Fluid Behavior Research Articles

Effect of deflocculants on the rheological behavior of high alumina matrix suspensions for self-flowing bauxite castable

This study investigates the influence of commercially available polyphosphates and polycarboxylate ethers as deflocculants on aqueous suspensions containing high alumina cement (HAC), reactive alumina (RA), and various matrix compositions. Utilizing rheological methods, the research explores the interplay between dispersant concentration and the apparent viscosity and flow behavior of RA suspensions and matrix mixtures. The Casson model is employed to effectively describe the obtained flow data. Moreover, the study discerns specific impacts of polycarboxylate ethers on the thickening properties of matrix mixtures characterized by varying RA and HAC contents. Additionally, the research evaluates the physical and mechanical properties of low-cement bauxite castables treated with a range of polycarboxylate esters. The findings demonstrate that all deflocculated suspensions exhibit Non-Newtonian structured fluid behavior with a discernible yield stress (τ0) at shear rates below 20 s-1. At higher shear rates, there is a significant reduction in apparent viscosity, aligning well with the Casson model. Comparative assessments, based on flow curve values τ0, elucidate differing degrees of suspension flocculation depending on the type of dispersant used.

Analytical investigation of porous medium effects on the flow of two micropolar fluids in a rotating annulus

Fluids with microstructures and microinertia play a vital role in microfluidics and nanfluidics system. One of such significant fluid is micropolar fluid. The characteristic behavior of micropolar fluid flow in conduit/pipe, etc. filled with porous medium helps us understand the flow behavior of biological fluids in porous media, groundwater flow in aquifiers, rotatory machines or viscometer. To understand such real-world problems, it is necessary to get into the mathematical model of such flow models. One such model with wide number of application is presented in this paper. This work investigated the flow of two micropolar fluids between the region formed by two concentric cylinders. Authors have considered inner cylinder to be at rest and outer cylinder rotating at a constant angular velocity. The region between two concentric cylinder is filled with an isotropic porous material. A slip condition at the outer wall and continuity conditions at interface of two fluids has been utilized to obtain an analytical solution for the proposed model. The numerical solution of the obtained solution for present problem is used to graphically analyze the motion of immisicble micropolar fluids rotating in an annulus filled with the porous medium. It is found that an outer cylinder has a notable influence on the flow behavior of immiscible micropolar fluids, contrary to the effect observed within the inner region. An analytical approach of this work not only helps us obtain precise results and analysis of the flow, but it also serves as a useful validation for future approximations within the scope of this work.

Entropy generation outcomes in peristalsis of Carreau–Yasuda nanofluid flow with activation energy

AbstractThis paper focuses on the study of activation energy and entropy generation in the peristaltic flow of a Carreau–Yasuda nanofluid. Peristaltic transport, coupled with entropy generation and activation energy in a curved geometry, has significant applications in biomedical and industrial processes involving non‐Newtonian fluids. Blood flow in the arteries, the movement of chyme in the gastrointestinal tract, and peristaltic motion replicate the natural muscular contractions that drive fluid flow in the physiological systems. The integration of entropy generation allows for the evaluation of energy efficiency and the analysis of losses due to viscous dissipation. Activation energy plays a crucial role in processes such as drug delivery, where temperature‐sensitive reactions or biochemical changes affect fluid behavior. In industrial applications, like peristaltic pumps in chemical reactors or polymer processing, the consideration of entropy and activation energy aids in optimizing thermal management and reaction rates. The mathematical model is developed under these assumptions, and the governing equations are numerically solved using the NDSolve function in Mathematica. Graphical results show that higher activation energy and concentration reduce the reaction rate, while the Bejan number and entropy generation increase with a larger Brinkman number. Velocity and temperature increase under slip conditions, whereas concentration decreases, and a stronger radial magnetic field reduces both velocity and the size of the trapped bolus.

Probing the Behaviour of Fluids Confined in Porous Materials by Neutron Scattering: Applications to CO2 Sequestration and Enhanced Oil and Gas Recovery.

The current review presents a discussion on the utility of neutron scattering, with emphasis on neutron total scattering and small-angle neutron scattering (SANS), to explore the structural properties and the phase behaviour of fluids confined in nanopores. The effectiveness of contrast matching SANS on the evaluation of accessibility of porous materials to invading fluids is highlighted too. This review provides also an overview regarding the neutron scattering studies on the structure and the accessibility of greenhouse gases in the complex pore network of geomaterials, with applications to CO2 geological sequestration and enhanced oil and gas recovery.

Investigation of heat generation and radiation effects on boundary layer flow of Prandtl liquid with Cattaneo–Christov double diffusion models

In this analysis, a bidirectional stretched sheet is used to produce a 3D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{D}$$\\end{document} flow of Prandtl liquid with improve mass diffusion and heat conduction models. This study advances knowledge of magnetohydrodynamics, radiation impacts, and heat production in fluid dynamics and transport processes. The Prandtl fluid model is critical for modeling non-Newtonian fluids, capturing its viscoelastic features, and allowing for precise simulation in industrial applications. It gives a mathematical foundation for analyzing complex fluid behaviors, which is necessary for optimizing operations utilizing such fluids. It uses the boundary layer method to simplify the fundamental equations and Cattaneo–Christov double diffusion models. The optimal homotopy analysis method is used to solve nonlinear ODEs caused by non-dimensional similarity variables. This investigation undertakes the calculation of drag coefficient for surfaces mass transfer rates and heat transfer rates proximate to the solid boundary. Furthermore, it conducts a comprehensive analysis of the influences exerted by various parameters on concentration and temperature profiles employing graphical representations for a rigorous examination. The Prandtl fluid model describes the viscoelastic characteristics of non-Newtonian fluids through constitutive equations, dimensional evaluation, and numerical simulations, which are frequently validated by experiments. The results show that changes in thermal and concentration relaxation parameters are accompanied by a decline in temperature. Temperature field rises as the thermal radiation parameter and heat generation increases. The work's novelty consists in its advanced modeling of Prandtl non-Newtonian fluids via Cattaneo–Christov double diffusion models, which incorporate magnetohydrodynamics and radiation effects and use optimal homotopy analysis for accurate parametric analyses of heat and mass transfer.

An Analytical Analysis of Mixed Convective MHD Casson Flow with Ramped Wall Temperature

This research discusses the behavior of magnetohydrodynamic Casson fluid subjected to a ramped wall temperature along an infinitely inclined plate. Non-Newtonian fluid, specifically the Casson fluid, is employed to characterize fluid behavior in this research. The effects of porous media, chemical reactions, and radiation are considered. In practical applications, non-Newtonian fluids find use in lubrication such as grease, engine oil, etc. The Laplace transform technique has been applied during this study where ordinary differential equations are converted from the governing partial differential equations with suitable boundary conditions. These transformed dimensionless equations are subsequently solved numerically with Mathematica, and we have achieved the exact solutions of momentum, followed by energy and finally concentration. In the results section, we have analyzed the behavior of flow features under varying conditions of key parameters, including the governing parameters, the unsteadiness parameter, and the Casson parameter. All the results are shown and analyzed in graphs.

Heat and mass transfer analysis of s-PTT nanofluid in microchannels under combined electroosmotic and pressure-driven flows with wall slip using the homotopy perturbation method

The heat and mass transfer of the electroosmotic flow in microchannel transporting viscoelastic nanofluid is investigated considering Brownian motion of nanoparticles and slip boundary conditions. The simplified Phan-Thien-Tanner model is employed to describe the rheological behavior of fluid and the nonlinear Navier model with non-zero slip critical shear stress is considered at walls. The governing nonlinear momentum, mass, and heat transfer equations are solved using the Homotopy Perturbation Method. The study reveals that increasing the fluid elasticity, nanoparticle concentration, and size significantly enhances the flow rate, heat and mass transfer. Additionally, elasticity and Reynolds number decrease the friction factor. Reducing the double-layer thickness and increasing the Reynolds number lead to higher flow rates and fluid velocities. Notably, the findings emphasize the critical role of the slip conditions on the Sherwood and Nusselt numbers.

Non-Newtonian fluids effects on the steady-state performance of two-lobe journal bearings

This research aims to investigate the behavior of non-Newtonian fluid obeying the power law model in a laminar flow regime for a two-lobe journal bearing. The investigation involves calculating the static characteristics in terms; of load-carrying capacity, attitude angle, friction coefficient, friction force, and side leakage, for various values of the power law index and different eccentricity ratios. To determine the static characteristics, the pressure distributions are obtained by the numerical solution of the modified Reynolds equation considering the effect of non-Newtonian behavior of the fluids using the finite difference method. This study reveals that increasing both the eccentricity ratio and power law index produce an increase in the load-carrying capacity, friction force, and side leakage while lead to a decrease in the attitude angle and friction coefficient for the two-lobe journal bearing. In addition, compared to Newtonian fluid the results show that the using of non-Newtonian fluids as lubricants improves the static characteristics of the two-lobe journal bearing especially for the shear-thickening lubricants.

A comparative study of finite difference approach and bvp4c techniques for water base hybrid nanofluid containing multiple walls carbon nanotubes and magnetic oxide

This study investigates the thermal behaviour of unsteady hybrid nanofluid flow on an infinite vertical plate. The investigation takes into account parameters such as magnetohydrodynamics and radiation effects, as well as the stratified medium. The systems of equations were solved by employing the explicit finite difference approach of Dufort-Frankel method. The main motivation of the study is to compare the performance of water, magnetic oxide, and multi-wall carbon nanotubes as working fluids. Additionally, velocity, temperature, and concentration outlines are visualized through plots, elucidating the fluid behaviour. Tables are provided for the Skin friction, Nusselt number, and Sherwood number, offering comprehensive insights crucial for optimizing performance in engineering applications ranging from thermal management systems to renewable energy technologies. The main finding of this study indicates that the quantitative result reveals that the temperature outline escalates among increasing values of radiation. In contrast, the outlines of a velocity and concentration show a decrease as the values of magnetohydrodynamics increase. In addition, multi-walled carbon nanotubes consume a larger outcome on temperature. A statistical study displays that the thermal stream rate of magnetic oxide-multi-wall carbon nanotubes-water increases from 1.7615 percentages to 7.4415 percentages, respectively, when the volume fraction of nanoparticles rises from 0.01 to 0.05. Future research is important to understanding hybrid nanofluid flows and their applications in thermal engineering systems such as energy systems, nuclear reactors, biomedical applications, electronics cooling, solar thermal systems, chemical processing, and other heat transfer applications where improved thermal performance is crucial.

Developing a machine learning-based methodology for optimal hyperparameter determination—A mathematical modeling of high-pressure and high-temperature drilling fluid behavior

Drilling fluids exhibit complex rheological behavior due to a non-linear response to shear rate variations and high sensitivity to changes in temperature, time, and pressure conditions. The prediction of drilling fluid rheological behavior is crucial for the success of oil well drilling, and it directly impacts the fluid's performance. The dataset used in this study was obtained from extensive rheometric tests of water-based and olefin-based drilling fluids in steady-state flow curves. The optimal hyperparameters were guided by performance metrics and compared with alternative models such as Power-law and Herschel-Bulkley rheological models. Different configurations with different hidden layers, using neuron sequences of 16, 32, and 64, learning rates of 0.001 and 0.01, and the ReLU activation function were used to improve the model's performance. Additionally, the paper delved into the impact of the number of training epochs on the accuracy of shear stress predictions. Finding this equilibrium was identified as a crucial factor in achieving precise results. The neural network model demonstrated remarkable accuracy when using the ML-C3 configuration, with MAE values of 0.535 and R2 of 0.987 in predicting the steady-state flow curves of drilling fluids, establishing itself as a powerful tool for forecasting the rheological behavior of these fluids under diverse operational conditions. The present research significantly contributes to the field of drilling fluid rheology and provides valuable insights for optimizing drilling operations in HPHT environments.

Magnetohydrodynamic Motions of Oldroyd-B Fluids in Infinite Circular Cylinder That Applies Longitudinal Shear Stresses to the Fluid or Rotates Around Its Axis

Two classes of magnetohydrodynamic (MHD) motions of the incompressible Oldroyd-B fluids through an infinite cylinder are analytically investigated. General expressions are firstly established for shear stress and velocity fields corresponding to the motion induced by longitudinal shear stress on the boundary. For validation, the expression of the shear stress is determined by two different methods. Using an important remark regarding the governing equations for shear stress and fluid velocity corresponding to the two different motions, this expression is then used to provide the dimensionless velocity field of the MHD motion of the same fluids generated by a cylinder that rotates around its symmetry axis. Obtained results can generate exact solutions for any motion of this kind of Oldroyd-B fluids. Consequently, both types of motions are completely solved. For illustration, some case studies are considered, and adequate velocity fields are provided. The steady-state components of these velocities are presented in different forms whose equivalence is graphically proved. The influence of the magnetic field on the fluid behavior is graphically investigated. It was found that the fluid flows slower, and a steady state is earlier reached in the presence of a magnetic field. The fluid behavior when shear stress is given on the boundary is also investigated.

On the Role of Substrate in Hydroxyapatite Coating Formation by Cold Spray

The deposition of agglomerated hydroxyapatite (HAp) powders by low-pressure cold spray has been a topic of interest in recent years. Key parameters influencing the deposition of HAp powders include particle morphology and impact kinetic energy. This work examines the deposition of HAp powders on various metal surfaces to assess the impact of substrate properties on the formation of HAp deposits via cold spray. The substrates studied here encompass metals with varying hardness and thermal conductivities, including Al6061, Inconel alloy 625, AISI 316 stainless steel, H13 tool steel, Ti6Al4V, and AZ31 alloy. Single-track experiments offer insights into the initial interactions between HAp particles and different substrate surfaces. In this study, the results indicate that the ductility of the substrate may enhance HAp particle deposition only at the first deposition stages where substrate/particle interaction is the most critical factor for deposition. Features on the substrate associated with the first deposition sprayed layer include localized substrate deformation and the formation of clusters of HAp agglomerates, which aid in HAp deposition. Furthermore, after multiple spraying passes on the various metallic surfaces, deposition efficiency was significantly reduced when the build-up process of HAp coatings shifted from ceramic/metal to ceramic/ceramic interactions. Overall, this study achieved agglomerated HAp deposits with high deposition efficiencies (30–60%) through single-track experiments and resulted in the preparation of HAp coatings on various substrates with thickness values ranging from 24 to 53 µm. These coatings exhibited bioactive behavior in simulated body fluid.

Experimental and theoretical determination of minimum miscibility pressure of supercritical CO2 and alkanes at nanoconfinement

The minimum miscibility pressure (MMP) is crucial for CO2 Enhanced Oil Recovery (EOR). However, accurately determining MMP within nanoconfinement has been challenging due to intricate molecular interactions and reduced permeability. This study leveraged nanofluidic technology to determine MMP for supercritical CO2-alkanes at the nanoscale by observing the vanishing interface, noting a 5.1 % reduction for CO2-octane at 30 nm versus 1 μm at 80 ℃. It further explored the impact of alkane type and temperature on nanoconfinement, elucidating the underlying mechanisms. Additionally, a theoretical method was developed to estimate MMP ranging from 10 to 1000 nm, aligning well with the experimental results. The findings highlight the lower nanoscale MMP values compared to the bulk phase. This research presents methods for investigating thermodynamic properties under nanoconfinement, providing insights into the abnormal behaviors of fluids at the nanoscale and contributing to EOR.

Multiphase Behavior of the Water + 1-Butanol + Deep Eutectic Solvent Systems at 101.3 kPa

The growing demand for more sustainable routes and processes in the mixture separation and purification industry has generated a need to search for innovations, with new solvent alternatives being a possible solution. In this context, a new class of green solvents, known as deep eutectic solvents (DESs), has been gaining prominence in recent years in both academic and industrial spheres. These solvents, when compared to ionic liquids (ILs), are more environmentally friendly, less toxic, low-cost, and easier to synthesize. In addition, they have significantly lower melting points than their precursors, offering a promising option for various applications in this industrial sector. Understanding and studying the thermodynamic behavior of systems composed of these substances in purification and separation processes, such as liquid–liquid extraction and azeotropic distillation, is extremely important. This work aimed to study the phase behavior of liquid–liquid equilibrium (LLE) and vapor–liquid equilibrium (VLE) of water + 1-butanol + DES (choline chloride + glycerol) systems with a molar ratio of 1:2. Experimental LLE data, obtained at 298.15 K and 101.3 kPa, and VLE data, obtained at 101.3 kPa and in the temperature range of 364.05 K–373.85 K, were submitted to the thermodynamic quality/consistency test, proposed by Marcilla et al. and Wisniak, and subsequently modeled using the gamma–gamma approach for the LLE and gamma–phi for the VLE. The non-random two-liquid (NRTL) model was used to calculate the activity coefficient. The results are presented for the VLE in a temperature–composition phase diagram (triangular prism) and triangular phase diagrams showing the binodal curve and tie lines (LLE). The separation and distribution coefficients of LLE were determined to evaluate the extractive potential of the DES. For the VLE, the values of the relative volatility of the system were calculated, considering the entrainer free-basis, to evaluate the presence or absence of azeotropes in the range of collected points. From these data, it was possible to compare DES with ILs as extracting agents, using data from previous studies carried out by the research group. Therefore, the results indicate that the NRTL model is efficient at correlating the fluid behavior of both equilibria. Thus, this study serves as a basis for future studies related to the understanding and design of separation processes.

Biopharmaceutical modulatory effects of newly engineered bile acid-Tyloxapol nanogels for attenuation of cytotoxicity in auditory cells

This study presents novel thermoresponsive nanogels composed of chenodeoxycholic acid and Tyloxapol for potential inner ear drug delivery. The nanogels exhibit non-Newtonian, shear-thinning fluid behaviour and rapid gelation at body temperature. Biocompatibility studies were conducted on auditory and macrophage cell lines. Nanogels had a minimal impact on cellular viability, glycolysis, and mitochondrial respiration of auditory cells after 24 h of exposure. However, mitochondrial function analysis in macrophages revealed a significant decrease in oxidative phosphorylation and coupling efficiency after nanogel exposure, accompanied by increased proton leakage. Despite these metabolic disruptions, glycolysis remained unaffected. The Poloxamer matrix appears to be responsible for these effects, independent of the presence of bile acids or Tyloxapol. This study highlights the potential of bile acid-enriched nanogels in drug delivery, particularly their biocompatibility and injectability while acknowledging challenges related to mitochondrial dysfunction in immune cells. These findings suggest that thermoresponsive bile acid and Tyloxapol nanogels have the potential to be safe and effective drug delivery vehicles for inner ear applications.

An investigation of the behaviour of polymer fluids in the American Petroleum Institute filter press

The American Petroleum Institute (API) filter press test has been used for decades in the construction industry as part of the quality control regime for bentonite-based excavation support fluids. The industry has carried over the use of this test to polymer fluids despite the lack of published evidence of its suitability for these fluids and the very different mechanisms by which polymer fluids and bentonite slurries achieve excavation support. This paper presents the first systematic investigation of this issue through a combination of laboratory testing and theoretical analysis. The investigation demonstrates the very different behaviours of bentonite slurries and polymer fluids. In contrast to the results for bentonite slurries, API filter press results for polymers are shown to be highly sensitive to the filter paper used. In particular, repeatability testing revealed a substantial variation in the polymer fluid loss rates attributable to three primary factors: (a) the filter paper pore size; (b) filter paper damage resulting from the applied test pressure; (c) apparent ‘clogging’ of the filter paper pore space. Furthermore, the study demonstrates the poor repeatability of the API filter press test for polymer fluids even when filter papers of the same type are used. Interestingly, analysis of polymer flow with respect to filter paper pore size and the applied pressure showed that the filter papers were behaving as porous media rather than a simple bundle of capillaries; their behaviour could not be modelled using a simple capillary bundle model. Importantly, this finding shows that the filter press may provide a rapid method of assessing the apparent viscosity of polymer fluids in porous media at high shear rates – data that cannot be obtained by rotational viscometry, and would otherwise require resort to permeameter testing of coarse soils. The investigation demonstrates that the filter press test is not useful for the on-site quality control of polymer fluids but, given the theory presented in the paper, it can be a useful laboratory tool that provides valuable insight into polymer fluid flow behaviour in soils of high hydraulic conductivity, the most challenging soils for polymer fluid support.

Darcy-Brinkman Flow of a Micropolar Fluid through an Anisotropic Porous Channel

This study investigates the Darcy-Brinkman flow of micropolar fluid through an anisotropic porous channel, a configuration relevant to various industrial and natural processes involving complex fluid flow. The anisotropy of the porous medium is characterized by its permeability aligned along two principal axes, with one axis forming an angle with the horizontal direction. The model applies no-slip and no-spin boundary conditions at the channel’s impermeable walls. Using a combination of analytical techniques and graphical analysis, we explore how key parameters such as the Darcy number, anisotropy angle, permeability ratio, and micropolar material parameters affect the flow behavior. Results reveal that increasing the anisotropy angle and permeability ratio leads to a reduction in both fluid velocity and micro rotational velocity, while the Darcy number promotes an increase in flow velocity. Additionally, the study discusses the impact of these parameters on shear stress and couple stress at the channel walls. The findings contribute to a deeper understanding of micropolar fluid behavior in porous media, with potential applications in filtration, lubrication, and subsurface fluid dynamics.

Lattice Boltzmann Model for Rarefied Gaseous Mixture Flows in Three-Dimensional Porous Media Including Knudsen Diffusion

Numerical modeling of gas flows in rarefied regimes is crucial in understanding fluid behavior in microscale applications. Rarefied regimes are characterized by a decrease in molecular collisions, and they lead to unusual phenomena such as gas phase separation, which is not acknowledged in hydrodynamic equations. In this work, numerical investigation of miscible gaseous mixtures in the rarefied regime is performed using a modified lattice Boltzmann model. Slip boundary conditions are adapted to arbitrary geometries. A ray-tracing algorithm-based wall function is implemented to model the non-equilibrium effects in the transition flow regime. The molecular free flow defined by the Knudsen diffusion coefficient is integrated through an effective and asymmetrical binary diffusion coefficient. The numerical model is validated with mass flow measurements through microchannels of different cross-section shapes from the near-continuum to the transition regimes, and gas phase separation is studied within a staggered arrangement of spheres. The influence of porosity and mixture composition on the gas separation effect are analyzed. Numerical results highlight the increase in the degree of gas phase separation with the rarefaction rate and the molecular mass ratio. The various simulations also indicate that geometrical features in porous media have a greater impact on gaseous mixtures’ effective permeability at highly rarefied regimes. Finally, a permeability enhancement factor based on the lightest species of the gaseous mixture is derived.

Density functional theory for responsive hard-sphere fluids

We investigate the equilibrium properties of responsive hard-sphere fluids, where the particle size is a coarse-grained property that fluctuates within an internal free-energy landscape, responding to changes in concentration or the application of external fields. For this purpose, we employ a generalised density functional theory for responsive colloids based on the fundamental measure theory for polydisperse hard-sphere mixtures. We find that increasing particle softness yields a substantial reduction in mean particle size, volume fraction and pressure. We also examine the density profiles and size segregation of responsive hard-sphere fluids subjected to three representative external potentials: a planar hard wall, gravitational and Archimedes buoyant fields. We observe that increasing stiffness or particle concentration enhances density oscillations, converging to the behaviour of a monodisperse fluid. In a gravitational field, size segregation occurs, with smaller particles accumulating at the bottom due to sedimentation. This effect is more pronounced when the Archimedes force is included, causing larger colloids to accumulate at the top, leading to density oscillations in this region that intensify with particle softness, an effect not observed in monodisperse systems. Finally, we demonstrate that responsiveness leads to distinct behaviour compared to conventional polydisperse non-responsive fluids, in which particle compression is not allowed.

A dissipative extension to ideal hydrodynamics

Abstract We present a formulation of special relativistic, dissipative hydrodynamics (SRDHD) derived from the well-established Müller-Israel-Stewart (MIS) formalism using an expansion in deviations from ideal behaviour. By re-summing the non-ideal terms, our approach extends the Euler equations of motion for an ideal fluid through a series of additional source terms that capture the effects of bulk viscosity, shear viscosity and heat flux. For efficiency these additional terms are built from purely spatial derivatives of the primitive fluid variables. The series expansion is parametrized by the dissipation strength and timescale coefficients, and is therefore rapidly convergent near the ideal limit. We show, using numerical simulations, that our model reproduces the dissipative fluid behaviour of other formulations. As our formulation is designed to avoid the numerical stiffness issues that arise in the traditional MIS formalism for fast relaxation timescales, it is roughly an order of magnitude faster than standard methods near the ideal limit.