Reference Fluid Research Articles

Chaotic behavior of gas bubble in non-Newtonian fluid: a numerical study

In the present paper, the nonlinear behavior of bubble growth under the excitation of an acoustic pressure pulse in non-Newtonian fluid domain has been investigated. Due to the importance of the bubble in the medical applications such as drug, protein or gene delivery, blood is assumed to be the reference fluid. Effects of viscoelasticity term, Deborah number, amplitude and frequency of the acoustic pulse are studied. We have studied the dynamic behavior of the radial response of bubble using Lyapunov exponent spectra, bifurcation diagrams, time series and phase diagram. A period-doubling bifurcation structure is predicted to occur for certain values of the effects of parameters. The results show that by increasing the elasticity of the fluid, the growth phenomenon will be unstable. On the other hand, when the frequency of the external pulse increases the bubble growth experiences more stable condition. It is shown that the results are in good agreement with the previous studies.

Label-free viscosity measurement of complex fluids using reversal flow switching manipulation in a microfluidic channel

The accurate viscosity measurement of complex fluids is essential for characterizing fluidic behaviors in blood vessels and in microfluidic channels of lab-on-a-chip devices. A microfluidic platform that accurately identifies biophysical properties of blood can be used as a promising tool for the early detections of cardiovascular and microcirculation diseases. In this study, a flow-switching phenomenon depending on hydrodynamic balancing in a microfluidic channel was adopted to conduct viscosity measurement of complex fluids with label-free operation. A microfluidic device for demonstrating this proposed method was designed to have two inlets for supplying the test and reference fluids, two side channels in parallel, and a junction channel connected to the midpoint of the two side channels. According to this proposed method, viscosities of various fluids with different phases (aqueous, oil, and blood) in relation to that of reference fluid were accurately determined by measuring the switching flow-rate ratio between the test and reference fluids, when a reverse flow of the test or reference fluid occurs in the junction channel. An analytical viscosity formula was derived to measure the viscosity of a test fluid in relation to that of the corresponding reference fluid using a discrete circuit model for the microfluidic device. The experimental analysis for evaluating the effects of various parameters on the performance of the proposed method revealed that the fluidic resistance ratio ( R J L / R L , fluidic resistance in the junction channel ( R J L ) to fluidic resistance in the side channel ( R L )) strongly affects the measurement accuracy. The microfluidic device with smaller R J L / R L values is helpful to measure accurately the viscosity of the test fluid. The proposed method accurately measured the viscosities of various fluids, including single-phase (Glycerin and plasma) and oil-water phase (oil vs. deionized water) fluids, compared with conventional methods. The proposed method was also successfully applied to measure viscosities of blood with varying hematocrits, chemically fixed RBCS, and channel sizes. Based on these experimental results, the proposed method can be effectively used to measure the viscosities of various fluids easily, without any fluorescent labeling and tedious calibration procedures.

Densities of Cresols and Linear Alkane Mixtures at High Pressure

This work reports experimental densities for o-, m-, and p-cresol and the m-cresol (x) + o-cresol (1 – x) mixture at x = 0.4891 and heptane (x) + undecane (1 – x) mixtures at x = 0.0, 0.05, 0.2346, 0.5063, 0.7482, and 0.9511, in the compressed liquid region from (313 to 363) K and from (1 to 25) MPa. Vibrating periods of each fluid or mixture under study were carried out in a commercial vibrating tube densimeter from Anton Paar. Then, their corresponding densities were obtained by relating density and vibrating periods of water and nitrogen or water and R134a as reference fluids with the vibrating period of the concerning fluids. Uncertainties for the measured properties are estimated to be ρ ± 0.2 kg·m–3, p ± 0.008 MPa, T ± 0.02 K, and x ± 0.0005. Experimental densities were represented within the experimental uncertainty using an empirical equation of six parameters. Thermodynamic-derived properties were also computed from this equation. Excess molar volumes for the binary mixtures of cresols and linear...

Viscosity measurements of three ionic liquids using the vibrating wire technique

The paper reports measurements of the viscosity of the ionic liquids 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([C6mim][NTf2]), 1-ethyl-3-methylimidazolium ethyl sulfate ([C2mim][EtSO4]) and 1-ethyl-3-methylpyridinium ethyl sulfate [C2mpy][EtSO4], by means of a vibrating wire viscometer. Density measurements on the same samples have been carried out using an Anton Paar U-tube density meter. Recently, we have studied the applicability of the vibrating-wire technique to the measurement of the viscosity of ionic liquids. The fact that these liquids are electrical conductors represents a source of additional experimental uncertainty, if a bare metallic wire is used as a sensor. The previous study involved the measurement of the viscosity of trihexyl(tetradecyl)phosphoniumdicyanamide [P6,6,6,14][dca], and it was shown that the effect of the electrical conductivity was essentially insignificant. The current study extends our work to liquids 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([C6mim][NTf2]), 1-ethyl-3-methylimidazolium ethyl sulfate ([C2mim][EtSO4]) and 1-ethyl-3-methylpyridinium ethyl sulfate ([C2mpy][EtSO4]) which have an order of magnitude higher electrical conductivity than [P6,6,6,14][dca]. The main aim of the present work remains the study of the effect of the electrical conductivity on the performance of the vibrating wire instrument used. One important difference from our previous work, however, is the fact that [C6mim][NTf2] has been proposed to be a reference fluid for several thermophysical properties by IUPAC, for which a round-robin set of thermophysical property measurements has recently been carried out. Therefore another of the main goals of this work is to compare our vibrating wire results for the viscosity of the reference liquid [C6mim][NTf2] with those data. The present results agree within ±2% with a correlation of those results obtained with the IUPAC sample that report water contamination below 120mgkg−1.

Three new branched chain equations of state based on Wertheim's perturbation theory

In this work, we present three new branched chain equations of state (EOS) based on Wertheim's perturbation theory. The first represents a slightly approximate general branched chain solution of Wertheim's second order perturbation theory (TPT2) for athermal hard chains, and the second represents the extension of first order perturbation theory with a dimer reference fluid (TPT1-D) to branched athermal hard chain molecules. Each athermal branched chain EOS was shown to give improved results over their linear counterparts when compared to simulation data for branched chain molecules with the branched TPT1-D EOS being the most accurate. Further, it is shown that the branched TPT1-D EOS can be extended to a Lennard-Jones dimer reference system to obtain an equation of state for branched Lennard-Jones chains. The theory is shown to accurately predict the change in phase diagram and vapor pressure which results from branching as compared to experimental data for n-octane and corresponding branched isomers.

Experimental density measurements of bis(2-ethylhexyl) phthalate at elevated temperatures and pressures

Experimental high-temperature, high-pressure (HTHP) density data for bis(2-ethylhexyl) phthalate (DEHP) are reported in this study. DEHP is a popular choice as a reference fluid for viscosity calibrations in the HTHP region. However, reliable HTHP density values are needed for accurate viscosity calculations for certain viscometers (e.g. rolling ball). HTHP densities are determined at T=(373, 424, 476, 492, and 524)K and P to 270MPa using a variable-volume, high-pressure view cell. The experimental density data are satisfactorily correlated by the modified Tait equation with a mean absolute percent deviation (δ) of 0.15. The experimental data are modeled with the Peng–Robinson (PREoS), volume-translated PREoS (VT-PREoS), and perturbed chain statistical associating fluid theory (PC-SAFT EoS) models. The required parameters for the two PREoS and the PC-SAFT EoS models are determined using group contribution methods. The PC-SAFT EoS performs the best of the three models with a δ of 2.12. The PC-SAFT EoS is also fit to the experimental data to obtain a new set of pure component parameters that yield a δ of 0.20 for these HTHP conditions.

Siloxanes as Working Fluids for Mini-ORC Systems Based on High-Speed Turbogenerator Technology

This paper presents a study aimed at evaluating the use of siloxanes as the working fluid of a small-capacity (≈10kWe) ORC turbogenerator based on the “high-speed technology” concept, combining the turbine, the pump, and the electrical generator on one shaft, whereby the whole assembly is hermetically sealed, and the bearings are lubricated by the working fluid. The effects of adopting different siloxane working fluids on the thermodynamic cycle configuration, power output, and on the turbine and component design are studied by means of simulations. Toluene is included into the analysis as a reference fluid in order to make comparisons between siloxanes and a suitable low molecular weight hydrocarbon. The most influential working fluid parameters are the critical temperature and pressure, molecular complexity and weight, and, related to them, the condensation pressure, density and specific enthalpy over the expansion, which affect the optimal design of the turbine. The fluid thermal stability is also extremely relevant in the considered applications. Exhaust gas heat recovery from a 120 kW diesel engine is considered in this study. The highest power output, 13.1 kW, is achieved with toluene as the working fluid, while, among siloxanes, D4 provides the best simulated performance, namely 10.9 kW. The high molecular weight of siloxanes is beneficial in low power capacity applications, because it leads to larger turbines with larger blade heights at the turbine rotor outlet, and lower rotational speed if compares, for instance, to toluene.

Repeatability of heat transfer tests in a 5 × 5 bundle geometry

This paper describes the repeatability and reliability of bundle heat transfer data obtained in a 5×5 PWR-type bundle subassembly operating at PWR conditions of interest. The 5×5 fuel bundle simulator, installed in the OMEGA-2 loop, is equipped with simple support grids, designed to have a low impact on the flow and heat transfer. The nine central heaters were equipped with the novel sliding thermocouple technique, capable of measuring the detailed axial and circumferential temperature distributions during single-phase and boiling heat transfer tests.In order to obtain highly accurate bundle heat transfer measurements, appropriate experimental procedures and in situ calibrations of all essential instrumentation were employed. This includes (i) the employment of calibrated reference fluid temperature measurement devices, (ii) in situ calibrations of fluid and heater-sheath thermocouples, (iii) calibration of heater wall thickness based on in situ measurements, and (iv) selection of data that satisfy strict acceptance criteria.After applying these corrections and data screening criteria, the measurement accuracy and repeatability was assessed by means of three different tests: (i) single phase heat transfer tests, (ii) boiling tests, and (iii) onset of nucleate boiling (ONB) tests. The results demonstrate the capability of the OMEGA-2 loop in obtaining highly accurate and repeatable single-phase and boiling heat transfer measurements in PWR-type subassemblies.

Relationship between local molecular field theory and density functional theory for non-uniform liquids

The local molecular field theory (LMF) developed by Weeks and co-workers has proved successful for treating the structure and thermodynamics of a variety of non-uniform liquids. By reformulating LMF in terms of one-body direct correlation functions we recast the theory in the framework of classical density functional theory (DFT). We show that the general LMF equation for the effective reference potential φ(R)(r) follows directly from the standard mean-field DFT treatment of attractive interatomic forces. Using an accurate (fundamental measures) DFT for the non-uniform hard-sphere reference fluid we determine φ(R)(r) for a hard-core Yukawa liquid adsorbed at a planar hard wall. In the approach to bulk liquid-gas coexistence we find the effective potentials exhibit rich structure that can include damped oscillations at large distances from the wall as well as the repulsive hump near the wall required to generate the low density "gas" layer characteristic of complete drying. We argue that it would be difficult to obtain the same level of detail from other (non-DFT based) implementations of LMF. LMF emphasizes the importance of making an intelligent division of the interatomic pair potential of the full system into a reference part and a remainder that can be treated in mean-field approximation. We investigate different divisions for an exactly solvable one-dimensional model where the pair potential has a hard-core plus a linear attractive tail. Results for the structure factor and the equation of state of the uniform fluid show that including a significant portion of the attraction in the reference system can be much more accurate than treating the full attractive tail in mean-field approximation. We discuss further aspects of the relationship between LMF and DFT.

Liquid-liquid equilibria in demixing amines: a thermodynamic approach

Carbon dioxide (CO2) Capture from post-combustion industrial effluents will substantially contribute to the reduction of anthropogenic emission of carbon responsible for global warming. The chemical absorption of CO2 in mixed solvents (typically aqueous solution of alkanolamines [1]) is considered as a promising avenue for its capture before transportation and storage [2]. Research projects are developed in order to reduce the energy costs of the regeneration step in process working on absorption-desorption cycles. CO2 desorption requires substantial heating of the whole system containing the products resulting from chemical reactions of CO2. This presentation concerns the use of demixing amines to reduce of the energy involved in capture process. These amines show a liquid-liquid phase separation at moderately elevated temperatures [3]. Such a phase separation occurring at the output of the absorber unit will concentrate carbon in water rich phase that is the only part of the solvent that needs to be regenerated. The presentation will focus on the study of those phase separations for water + amine mixtures. It is proposed to investigate a group of piperidine derivatives and to analyse the effect of substitution in different positions on the ring. First measurements will also be reported for evaluating the influence of CO2 on the temperature of liquid-liquid phase separation. The phase diagrams will be obtained in combining two different methods. A microcalorimeter from setaram was used to determine the liquid-liquid separation temperature. The calorimeter is based on calvet principle and is able to operate in scanning temperature mode from 253 K to 393 K. it allows to measure the differential thermal flux between the measuring cell filled with the solution and the reference cell filled with water as reference fluid. The liquid-liquid separation temperature is determined by evaluating the first point when the thermal flux diverges from the baseline. Simultaneously to these calorimetric measurements, a phase equilibrium cell was developed to get optical information on the liquid-liquid separation. The binary solution was introduced in the cell, and the solution was observed during scanning of temperature. The scanning rate chosen was similar to calorimetric measurements in order to be able to compare directly the results. The separation temperature was noted when the first turbidity is observed. REFERENCES [1] L. Rodier, K. Ballerat-Busserolles, J-Y. Coxam, J. Chem. Thermodynamics, 42, 773-780 (2010). [2] L. Raynal, P-A. Bouillon, A. Gomez, P. Broutin, Chemical Engineering Journal, 10.1016/j.cej.2011.01.008 [3] Y. Coulier, K. Ballerat-Busserolles, L. Rodier, J-Y. Coxam, Fluid Phase Equilibria, 296, 206-212 (2010)

Non-invasive optoacoustic probing of the density and stiffness of single biological cells

Recently, the coherent generation of GHz acoustic waves using ultrashort laser pulses has demonstrated the ability to probe the sound velocity in vegetal cells and in cell-mimicking soft micro-objects with micrometer resolution, opening tremendous potentialities for single-cell biology. However, manipulating biological media in physiological conditions is often a technical challenge when using a laser-based setup. In this article, we present a new opto-acoustic bio-transducer composed of a thin metal film sputtered on a transparent heat sink that allows reducing importantly the laser-induced cellular stresses, and offers a wide variety of optical configurations. In particular, by exploiting the acoustic reflection coefficient at the sample-transducer interface and the photoacoustic interaction inside the transparent sample, the density and compressibility of the sample can be probed simultaneously. Using an ad hoc signal analysis based on Hilbert and wavelet transforms, these quantities are measured accurately for a reference fluid. Similar analysis performed in a single vegetal cell also suggests high sensitivity to the state of the transducer-cell interface, and notably to the presence of the plasma membrane that encloses the cell vacuole.

Solvation of complex surfaces via molecular density functional theory

We show that classical molecular density functional theory, here in the homogeneous reference fluid approximation in which the functional is inferred from the properties of the bulk solvent, is a powerful new tool to study, at a fully molecular level, the solvation of complex surfaces and interfaces by polar solvents. This implicit solvent method allows for the determination of structural, orientational, and energetic solvation properties that are on a par with all-atom molecular simulations performed for the same system, while reducing the computer time by two orders of magnitude. This is illustrated by the study of an atomistically-resolved clay surface composed of over a thousand atoms wetted by a molecular dipolar solvent. The high numerical efficiency of the method is exploited to carry a systematic analysis of the electrostatic and non-electrostatic components of the surface-solvent interaction within the popular Clay Force Field (CLAYFF). Solvent energetics and structure are found to depend weakly upon the atomic charges distribution of the clay surface, even for a rather polar solvent. We conclude on the consequences of such findings for force-field development.

Evaluation of axial dispersion and mixing performance in oscillatory baffled reactors using CFD

AbstractBackgroundThe paper reports extensive CFD work and analyses of an oscillatory baffled reactor (OBR) planned to be used for the production of polyaniline continuously. In the polyaniline process, viscosity changes during the course of the reaction. Two non‐Newtonian fluids were used to represent the stages of fluids during the reaction in a simulation, in addition to water as the reference fluid. Two quantitative measures derived from the CFD results are employed to evaluate OBR reactor performance: the axial dispersion coefficient and the ratio of axial and transverse velocities.ResultsThe CFD data showed that the dispersion coefficient as a function of viscosity exhibits a maximum for given oscillation parameters. In the turbulent regime, the axial dispersion is often correlated with the oscillatory Reynolds number in OBR or equivalent Reynolds numbers in other reactor devices. In the high viscosity regime, such a general correlation is not valid for different operational parameters. The results of the CFD simulations in the moving baffle‐OBR indicate, for the first time, that the axial dispersion coefficients in the moving baffle arrangement is 10–17% higher than that in the moving fluid type, due to enhanced shear rate in the former device. This quantitative information is valuable for the design and smooth transition from batch to continuous reactors.ConclusionThe established dependence of axial dispersion and the ratio of axial to transverse velocities on both viscosity and the operational parameters enhanced the understanding of mixing and dispersion characteristics of the OBR. The CFD analysis supplied the information needed to determine the design parameters for the reactor used in continuous production of polyaniline.© 2012 Society of Chemical Industry

Integrated microfluidic viscometer equipped with fluid temperature controller for measurement of viscosity in complex fluids

In the study described herein, a microfluidic viscometer equipped with fluid temperature controller is proposed for measuring the viscosity of complex liquids containing cells or particles. The microfluidic viscometer is composed of a microfluidic device and a fluid temperature controller. The microfluidic device has two inlets, for the introduction of the sample and reference fluids, respectively, and a spacious diverging channel with a large number of identical indicating channels. A fluid temperature controller, which contained a Peltier chip, micro thermocouples, and a feedback controller, is applied for the consistent control of the temperature of the fluids in the microfluidic channels. For accurately identifying fluid viscosity, an effective design criterion is discussed using an enhanced mathematical model for complex fluid networks. The accuracy of the proposed model is sufficiently investigated via numerical simulations as well as experimental measurements. As performance demonstrations, pure liquids [five different concentrations of SDS (Sodium Dodecyl Sulphate)] and complex fluids (four different blood samples) were used to evaluate the performance of the proposed microfluidic viscometer. This investigation indicated that the proposed microfluidic viscometer is capable of accurately and simply measuring both Newtonian and non-Newtonian fluids, even without the need for calibration procedures, and artifacts faced with a conventional viscometer. We therefore conclude that our proposed microfluidic viscometer has considerable potential for the precise and easy measurement of complex fluid viscosity.

Numerical calculation of thermal effect on cavitation in cryogenic fluids

A key design issue related to the turbopump of the rocket engine is that cavitation occurs in cryogenic fluids when the fluid pressure is lower than the vapor pressure at a local thermodynamic state. Cavitation in cryogenic fluids generates substantial thermal effects and strong variations in fluid properties, which in turn alter the cavity characteristics. To date, fewer investigate the thermal effect on cavitation in cryogenic fluids clearly by the numerical methods due to the difficulty of the heat transfer in the phase change process. In order to study the thermal effect on cavitation in cryogenic fluid, computations are conducted around a 2D quarter caliber hydrofoil in liquid nitrogen and hydrogen respectively by implementing modified Merkle cavitation model, which accounts for the energy balance and variable thermodynamic properties of the fluid. The numerical results show that with the thermal effect, the vapour content in constant location decreases, the cavity becomes more porous and the interface becomes less distinct which shows increased spreading while getting shorter in length. In the cavity region, the temperature around the cavity depresses due to absorb the evaporation latent heat and the saturation pressure drops. When the vapour volume fraction is higher, the temperature depression and pressure depression becomes larger. It is also observed that a slight temperature rise is found above the reference fluid temperature at the cavity rear end attributed to the release of latent heat during the condensation process. When the fluid is operating close to its critical temperature, thermal effects on cavitation are more obviously in both the liquid nitrogen and hydrogen. The thermal effect on cavitation in liquid hydrogen is more distinctly compared with that in liquid nitrogen due to the density ratio, vapour pressure and other variable properties of the fluid. The investigation provides aid for the design of the cryogenic pump of the liquid rocket.

SQUARE-WELL POTENTIAL WITH TEMPERATURE-DEPENDENT WIDTH OF THE ATTRACTIVE WELL: CALCULATION OF CRITICAL POINTS

In the present work, a perturbed virial expansion is applied to calculate fluid critical points. The paper contains two main parts. In the first part, we study the effect of a reference fluid on critical properties. In the second part, we use the square-well potential model and consider a temperature-dependent width of the attractive well to obtain the critical properties of several real fluids. It is found that: (i) The critical temperatures and pressures obtained using a temperature-dependent width of the attractive well have been improved with respect to experimental data except for some fluids. (ii) The best values for critical temperatures and pressures can be obtained using a temperature-dependent width of the attractive well as well as choosing a suitable reference fluid. (iii) Applying a temperature-dependent width of the attractive well is a simple method for obtaining better results.

Fourier space approach to the classical density functional theory for multi-Yukawa and square-well fluids

We present a Fourier space density functional approach for hard particles with attractive interactions, which is based on a previously developed two-dimensional approach [S. Hlushak, W. Rżysko, and S. Sokołowski, J. Chem. Phys. 131, 094904 (2009)] for hard-sphere chains. The interactions are incorporated by means of a three-dimensional Fourier image of the direct correlation function that is obtained from the first-order mean-spherical approximation. In order to improve the computational efficiency, we make extensive use of fast Fourier transforms for calculating density convolution integrals. A two-dimensional implementation of the new density functional approach, based on the expansion of the functional around the bulk fluid density, is used to study structure and adsorption of two model fluids in narrow cylindrical pores. We also investigate two methods that improve the accuracy of the theory as compared to the conventional DFT approach, which expands the free energy functional around the bulk fluid density: One a variant of the reference fluid density functional theory used by Gillespie et al. [Phys. Rev. E 68, 031503 (2003)], and the second a weighted density approach with energy route thermodynamics. Results from these two methods are compared to the conventional approach and also to the results of Monte Carlo simulations. We find that the method of Gillespie et al. and the weighted density approach with energy route thermodynamics yield significant improvement over the conventional approach.

Viscosity of pure fluids—Enskog-2σ model

In this work, we propose a new kinetic theory model (Enskog-2σ model) to analyze and predict the viscosity of simple fluids. The model is based on the Enskog formulation and makes use of two effective diameters to represent two aspects of molecular interactions in Enskog's treatment; namely, the effective diameter representing the excluded volume of a molecule and the effective diameter accounting for the increased probability of collision in comparison to the dilute gas. We have tested the model by analyzing the viscosity of five simple fluids (Ar, CH4, N2, CO2 and SF6) of increasing complexity at supercritical temperatures. The new Enskog-2σ model outperforms previous approaches based on Enskog theory in terms of its correlative ability. We demonstrate that the effective diameter associated with the excluded volume exhibits a universal behaviour as a function of reduced temperature. The conformal behaviour can be achieved by means of a single fluid-dependent length scaling parameter. We make use of this finding to develop a general model that allows the prediction of the viscosity of one fluid from the knowledge of the viscosity of a reference fluid, which in this work was chosen to be Ar. The accuracy of the predicted viscosity depends on the way in which the length scaling parameter was estimated. If the length scaling parameter is obtained from the knowledge of viscosity along a single isotherm, the accuracy of the predicted viscosity is similar to the uncertainty of the original correlation over its entire supercritical range. If a single viscosity value is used to estimate the length scaling parameter, the viscosities of supercritical CH4, N2, CO2 and SF6 are predicted with the maximum deviation of 3.3%, 4.2%, 9.9% and 10.5% respectively over the entire range of validity of the Enskog-2σ model.

Two-phase experimental heat transfer studies on a water-diesel system in a shell and tube heat exchanger

Two-phase heat transfer involving two immiscible systems is gaining importance in petrochemical and allied industries. Varying compositions of diesel and water were experimentally studied in a 1:2 shell and tube heat exchanger. The data on pure water and diesel were fitted to an equation of the form. h1φ = a NmRe.The two-phase multiplier, Φ L, was related to the Lockhart Martinelli (L-M) parameter, χtt², using the two-phase data and a correlation Φ L = b+c(χtt²)+d/(χtt²)² was established. The two-phase heat transfer coefficient was calculated based on the coefficients 'a' and 'm' for pure diesel and pure water along with ФL and the L-M parameter. The calculated values of the two-phase heat transfer coefficient h2φ based on pure diesel and pure water suggest that diesel is a better reference fluid since the average error is much smaller compared to pure water as reference.

Toward Quantitative Coarse-Grained Models of Lipids with Fluids Density Functional Theory.

We describe methods to determine optimal coarse-grained models of lipid bilayers for use in fluids density functional theory (fluids-DFT) calculations. Both coarse-grained lipid architecture and optimal parametrizations of the models based on experimental measures are discussed in the context of dipalmitoylphosphatidylcholine (DPPC) lipid bilayers in water. The calculations are based on a combination of the modified-iSAFT theory for bonded systems and an accurate fundamental measures theory (FMT) for hard sphere reference fluids. We furthermore discuss a novel approach for pressure control in the fluids-DFT calculations that facilitates both partitioning studies and zero tension control for the bilayer studies. A detailed discussion of the numerical implementations for both solvers and pressure control capabilities are provided. We show that it is possible to develop a coarse-grained lipid bilayer model that is consistent with experimental properties (thickness and area per lipid) of DPPC provided that the coarse-graining is not too extreme. As a final test of the model, we find that the predicted area compressibility moduli and lateral pressure profiles of the optimized models are in reasonable agreement with prior results.