Fluid Theory Research Articles

Thermal convection in a higher-gradient Navier–Stokes fluid

We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing models for thermal convection, analysing these in detail, and deriving critical Rayleigh and wave numbers for the onset of convective fluid motion. In addition to linear instability theory we present a careful analysis of fully nonlinear stability theory. The theories analysed all possess a bi-Laplacian term in addition to the normal spatial derivative term. The theories discussed are Stokes couple stress theory, dipolar fluid theory, Green–Naghdi theory, Fried–Gurtin–Musesti theory, and a second theory of Fried and Gurtin. We show that the Stokes couple stress theory and the Fried–Gurtin–Musesti theory involve the same partial differential equations while those of Green–Naghdi and dipolar theory are similar. However, we concentrate on boundary conditions which are crucial to understand all five theories and their differences.

A Workflow for Crystallization Process Design with Simultaneous Process Optimization and Solvent Selection based on the Perturbed‐Chain Statistical Associating Fluid Theory

AbstractSolvent selection is a critical part of crystallization process design and is inherently intertwined with optimization of the operating conditions. Computer‐aided tools can greatly assist in solving these two problems simultaneously. However, the integration of predictive thermodynamic models and process optimization tools is often complicated, which may hamper industry adoption. This work presents a workflow for simultaneous solvent selection and process optimization for solution crystallization processes based on the perturbed‐chain statistical associating fluid theory (PC‐SAFT) equation of state. The workflow is provided with readily executable computational tools and aims to strike a balance between the resources needed to obtain experimental input data and good prediction performance. The use of the workflow is demonstrated through a case study involving aspirin crystallization, which shows that the workflow can provide suitable solvents and operating conditions for the crystallization process based on either cooling, antisolvent, or evaporative crystallization.

Thermodynamic Mechanism of Physical Stability of Amorphous Pharmaceutical Formulations

Hygroscopicity is an important factor affecting the physical stability of amorphous solid dispersions (ASDs) during long-term storage. In this work, the effects of temperature, relative humidity (RH), and polymeric excipients on the phase behavior of amorphous irbesartan (IRB) and oxaprozin (OXA) were systematically investigated. The ASDs were prepared by the solvent evaporation method. The water sorption in formulations was measured under the conditions of 25 °C, 60% RH, 25 °C, 90% RH, and 40 °C, 75% RH. The results showed that the hygroscopicity of formulations containing polyvinylpyrrolidone (PVP) was stronger than that containing poly(vinylpyrrolidone-co-vinyl acetate) (PVPVA 46) and the hygroscopicity increased with increasing temperature and RH. With increasing content of active pharmaceutical ingredients (APIs), the recrystallization phenomenon is significant at the same RH. PVP can better inhibit IRB recrystallization than PVPVA 46. In contrast, PVPVA 46 can better maintain the amorphous form of OXA than PVP. The thermodynamic phase diagrams of amorphous API/polymer formulations at 60% RH and anhydrous conditions were predicted using perturbed chain statistical associated fluid theory (PC-SAFT) and the Gordon–Taylor equation. Furthermore, the electrostatic potential (ESP) and binding energies between APIs and polymers were calculated with density functional theory (DFT), which explained the molecular interaction mechanism of ASDs. This work is expected to guide the screening of excipients and API loadings for designing ASDs and the selection of storage conditions.

Effect of CO2 Corrosion and Adsorption-Induced Strain on Permeability of Oil Shale: Numerical Simulation

Permeability is a crucial parameter for enhancing shale oil recovery through CO2 injection in oil-bearing shale. After CO2 is injected into the shale reservoir, CO2 corrosion and adsorption-induced strain can change the permeability of the oil shale, affecting the recovery of shale oil. This study aimed to explore the influence of CO2 corrosion and adsorption-induced strain on the permeability of oil shale. The deformation of the internal pore diameter of oil shale induced by CO2 corrosion under different pressures was measured by low-pressure nitrogen gas adsorption in the laboratory, and the corrosion model was fitted using the experimental data. Following the basic definitions of permeability and porosity, a dynamic mathematical model of porosity and permeability was obtained, and a fluid–solid coupling mathematical model of CO2-containing oil shale was established according to the basic theory of fluid–solid coupling. Then the effects of adsorption expansion strain and corrosion compression strain on permeability evolution were considered to improve the accuracy of the oil shale permeability model. The numerical simulation results showed that adsorption expansion strain, corrosion compression strain, and confining pressure are the important factors controlling the permeability evolution of oil shale. In addition, adsorption expansion strain and corrosion compression strain have different effects under different fluid pressures. In the low-pressure zone, the adsorption expansion strain decreases the permeability of oil shale with increasing pressure. In the high-pressure zone, the increase in pressure decreases the influence of expansion strain while permeability gradually recovers. The compressive strain increases slowly with increasing pressure in the low-pressure zone, slowly increasing oil shale permeability. However, in the high-pressure area, the increase in pressure gradually weakens the influence of corrosion compressive strain, and the permeability of oil shale gradually recovers.

CO2 solubility and diffusivity in poly(vinyl acetate) studied using the PC-SAFT and free volume theory

Poly (vinyl acetate) (PVAc) is a polymer used in various industrial applications, and the quantitative determination of CO2 solubility and diffusion coefficient is important for designing foaming processes involving supercritical CO2. In this study, these two physical properties were obtained experimentally and theoretically using the perturbed chain–statistical associating fluid theory (PC–SAFT) and free volume theory at temperatures between 353 K and 473 K and pressures up to 20 MPa. CO2 solubility increased almost linearly with pressure and could be correlated with the PC–SAFT equation of state and binary interaction parameter kij within the average relative deviation of 2.1%. Furthermore, the fitted plot of kij versus temperature can be used to predict CO2 solubility at lower temperatures. The diffusion coefficient of CO2 in PVAc was experimentally determined from CO2 sorption curves. Its value increased with increasing CO2 solubility and temperature, which was consistent with the free volume theory.

Activity-driven tissue alignment in proliferating spheroids.

We extend the continuum theory of active nematic fluids to study cell flows and tissue dynamics inside multicellular spheroids, spherical, self-assembled aggregates of cells that are widely used as model systems to study tumour dynamics. Cells near the surface of spheroids have better access to nutrients and therefore proliferate more rapidly than those in the resource-depleted core. Using both analytical arguments and three-dimensional simulations, we find that the proliferation gradients result in flows and in gradients of activity both of which can align the orientation axis of cells inside the aggregates. Depending on environmental conditions and the intrinsic tissue properties, we identify three distinct alignment regimes: spheroids in which all the cells align either radially or tangentially to the surface throughout the aggregate and spheroids with angular cell orientation close to the surface and radial alignment in the core. The continuum description of tissue dynamics inside spheroids not only allows us to infer dynamic cell parameters from experimentally measured cell alignment profiles, but more generally motivates novel mechanisms for controlling the alignment of cells within aggregates which has been shown to influence the mechanical properties and invasive capabilities of tumors.

Treating diabetic peripheral neuropathy from "Qi"

Diabetic Peripheral Neuropathy (DPN) refers to a series of clinical symptoms resulting from the symptom-complex of excessive eating for a long time, a deficiency of qi, blood and body fluids, and blocked body channels. According to the theories of traditional Chinese medicine, the qi, blood and body fluids comes from the same source. Qi can not only generate body fluids, but can also promote the activity of body fluids and circulation of blood. Meanwhile, qi is also the fundamental substance constituting and maintaining the living activities of a human body. Therefore, treatment of DPN should focus on boosting qi, nourishing yin, as well as activating qi and promoting the circulation of blood. Clinically, treatment and diagnosis of DPN need to be considered in combination with other symptoms, with comprehensive analysis conducted on the basis of the four diagnostic examination methods.

VLE property measurements and PC-SAFT/ CP- PC-SAFT/ E-PPR78 modeling of the CO2 + n-tetradecane mixture

This paper presents a new experimental VLE property data in the binary system of carbon dioxide – n -tetradecane at three selected isotherms of 313.15 K, 333.15 K, and 353.15 K in the pressure range from (3.8 to 19.0) MPa. The measurements were made using a high-temperature and high-pressure optical cell. The standard absolute u and relative u r uncertainties of temperature, pressure, concentration measurements are: u ( T ) =7.5 mK; u r ( P ) =0.00025; u r ( x ) =0.015; and u r ( y ) =0.015. The measured VLE data were used to determine the critical P C - T C curve data. Based on the derived values of the critical parameters of CO 2 + n -tetradecane mixture the value (-67.58 MPa) of the Krichevskii parameter has been determined. The predictive capabilities of the perturbed chain-statistical associating fluid theory (PC-SAFT), the critical point-based modification of PC-SAFT (CP-PC-SAFT), and the Enhanced -Predictive-Peng-Robinson-78 ( E -PPR78) models were examined.

On a variational principle for the Upper Convected Maxwell model

A variational principle for the Upper Convected Maxwell model is presented. The stationary value of the appropriate functional is the drag on an immersed object. From the principle, a formula is derived for the derivative of the drag with respect to the Deborah number for an arbitrarily shaped particle in a circular duct under creeping flow conditions. The formalism is compared with the conventional reciprocal theorem. Whereas the reciprocal theorem gives the drag as a volume integral involving the Stokesian stress tensor, the variational principle involves the stress from the adjoint equation. For low Deborah numbers both approaches provide the correction to the Stokes drag as a volume integral involving only the Stokesian rate-of-strain tensor, in line with second-order fluid theory. • A variational principle for the Upper Convected Maxwell model is presented. • At stationarity the functional equals the drag on a partcle in a duct. • For low Deborah numbers the drag correction involves only the Stokesian strain rate. • This is in correspondence with the reciprocal theorem and second-order fluid theory.

Molecular dynamics simulation of the coalescence of surfactant-laden droplets.

We investigate the coalescence of surfactant-laden water droplets by using several different surfactant types and a wide range of concentrations by means of a coarse-grained model obtained by the statistical associating fluid theory. Our results demonstrate in detail a universal mass transport mechanism of surfactant across many concentrations and several surfactant types during the process. Coalescence initiation is seen to occur via a single pinch due to aggregation of surface surfactant, and its remnants tend to become engulfed in part inside the forming bridge. Across the board we confirm the existence of an initial thermal regime with constant bridge width followed by a later inertial regime with bridge width scaling roughly as the square root of time, but see no evidence of an intermediate viscous regime. Coalescence becomes slower as surfactant concentration grows, and we see evidence of the appearance of a further slowdown of a different nature for several times the critical concentration. We anticipate that our results provide further insights in the mechanisms of coalescence of surfactant-laden droplets.

Thermodynamic modeling of gas solubility in ionic liquids using equations of state

This work aimed at the thermodynamic modeling of gas solubility in ionic liquids (ILs) using the Soave-Redlich-Kwong (SRK), cubic-plus-association (CPA), and perturbed-chain statistical associating fluid theory (PC-SAFT) equations of state. Wherefore, the routines were developed for the parameterization of ILs. Then, the ILs were implemented in the Aspen plus simulator to evaluate the equations of state and explore the phase equilibrium data with the predictive equations and the correlation of the binary interaction parameter. Hence, it was verified the correlation of the density and speed of sound curves presented limitations to correcting the slope of the curves of pure ILs. Nonetheless, the PC-SAFT with the 4C associative scheme demonstrated a better fit for the thermophysical properties. As for the prediction of phase equilibrium for the [EMIM][TfO], the PC-SAFT with the 2B scheme showed a better fit with CO2, while the CPA with the 2B scheme presented the best result for H2S. For [OMIM][NTf2], the PC-SAFT with the 1A scheme showed better results with CO2, and the CPA with the 2B scheme showed the lowest deviation with H2S.

Twisted plasma waves driven by twisted ponderomotive force

We present the results of twisted plasma waves driven by twisted ponderomotive force. With the beating of two, co-propagating, Laguerre-Gaussian (LG) orbital angular momentum (OAM) laser pulses with different frequencies and also different twist indices, we can obtain the twisted ponderomotive force. Three-dimensional particle-in-cell simulations are used to demonstrate the twisted plasma waves driven by lasers. The twisted plasma waves have an electron density perturbation with a helical rotating structure. Different from the predictions of the linear fluid theory, the simulation results show a nonlinear rotating current and a static axial magnetic field. Along with the rotating current is the axial OAM carried by particles in the twisted plasma waves. A detailed theoretical analysis of twisted plasma waves is also given.

Predicting CO2 solubility in aqueous and organic electrolyte solutions with ePC-SAFT advanced

Solvent influence and salt influence on CO2 solubility are essential factors toward the development of processes involving CO2 conversion. In this work, the equation of state (EOS) electrolyte Perturbed-Chain Statistical Associating Fluid Theory (ePC-SAFT advanced) was applied to model the CO2 solubility in single organic solvents (methanol, ethanol, N-methyl-2-pyrrolidone, dimethyl sulfoxide, tetrahydrofuran, dimethylformamide, γ-valerolactone, and acetonitrile). Further, CO2 solubility was predicted in aqueous solvent mixtures and in aqueous electrolyte solutions (NaCl, KCl, CsCl, MgCl2, CaCl2, NaNO3, KNO3, Mg(NO3)2, Ca(NO3)2, Na2SO4, K2SO4, MgSO4, NaHCO3, and K2CO3) with water as single solvent as well as in aqueous alcoholic solvent mixtures. CO2 solubility in systems with a lack of data (CsCl) was measured in this work with a high-pressure variable-volume view cell. Broad ranges of temperatures, pressures, and high concentrations of electrolytes were considered, and solvent effects, ion effects, and pH effects were studied. The nature of the considered systems required including dissociation reactions of carbonic acid in the modeling framework, most importantly for the systems containing carbonate salts. The results showed that i) CO2 solubility was the highest in non-polar solvents, ii) all salts caused salting-out effects on the CO2 solubility except carbonates (an apparent salting-in due to a pH shift), and that iii) the strength of salting-out effect was related to the charge density of the ions. The salt influence on CO2 solubility was predicted qualitatively correct with ePC-SAFT advanced; that is, fitting binary interaction parameters between ions and CO2 was not necessary, which is a result found for the first time. Finally, ePC-SAFT advanced allowed predicting the CO2 solubility in multi-component systems containing solvent mixtures, salt mixtures, or a solvent mixture with an additional salt over a broad range of conditions in good agreement with available literature data.

Investigation of the Antisolvent Effect on the Phase Behavior of Amino Acid Solid Solutions

This work focuses on the experimental measurement and modeling of solid–liquid equilibria containing continuous binary solid solutions crystallized from solvent mixtures for the usage in antisolvent crystallization. The newly constructed quaternary phase diagrams of l-valine/l-leucine in water/2-propanol and water/acetone systems are analyzed and compared to those of water/ethanol mixtures. Experimental data sets are determined via high-performance liquid chromatography, while the formation of solid solutions is confirmed with powder X-ray diffraction. Our validated modeling approach for the ternary l-valine/l-leucine/water mixture is extended to the aforementioned quaternary systems. The modeling combines the Perturbed Chain-Statistical Associating Fluid Theory and the Non-Random Two-Liquid model to describe the liquid and solid phases, respectively. Additionally, two modeling approaches (predictive and semi-predictive) are proposed. Both models show good agreement with the experimental solubility data sets of the binary solutions. However, larger deviations were observed in three- and four-component systems, especially toward the solubility maxima. Therefore, the modeling approach should be used for qualitative initial antisolvent screenings for the separation of solid solutions using counter-current crystallization.

Non-ideal gas behavior matters in hydrodynamic instability

Hydrodynamic instability, the foundation for flow’s laminar-turbulent transition and various predicting models, has been helping to understand the physics and shape the design of aerodynamic devices. While for hypersonic flow it is clear that thermodynamic/-chemical effects need be accounted for due to the high temperatures occurring, this letter unveils that also for low-speed flow at ambient temperatures non-ideal, i.e. real-gas effects can play a strong role—a feature missed by the classic theory for Newtonian fluids. By considering a three-dimensional low-speed boundary-layer flow in different thermodynamic regimes—subcritical, supercritical and transcritical—we show the importance of coupling thermodynamics by sensitivity studies of the perturbation growth rate to various inputs of the full stability equations. High sensitivities are found, and not only the transition-onset location but also the transition mechanism may be concerned.

Analytical studies of Eyring-Powell fluid models

PurposeWhen the literature is reviewed carefully, the analytical solutions of these types of models are missing. First using appropriate similarity transformation, the equations are reduced to dimensionless form (NODE). To solve the reduced models, ansatz-based methods are considered. Finally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. This study aims to discuss the aforementioned solution.Design/methodology/approachOne of the non-Newtonian fluids is Eyring-Powell (EP) fluid which is derived from the kinetic theory of fluids. Two variations of EP model are considered to obtain the exact solutions that are missing in the literature. In order to obtain exact solutions, one of the ansatz-based methods is considered. The effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. The results will guide to develop the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available.FindingsFinally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number are shown in the figures. The results will guide to develop of the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available. For the modified EP models, only special cases are considered. The generalized form, i.e. the modified EP models, which include deformation parameters, will be considered in the authors’ future work.Originality/valueWhen the literature is reviewed carefully, the analytical solutions of these types of models are missing so by this work, the gap in the literature is filled. The explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures.

Measurements of Isothermal Vapor–Liquid Equilibrium and Critical Point-Based Perturbed-Chain Statistical Association Fluid Theory Phase Behavior Modeling of the Propane + Phenol and Tetracosane + Propane/n-Butane Mixtures

The isothermal vapor–liquid equilibrium (VLE, pressure, temperature, and composition of coexisting vapor and liquid phases, PTxy) was directly determined using a high-pressure optical cell for binary propane + phenol and ternary tetracosane + propane/n-butane systems. Measurements were carried out at three selected isotherms of 383.15, 403.15, and 423.15 K at pressures from 0.94 to 14.5 MPa for propane + phenol and 403.15, 423.15, and 443.15 K at pressures up to 7.5 MPa for tetracosane + propane/n-butane systems. The critical property data (TC and PC) for both mixtures have been derived from the measured VLE data. Based on the initial slopes of the critical lines (shape of the critical lines), the qualitative behavior (pure- and mixture-like behavior) of the isochoric heat capacity (CVx, weak singular property), isobaric heat capacity (CPx), and isothermal compressibility (KTx, strong singular property) of the propane + phenol binary mixture near the critical point has been studied. It is demonstrated that the simplest version of critical point-based perturbed-chain statistical association fluid theory neglecting the complex molecular background of phenol yields reasonably accurate predictions of its pure compound properties. With the value of k12 obtained by fitting the present data of propane + phenol, this model yields reliable predictions for VLE in the systems of other n-alkanes, benzene, carbon monoxide, and nitrogen.

Fractional Calculus Extension of the Kinetic Theory of Fluids: Molecular Models of Transport within and between Phases

The application of fractional calculus in the field of kinetic theory begins with questions raised by Bernoulli, Clausius, and Maxwell about the motion of molecules in gases and liquids. Causality, locality, and determinism underly the early work, which led to the development of statistical mechanics by Boltzmann, Gibbs, Enskog, and Chapman. However, memory and nonlocality influence the future course of molecular interactions (e.g., persistence of velocity and inelastic collisions); hence, modifications to the thermodynamic equations of state, the non-equilibrium transport equations, and the dynamics of phase transitions are needed to explain experimental measurements. In these situations, the inclusion of space- and time-fractional derivatives within the context of the continuous time random walk (CTRW) model of diffusion encodes particle jumps and trapping. Thus, we anticipate using fractional calculus to extend the classical equations of diffusion. The solutions obtained illuminate the structure and dynamics of the materials (gases and liquids) at the molecular, mesoscopic, and macroscopic time/length scales. The development of these models requires building connections between kinetic theory, physical chemistry, and applied mathematics. In this paper, we focus on the kinetic theory of gases and liquids, with particular emphasis on descriptions of phase transitions, inter-phase mixing, and the transport of mass, momentum, and energy. As an example, we combine the pressure–temperature phase diagrams of simple molecules with the corresponding anomalous diffusion phase diagram of fractional calculus. The overlap suggests links between sub- and super-diffusion and molecular motion in the liquid and the vapor phases.

Viscous Damping Performance Analysis and Prediction of Axisymmetric Cylindrical Oscillating Buoys With Different Geometrical Configurations

Abstract With the intensification of the world's energy demand, clean and efficient marine energy has received more attention, and energy conversion devices are particularly important. As an important part of the oscillating wave energy conversion device, the hydrodynamic characteristics of cylindrical absorbers have a great impacton wave energy conversion efficiency. When cylindrical buoys with different bottom configurations heave under the action of waves, the oscillating motion and flow field become more complex. At present, potential flow theory is usually used to predict the motion response of cylindrical buoys in waves. Although the calculation speed is fast, there will be large errors due to the lack of consideration of the effect of fluid viscosity. To explore this error range, a three-dimensional numerical wave pool is established based on the viscous fluid theory and STARCCM+ software to study the response of buoy and wave coupling action considering the viscous effect. At the same time, based upon the potential flow theory, the analytical solution of the cylindrical buoy oscillating in waves is established. Combined with the computational fluid dynamics numerical simulation results, the oscillation laws of the buoys with different bottom configurations in waves with different periods are compared, and the effects of viscosity on the buoys' motion are also explored. According to the calculation results of floating buoy movement under viscous and nonviscous fluid, the statistical correction algorithmis adopted to obtain the viscous hydrodynamic correction algorithm of floating buoy movement based on the potential flow theory, and the feasibility is verified by viscous numerical simulation under other wave periods.

Toward Advanced, Predictive Mixing Rules in SAFT Equations of State

A novel mixing rule that bridges the Statistical Associating Fluid Theory (SAFT)-type equations of state and activity coefficient models is proposed. Applying this mixing rule to the PC-SAFT equation of state is the focus of this article. In comparison to the original PC-SAFT equation, and even the underlying activity coefficient model, this mixing rule provides high-accuracy predictions of equilibrium properties for a range of mixtures, being able to predict phenomena that neither PC-SAFT or the underlying activity coefficient model would be able to predict on their own. A few limitations are identified including the case of cross-associating mixtures, due to the difficulty of separating associative interactions from dispersive interactions in activity coefficient models. Nevertheless, it is also shown that the new mixing rule is able to predict bulk properties very accurately, including volumetric properties which activity coefficient models alone are not able to predict. Given that one is able to use predictive activity coefficient models within this mixing rule, such as UNIFAC and COSMO-SAC, this new mixing rule opens the doors for the development of fully predictive SAFT equations of state for mixture systems.