfamerazine–cyclodextrin interactions and their implications for pharmaceutical and biological systems. Full article

The interaction between sodium salicylate (NaSal) and the two macrocycles 5,11,17,23-tetrakissulfonatomethylene-2,8,14,20-tetra(ethyl)resorcinarene (Na₄EtRA) and β-cyclodextrin (β-CD) has been studied by the determination of ternary mutual diffusion coefficients, and spectroscopic and computational techniques. The results obtained by the Job method suggest that the complex formation is given in a 1:1 ratio for all systems. The mutual diffusion coefficients and the computational experiments have shown that the β-CD-NaSal system presents an inclusion process, whereas the Na₄EtRA-NaSal system forms an outer-side complex. This fact is also in line with the results obtained from the computational experiments, where the calculated solvation free energy has been found to be more negative for the Na₄EtRA-NaSal complex because of the partial entry of the drug inside the Na₄EtRA cavity. Full article

Experimental binary diffusion coefficients for short-chain alcohols in supercritical carbon dioxide were measured using the Taylor dispersion technique in a temperature range of 306.15 K to 331.15 K and along the 10.5 MPa isobar. The obtained diffusion coefficients were in the order of 10⁻⁸ m² s⁻¹. The dependence of D on temperature and solvent density was examined together with the influence of molecular size. Some classic correlation models based on the hydrodynamic and free volume theory were used to estimate the diffusion coefficients in supercritical carbon dioxide. Predicted values were generally overestimated in comparison with experimental ones and correlations were shown to be valid only in high-density regions. Full article

In this article, the transmission dynamical model of the deadly infectious disease named Ebola is investigated. This disease identified in the Democratic Republic of Congo (DRC) and Sudan (now South Sudan) and was identified in 1976. The novelty of the model under discussion is the inclusion of advection and diffusion in each compartmental equation. The addition of these two terms makes the model more general. Similar to a simple population dynamic system, the prescribed model also has two equilibrium points and an important threshold, known as the basic reproductive number. The current work comprises the existence and uniqueness of the solution, the numerical analysis of the model, and finally, the graphical simulations. In the section on the existence and uniqueness of the solutions, the optimal existence is assessed in a closed and convex subset of function space. For the numerical study, a nonstandard finite difference (NSFD) scheme is adopted to approximate the solution of the continuous mathematical model. The main reason for the adoption of this technique is delineated in the form of the positivity of the state variables, which is necessary for any population model. The positivity of the applied scheme is verified by the concept of M-matrices. Since the numerical method gives a discrete system of difference equations corresponding to a continuous system, some other relevant properties are also needed to describe it. In this respect, the consistency and stability of the designed technique are corroborated by using Taylor’s series expansion and Von Neumann’s stability criteria, respectively. To authenticate the proposed NSFD method, two other illustrious techniques are applied for the sake of comparison. In the end, numerical simulations are also performed that show the efficiency of the prescribed technique, while the existing techniques fail to do so. Full article

Hard-coated surfacing of a few micrometers is widely applied to increase the efficiency of tools, e.g., for cutting, forming, and casting applications. Therefore, the base thermodiffusion surface treatment is a practical solution to these issues by hardening surface layers with interstitial elements such as carbon, nitrogen, and boron. In particular, within this study, the growth kinetics of an iron boride layer on ASTM 283 steel were investigated with two diffusion models of the powder-pack boriding technique in the temperature range of 1123–1273 K with different treatment periods. The first model, called the steady-state diffusion model, used the modified version of the mass balance equations at the Fe₂B/substrate growth interface, the parabolic growth law, and the solution of Fick’s second law without time dependence. At the same time, the second diffusion model was based on Goodman’s method, also called the integral heat balance method. Afterward, the diffusion coefficient of boron in the Fe₂B phase was calculated by fitting the experimental data to the models. Nevertheless, the estimated value for the activation energy of ASTM A238 steel in both diffusion models was coincident (168.2 kJ∙mol⁻¹). A mathematical analysis was implemented by means of a power series (Taylor series) to explain this similarity. The SEM examinations showed a solid tendency to saw-tooth morphology at the growth interface with the formation of the Fe₂B layer, whose presence was verified by XRD analysis. The tribological characterizations, including the tests of Rockwell-C indentation, pin-on-disc, and Vickers hardness test method, were used to analyze the antiwear features of the Fe₂B layers. Finally, this value of energy was compared to the literature for its experimental validation. Full article

In this study, diffusion coefficients of ammonium vanadate at tracer concentrations in artificial saliva with and without sodium fluoride, at different pH values, were measured using an experimental model based on the Taylor dispersion technique. Ternary mutual diffusion coefficients (D₁₁, D₂₂, D₁₂, and D₂₁) for four aqueous systems {NH₄VO₃ (component 1) + β-cyclodextrin (β-CD) (component 2),} {NH₄VO₃ (component 1) + β-cyclodextrin (HP-β-CD) (component 2)}, {NH₄VO₃ (component 1) + sodium dodecyl sulphate (SDS) (component 2)} and {NH₄VO₃ (component 1) + sodium hyaluronate (NaHy) (component 2)} at 25.00 °C were also measured by using the same technique. These data showed that diffusion of ammonium vanadate was strongly affected in all aqueous media studied. Furthermore, a significant coupled diffusion of this salt and β-CD was observed through the non-zero values of the cross-diffusion coefficients, D₁₂, allowing us to conclude that there is a strong interaction between these two components. This finding is very promising considering the removal, from the oral cavity, of vanadium resulting from tribocorrosion of Ti-6Al-4V prosthetic devices. Full article

Diffusion coefficients, D, for ethanol in supercritical carbon dioxide (scCO₂) were measured in the temperature range 306.15–331.15 K and along the 10.5 MPa isobar, using the Taylor dispersion technique. The obtained diffusivities ranged from 1.49 × 10⁻⁸ to 2.98 × 10⁻⁸ m² s⁻¹, an order of magnitude higher than in usual liquids. The dependence of D on temperature and solvent density was examined. Various correlation models based in the hydrodynamic theory were assessed to estimate the diffusion coefficients, with reasonable results obtained for the Wilke–Chang and Lai–Tan models. Full article

Metal ions such as cobalt (II) and chromium (III) might be present in the oral cavity, as a consequence of the corrosion of Co-Cr dental alloys. The diffusion of such metal ions into the organism, carried by saliva, can cause health problems as a consequence of their toxicity, enhanced by a cumulative effect in the body. The effect of the chlorhexidine digluconate, which is commonly used in mouthwash formulations, on the transport of these salts is evaluated in this paper by using the Taylor dispersion technique, which will allow an assessment of how the presence of chlorhexidine digluconate (either in aqueous solution or in a commercial formulation) may affect the diffusion of metal ions. The ternary mutual diffusion coefficients of metal ions (Co and Cr) in the presence of chlorhexidine digluconate, in an artificial saliva media, were measured. Significant coupled diffusion of CoCl₂ (and CrCl₃) and chlorhexidine digluconate is observed by analysis of the non-zero values of the cross-diffusion coefficients, D₁₂ and D₂₁. The observed interactions between metal ions and chlorhexidine digluconate suggest that the latter might be considered as an advantageous therapeutic agent, once they contribute to the reduction of the concentration of those ions inside the mouth. Full article

Mutual diffusion coefficients of chloroquine diphosphate (CDP) in aqueous solutions both without and with β-cyclodextrin (β-CD) were measured at concentrations from (0.0000 to 0.0100) mol dm⁻³ and 298.15 K, using the Taylor dispersion technique. Ternary mutual diffusion coefficients (D_ik) measured by the same technique are reported for aqueous CDP + β-CD solutions at 298.15 K. The presence of β CD led to relevant changes in the diffusion process, as showed by nonzero values of the cross-diffusion coefficients, D₁₂ and D₂₁. β-CD concentration gradients produced significant co-current coupled flows of CDP. In addition, the effects of β-CD on the transport of CDP are assessed by comparing the binary diffusion coefficient of aqueous CDP solutions with the main diffusion coefficient (D₁₁) measured for ternary {CDP(1) + β-CD(2)} solutions. These observations are supported by viscosity analysis. All data allow to have a better interpretation on the effect of cyclodextrin on the transport behavior of CDP. Full article