Fluid Regime Research Articles

FORMATION МODEL OF A CRACK IN A ROCK WITH NON-STATIONARY SHAPE PARAMETERS DURING HYDRAULIC FRACTURING

Currently, hydraulic fracturing (HF) is used for hard-to-recover hydrocarbon reserves. As a result of hydraulic fracturing, cracks are formed in productive formations. To select the technological parameters of hydraulic fracturing, it is necessary to be able to calculate the fracture shape parameters – length and width. In this regard, the creation of a mathematical model for calculating the parameters of the shape of a crack in a rock is an urgent task. The article presents a mathematical model for the development of a crack in a rock, taking into account the non-stationary parameters of its shape and the flow regimes of the hydraulic fracturing fluid. Also, the proposed mathematical model, unlike the existing ones, takes into account the variable nature of the coefficient of fluid leakage into the reservoir, and the criterion for opening a new rock element. The paper presents the results of a numerical experiment and compares the proposed mathematical model with the results of a numerical experiment. The scientific novelty of the work is the proposed mathematical model of a crack in the rock, taking into account the non-stationary parameters of its shape. The mathematical model, in contrast to the existing ones, is based on the differential equation of motion of the elementary rock element of the opening fracture, taking into account the leakage of hydraulic fracturing fluid into the rock formation. The recommendation for application in engineering practice of the obtained mathematical model is the obtained values of the crack shape, which are comparable with numerical experiments.

Graded Longitudinal Fins Having Spatially Varying Temperature-Dependent Thermophysical Properties

This paper reports transient responses of graded longitudinal fins subject to step change in base temperature and base heat flux wherein the graded fin materials are theorized to have spatial- and temperature-dependent thermal conductivity. Microstructure variations in graded materials (GMs) are addressed by axially varying the thermal conductivity; because GMs are potentially high-temperature application materials, consequently, thermal conductivity and heat generation are, respectively, assumed as polynomial and linear functions of temperature. Additionally, most of the applicable pragmatic fluid regimes are accounted for using the power law convection coefficient. The numerical solution of a typical nonlinear governing differential equation is obtained by using a particle tracking-based method called the lattice Boltzmann method (LBM). The LBM is a mesoscopic-based simulation method centered around the principles of kinetic theory and statistical mechanics. The LBM formulation accompanied with the in-house MATLAB code of the aforesaid problem with varying parameters is reported; also, it is validated with a previously available solution. The foregoing analysis is carried out to enhance the performance of a fin by using the superior thermomechanical property of graded materials. Furthermore, the inclusion of temperature-dependent thermophysical properties and heat generation will provide more accurate design data. The reported graph reveals that, even though a linear GM fin tip possesses thermal conductivity that is 25% less in magnitude in comparison to the Type-II homogeneous material (HM-2), the GM fin always yields a higher fin tip temperature because of grading. In addition, the tip temperature deficits between GMs and HM-2 proportionally increase from 0.4 to 2.1% for values of increasing from 0.1 to 2.0, respectively, for step changes in temperature; whereas in the case of the step change base flux, the deficits increase from 8.72 to 12.1% for values of decreasing from 3.0 to 1.0, respectively.

Numerical study of unsteady pipe flow of an elastoviscoplastic fluid

In this paper we investigate, numerically, unsteady Poiseuille flow of an elastoviscoplastic fluid. The material is described by the rheological model by Putz and Burghelea (2009). The model can describe an elastic solid regime for low stresses, a solid–fluid phase of stresses in the vicinity of the yield stress and a fully fluid regime for large stresses. We impose a time dependent pressure ramp with the form of a triangular function to drive the flow. We compare average velocity across the pipe as a function of pressure drop for different slip laws. We find that the solid–fluid transition is correlated to the slip-law used in the computations but the boundary conditions do not affect neither the deformation-rates nor stress at the bulk and the wall. • Unsteady pipe flow. • Elastoviscoplasticity. • Slip law.

Diffusive regimes in a two-dimensional chiral fluid

Diffusion is a fundamental aspect of transport processes in biological systems, and thus, in the development of life itself. And yet, the diffusive dynamics of active fluids with directed rotation, known as chiral fluids, has not been analyzed in detail so far. Here, we describe the diffusive regimes of a two-dimensional chiral fluid, composed in this case of a set of identical disk-shaped rotors. We found strong experimental evidence of odd diffusion. This odd diffusion emerges in the form of a two-dimensional tensor with an antisymmetric part. In particular, we show that chiral diffusion is complex, featuring transitions between super, quasi-normal, and sub diffusion, and very slowly aging. Moreover, we show that the diffusion tensor elements, including off-diagonal elements; i.e., odd diffusion coefficient, change sign according to flow vorticity. Therefore, the chiral fluid has a self regulated diffusion, controlled by its vorticity.

Efficient dynamical low-rank approximation for the Vlasov-Ampère-Fokker-Planck system

Kinetic equations are difficult to solve numerically due to their high dimensionality. A promising approach for reducing computational cost is the dynamical low-rank algorithm, which decouples the dimensions of the phase space by proposing an ansatz as the sum of separable (rank-1) functions in position and velocity respectively. The fluid asymptotic limit of collisional kinetic equations, obtained in the small-Knudsen number limit, admits a low-rank representation when written as f=Mg, where M is the local Maxwellian, and g is low-rank. We apply this decomposition to the Vlasov-Ampère-Fokker-Planck equation of plasma dynamics, considering the asymptotic limit of strong collisions and electric field. We implement our proposed algorithm and demonstrate the expected improvement in computation time by comparison to an implementation that evolves the full solution tensor f. We demonstrate that our algorithm can capture dynamics in the fluid regime with very low rank, thereby efficiently capturing the asymptotic fluid limit. Moreover we find that a modest rank of between 15 and 20 is sufficient to capture kinetic effects on the problems we consider, showing that the approach is applicable and efficient across a range of regimes.

842 An audit to assess adherence to the Tongue Reduction Integrated Care Pathway for Beckwith Wiedemann Syndrome

Abstract Aim Beckwith-Wiedemann Syndrome (BWS) is a congenital overgrowth syndrome that occurs in approximately 1 in 15,000 births. A cardinal is macroglossia which can lead to sleep apnoea, difficulties feeding, speech, drooling and malalignment of teeth/jaw. Some children require tongue reduction surgery and are managed with a specific protocol to ensure the correct analgesia, fluid regime and commencement of oral feeds are delivered post-operatively. The aim of the audit was to improve adherence and awareness of the protocol to improve the patient journey. Method Initial audit cycle between 22/01/21 – 03/02/21 in the form of anonymous staff survey. Following initial results staff underwent two separate teaching sessions and posters were applied in key wards and staff areas. Repeat audit was completed between 01/07/2021 – 01/08/2021. Results Initial audit results demonstrated 44% (11/25) of ward staff were unaware of the Tongue Reduction Integrated Care Pathway and 56% (14/25) did not know which condition this protocol and surgical procedure was related to. Following both sets of interventions there was an improvement to 77.8% (14/18) of staff being aware of the protocol and 88.9% (16/18) of staff members knew which syndrome was associated with this pathology. Additionally, in the re-audit we demonstrated that 100% of participants were aware of the analgesia protocol. Correct rationale for fluid regime was demonstrated in 56% vs 24% demonstrating there is still room for improvement in this domain. Conclusion We have demonstrated that through teaching and the implementation of a poster we have improved the awareness of the Tongue Reduction Protocol.

SP10.2.1 The FLIP Study – Fluid Resuscitation in Pancreatitis

Abstract Aim Acute pancreatitis (AP) is an emergency surgical presentation which can range in severity from mild to life-threatening. Intravenous fluids are the cornerstone of management. However, there is poor quality evidence regarding optimal intravenous fluid administration. We aimed to establish clinical practice regarding intravenous fluid administration in AP and the effect this has on mortality. Methods Prospective multi-centre audit of patients with AP. Data was collected on intravenous fluid administration within 72-hours of admission. Primary outcome was 30-day mortality and multivariable logistic regression was used to identify predictors of this. Results 254 participants were included. Volume of intravenous fluid delivered over the first three days (median and range) are as follows; Day 1=2L (0–10.5L), Day 2=1L (0–5L), Day 3=0L (0–7.5L). Those with severe pancreatitis (Glasgow score>=3) received more fluid; median 5.7L versus 4L in 72hrs (P=0.003). The following factors were significant predictors of 30-day mortality in our multivariable model: age, Glasgow score, CRP, IHD and pancreatitis aetiology. Overall, volume of intravenous fluid was not associated with mortality in this model (adjusted OR=0.932;0.766–1.134;P=0.483). However, the effect of intravenous fluid volume on mortality differed significantly depending on pancreatitis severity (interaction term P=0.042). In the severe pancreatitis group increased volume of intravenous fluid was associated with significant reductions in mortality (OR=0.655;0.459–0.936;P=0.020). Conclusion In severe pancreatitis more aggressive fluid prescribing is associated with decreased mortality. This is not the case in milder disease. The lack of published literature regarding the impact of fluid regime on outcomes in acute pancreatitis is reflected by the variation of fluid prescribing.

The Effect of Trailing Edge Profile Modifications to Fluid-Structure Interactions of a Vertical Axis Tidal Turbine Blade

Renewable energy has become an essential energy alternative since the continual depletion of non-renewable energy resources and increasing environmental issues. Tidal energy is a promising future renewable resource which can be extracted using a vertical axis tidal turbine. Since it was proposed, a tidal turbine performance requires improvements which can be obtained by a blade’s trailing edge modification. Modifying the blade’s trailing edge profile is confirmed to be one way to improve a turbine’s work. However, the influence of a trailing edge modifications on a vertical axis tidal turbine blade’s interaction with fluid has not been fully understood, thus the fluid induced vibration as the fluid behaviour working on a vertical axis tidal turbine blade has not been completely discovered. In this paper, 2D fluid-structure interactions of modified vertical axis tidal turbine blades are examined and modelled using OpenFOAM. Three different modified blade profiles are proposed: sharp, rounded, and blunt. The modified profiles are employed to an original NACA 0012 blade and their influences on a vertical axis tidal turbine blade interaction are observed. The result discovers the fluid behaviour and fluid-induced vibrations at all positions (represented by 12 positions) over one turbine’s cycle. The results demonstrate the frequency domain blade velocities and time domain blade displacements for all modified blades. The fluid behaviour around the blade is confirmed by pressure distribution plots over the blade’s upper and lower surfaces. The results show that the blunt profile provides less frequent vibrations due to a reducing vorticity in the downstream fluid regime. However, the vibration amplitude that occurs on the blunt blade is higher than those of rounded and sharp profiles. Based on this research, the blunt trailing edge profile appears to be more favourable to be applied and used for vertical axis tidal turbine blades.

Stable and unstable flow regimes for active fluids in the periodic setting

Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular, occurring instability for the manifold of ordered polar states caused by self-propulsion is proved. This represents the prerequisite for active turbulence patterns as observed in a number of applications. The approach is carried out in the periodic setting and is based on the generalized principle of linearized (in)-stability related to normally stable and normally hyperbolic equilibria.

Developing a Grey Forecasting Model for the Air Flowing across the Parallel Plate Duct

The focus of this work is on developing a nonlinear grey model for the laminar flow regime of carrier fluid across the flat plate collector. The trust region reflective algorithm was used to solve the nonlinear laminar flow problem and handle the sparse matrix. The stream function, dimensionless velocity, gradients of velocity components, carrier fluid temperature, and the absorber plate temperature were estimated for a flat plate collector operated with and without a circular chimney. Similarly, the same technique was adopted to determine a model for heat transfer across the absorber plate. The numerically obtained solution was also compared with the parameters obtained through the instrumental measurement. The relative tolerance was kept at 10−5 for the white and grey box solutions. The developed model was noticed to have a smaller deviation than the conventional analytical model to predict the experimental values. The slip condition was observed for the proposed scheme. The uncertainty in the temperature measurement through the proposed model varies from ±0.53 to ±1.47 K. The minimum absolute percentage error (MAPE) lies in the domain of 0.52–1.67% for the nonlinear grey model, whereas the linear grey model for measuring absorber plate temperature has a percentage error of 0.0011–0.02%.

Radiative heat transfer due to solar radiation in MHD Sisko nanofluid flow

AbstractIn the present work, the mathematical model for the solar thermal collectors is considered in the form of a nonlinearly stretching sheet. The radiative heat transfer due to solar radiation in magnetohydrodynamic Sisko nanofluid flow over a stretching sheet in the presence of variable thermal conductivity and a heat source is analyzed effectively. The Sisko fluid has been used as a working fluid in the solar collector. The governing boundary value problem is transformed into a system of nonlinear ordinary differential equations using the similarity transformation technique, which is then solved numerically using the finite difference method combined with the quasilinearization technique. The results shown graphically are discussed for the effects of the thermal conductivity parameter, radiation parameter, and heat source parameter on the flow regime. It is observed that increasing values of radiation parameters imply greater thermal conduction and less thermal radiation, as a result of which the nanofluid temperature in the fluid regime will decrease.

Numerical study on thermal enhancement in magnetohydrodynamic micropolar liquid subjected to motile gyrotactic microorganisms movement and Soret and dufour effects

Motile gyrotactic organism activity in micropolar fluid subjected to simultaneous heat and mass transfer in the presence of thermal diffusion and diffusion thermo effects is modeled. The base fluid is taken as kerosene oil. The immersion of nano-sized particles of C u − T i O 2 kerosene oil makes its rheological characteristics of micropolar fluid because nano-sized particles serve as micro-structures. In this case couple stress, vortex and spin gradient viscosities become significant and simultaneously linear and angular momenta become equally remarkable. So, micropolar theory is the best to model the immersion of nano-structures in the fluid. Similarity variables are used to transform the problems into their dimensionless forms. The mathematical models are solved numerically by applying the finite element method (FEM). The results are validated and numerical experiments are performed to analyze the key parameters of the unknown field variables. In order to analyze the impact of physical parameters on field variables, numerous simulations are performed. The micro-rotation of microparticles and nanoparticles due to fluid deformation motivates fluids particles to rotate faster. Therefore, linear motion is observed to be increased for higher values of vortex viscosity. The curvature parameter has significantly impacted the linear motion of the fluid particles. The impact of the curvature parameter on the movement of nanofluid is lesser than the impact of the curvature parameter on the motion of hybrid nanoparticles. Concentration gradient supports the diffusion of heat in the fluid regime and numerical experiments with variation of Dufour (that measures the effects of concentration gradient on heat diffusion) have shown that concentration gradient is more effective in the case of hybrid nanofluid relative to the mono nanofluid. The angular motion of fluid particles increases when vortex viscosity is increased. Numerical simulations have predicted that the angular motion of particles of hybrid nanofluid has a lesser angular speed than that of the angular motion of particles of mono nanofluid. The Soret number determines the impact of temperature gradient on the diffusion of solute in the fluid. Simulations for various values of Soret number have predicted that the impact of temperature gradient on the diffusion of solute in hybrid nanofluid is stronger than the impact of temperature gradient on the diffusion of solute in mono nanofluid.

Kinetic interpretation of the classical Rayleigh-Taylor instability.

Rayleigh-Taylor (RT) instabilities are prevalent in many physical regimes ranging from astrophysical to laboratory plasmas and have primarily been studied using fluid models, the majority of which have been ideal fluid models. This work presents a five-dimensional (two spatial dimensions, three velocity space dimensions) simulation using the continuum-kinetic model to study the effect of the collisional mean free path and transport on the instability growth. The continuum-kinetic model provides noise-free access to the full particle distribution function permitting a detailed investigation of the role of kinetic physics in hydrodynamic phenomena such as the RT instability. For long mean free path, there is no RT instability growth, but as collisionality increases, particles relax towards the Maxwellian velocity distribution, and the kinetic simulations reproduce the fluid simulation results. An important and novel contribution of this work is in the intermediate collisional cases that are not accessible with traditional fluid models and require kinetic modeling. Simulations of intermediate collisional cases show that the RT instability evolution is significantly altered compared to the highly collisional fluidlike cases. Specifically, the growth rate of the intermediate collisionality RT instability is lower than the high collisionality case while also producing a significantly more diffused interface. The higher moments of the distribution function play a more significant role relative to inertial terms for intermediate collisionality during the evolution of the RT instability interface. Particle energy flux is calculated from moments of the distribution and shows that transport is significantly altered in the intermediate collisional case and deviates much more so from the high collisionality limit of the fluid regime.

This Month in Anesthesiology

This Month in Anesthesiology

Epithermal Au–Ag–Se–Te Deposits of the Chukchi Peninsula (Arctic Zone of Russia): Metallogeny, Mineral Assemblages, and Fluid Regime

Abstract Numerous epithermal Au–Ag deposits and ore occurrences of the Chukchi Peninsula are localized in the Cretaceous Okhotsk–Chukotka (OCVB) continent-marginal and Late Jurassic–Early Cretaceous Oloi (OVB) island arc volcanic belts and in Early Cretaceous postcollisional volcanic troughs. Volcanotectonic depressions, calderas, and volcanic domes control the location of the deposits. The orebodies of the deposits are quartz–adularia veins, sometimes en-echelon ones forming extending vein zones, as well as isometric and linear stockworks. The auriferous veins of most deposits display complex breccia–crustification structures. The vein ores have rhythmically and colloform–banded structures, with a predominantly fine distribution of ore mineral grains, often with banded clusters of ore minerals (ginguro). Native gold is of low fineness; the dispersion of this index varies from low to high. Acanthite is widespread in the ores. Its highest contents are specific to deposits with the repeated redistribution of substance (Kupol, Corrida, and Valunistoe). Based on the results of mineralogical studies, most of the epithermal Au–Ag deposits of the Chukchi Peninsula can be assigned to the Se type. The ores of some deposits (Valunistoe, Dvoinoe, etc.) contain both Se and Te minerals. The telluride-richest sites of the Sentyabr’skoe and Televeem deposits are far from the main orebodies. Most of the Chukchi epithermal Au–Ag deposits have many common characteristics (low and moderate temperatures of fluids, low fluid salinity, domination of carbon dioxide over methane, etc.) typical of low-sulfidation deposits. The maximum temperatures and salinity are specific to fluids in the Central Chukchi sector of the OCVB and in the Baimka zone of the OVB, and the minimum ones are typical of fluids in the East Chukchi flank zone and inner zone of the OCVB. The average salinity of mineral-forming fluids in the inner zone of the OCVB is half as high as the salinity of fluids in the East Chukchi flank zone of this belt, although the sulfate content is higher. At the same time, the fluids in the inner zone of the OCVB are richer in carbon dioxide and bicarbonate ion than the fluids in the East Chukchi flank zone of this belt. The fluid inclusion data permit the Vesennee deposit (Baimka zone) to be regarded as an intermediate-sulfidation one and suggest the presence of epithermal high-sulfidation deposits in the inner zone of the OCVB.

Numerical study of natural convection in an annulus between two concentric cylinders provided with metal foam fins

Natural convection in an annular space provided with metal foam fins attached to the inner cylinder is studied numerically. The metal foam fins made of copper were inserted in different axial sections with three fins in each section. The temperature of the inner cylinder is kept constant while the annular outer surface is adiabatic. The thickness effect of the inner pipe wall was considered. Naiver Stokes equation with Boussinesq approximation is used for the fluid regime while Brinkman-Forchheimer Darcy model is used for metal foam. In addition, the local thermal non-equilibrium condition in the energy equation of the porous media is presumed. The effect of Rayleigh number and number of foam fins in the axial direction, on fluid flow and heat transfer characteristics, were examined. The current model was valid with the available published results and good agreement is noticed. Results showed that as the Rayleigh number increases the dominated of convection mode increases and average Nusselt increases. It was found that at Rayleigh of 106 Nusselt reached its higher value which is 4.6 for the case of adding seven axial metal foams. A comparison between adding foam fins and copper fins was established for a range of Rayleigh numbers between 104 and 106. It showed a good enhancement in Nusselt number and the greatest enhancement percentage was 45.9% at Rayleigh equal 106 for the case of using seven sections of foam fins.

From Darcy Equation to Darcy Paradox

This theoretical paper focuses on the single-phase fluid flow through a granular porous medium. The emphasis is on the Darcy flow regime (without free boundary) of a linear viscous fluid in a saturated, deformable, homogeneous porous medium. The approach is developed at the Darcy scale (also referred to as macroscale or phenomenological scale). Within this framework, some discrete aspects of the flow model are highlighted, the governing equations are revisited, the thermodynamic state functions are reconsidered, and the Darcy paradox is presented. The Darcy paradox is illustrated for the isoshoric-isothermal flow of a viscous fluid in the liquid state, in a homogenous porous medium. After some remarks about the intrinsic assumption of this kind of flow, the governing equations are reduced to a well-known parabolic equation. According to this equation, infinitesimal pressure disturbances diffuse at an infinite speed. To remove this paradox, a mathematical model, based on the elementary scales method, is employed.

Experimental Study of the Crystallization Conditions of Ongonites of the Ary-Bulak Massif (Eastern Transbaikalia)

Phase equilibria were studied experimentally in three rock samples of the Ary-Bulak massif at T = 800–700°C, P = 1 kbar, water content 10 wt %, and oxygen fugacity corresponding to the Ni–NiO and Mt–Hem buffers. Liquidus phases in melts obtained by melting of Ca-rich ongonites are fluorite, topaz, quartz, and plagioclase (andesine, bytownite). The liquid immiscibility of silicate and F–Ca salt melts described in the Ary-Bulak ongonites was not found in the experimental samples. The liquidus temperature of Ca-rich samples is ≥800°C, which is not typical for highly evolved differentiated granite melts. Based on the obtained factual material, it was concluded that simple experiments on melting–crystallization of rock samples of the Ary-Bulak massif do not fully reproduce its formation. It is possible that an important role in nature was played by irreversible processes that are not taken into account in this experimental series: interaction with host rocks, a sharp significant change in the fluid regime or P-T parameters, etc. The relicts of immiscible silicate and salt F–Ca melts described in natural Ca–F-rich samples also could be caused by one of these processes.

Fluid Regime of Gneiss Formation in the Meyeri Thrust Zone of the Northern Ladoga Area (South–Eastern Fennoscandian Shield)

Fluid Regime of Gneiss Formation in the Meyeri Thrust Zone of the Northern Ladoga Area (South–Eastern Fennoscandian Shield)

Records of fluid-rock interactions in the Degana tungsten deposit, India: Inferences from mineral paragenesis, whole-rock and mineral chemistry, and fluid inclusions

The Degana Granite, a F-rich, peraluminous, Neoproterozoic intrusion in NW India hosts the richest tungsten deposit in the country. This study on the Degana W deposit outlines its alteration history, and nature (and evolution) of pre-ore and ore-stage fluids. Moderate salinity (5.4 to 9.6 wt% NaCl equiv.), H2O-CO2 fluids with nearly consistent CO2/(H2O + CO2) ratios of 0.05–0.07 represent the magmatic stage. A pervasive, post-magmatic K (±Na) alteration occurred in a fluid regime dominated by moderate salinity H2O-CO2 fluids. In subsequent alteration stages, the activity of greisen fluids led to the development of steeply-dipping quartz veins (poorly-mineralized), sub-parallel wolframite-bearing greisenized granitic wall-rock (main ore body), and and a late phase of stockwork-type greisen veins. The greisenization is attributed to the incursion of moderate to high salinity (12–22 wt%) H2O-CO2 ore fluids. Such fluids led to K-feldspar and muscovite hydrolysis, and the growth of lithian ferroan muscovite, secondary topaz, and wolframite (±cassiterite, fluorite). Greisenization introduced additional Fe and Li (+W, Sn) in the wall-rock zone and concomitantly leached out Na, K, Cu, Ba, Sr, U, Zr, and Th. Greisen fluids caused Fe leaching along with incorporation of Li in the micas. The compositions of tri- and di-octahedral micas are controlled by distinct substitution mechanisms --VILi1+1IVSi4+2VIAl3+1VIξ1VIFe2+-3IVAl3+-2, and VILi1+4IVSi4+1VIFe2+-1IVAl3+-1VIAl3+-1VIξ-2 (where ξ = vacancy), respectively. We constrain the P-T conditions of W enrichment (380–450 °C and 1.2–1.8 kbar) by means of isochore intersections for coexisting aqueous and carbonic fluid inclusions hosted in greisenized wall rock. The fall in pH of the ore fluid due to fluid-silicate hydrolysis in concomitance with H2O-CO2 immiscibility promoted the decrease in W solubility and subsequent wolframite precipitation. It is surmised that the pervasive, post-magmatic potassic alteration that preceded the ore mineralization acted as a critical pre-conditioning process for ore formation. Both tri- and di-octahedral micas were critical for W enrichment, the former being the likely source for Fe (+W, Sn), and the latter as a reactant for pH-neutralization of greisen fluid, thereby limiting its W solubility.