AnalyticQuantitiesGaussianDumbbell.hpp

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/**
 * @file
 * Defines the OpenMPCD::AnalyticQuantitiesGaussianDumbbell class.
 */
 
#ifndef OPENMPCD_ANALYTICQUANTITIESGAUSSIANDUMBBELL_HPP
#define OPENMPCD_ANALYTICQUANTITIESGAUSSIANDUMBBELL_HPP
 
#include <OpenMPCD/Types.hpp>
 
namespace OpenMPCD
{
    /**
     * Computes analytic quantities for Gaussian Dumbbells.
     * Gaussian Dumbbells are described in
     * "Multiparticle collision dynamics simulations of viscoelastic fluids: Shear-thinning
     * Gaussian dumbbells" by Bartosz Kowalik and Roland G. Winkler. Journal of Chemical Physics 138,
     * 104903 (2013). http://dx.doi.org/10.1063/1.4792196
     * The formulas used can be found there.
     */
    class AnalyticQuantitiesGaussianDumbbell
    {
        private:
            AnalyticQuantitiesGaussianDumbbell(); ///< The constructor.
 
        public:
            /**
             * Returns the zero-shear Lagrangian multiplier \f$ \lambda_0 \f$.
             * @param[in] rootMeanSquareBondLength The root mean square bond length \f$ l \f$ of the dumbbell.
             */
            static FP zeroShearLagrangianMultiplier(const FP rootMeanSquareBondLength)
            {
                return 1.5 / (rootMeanSquareBondLength * rootMeanSquareBondLength);
            }
 
            /**
             * Returns the Lagrangian multiplier \f$ \lambda \f$.
             * @param[in] rootMeanSquareBondLength The root mean square bond length \f$ l \f$ of the dumbbell.
             * @param[in] shearRate                The shear rate \f$ \dot{\gamma} \f$.
             * @param[in] zeroShearRelaxationTime  The zero-shear relaxation time \f$ \tau_0 \f$ of the dumbbell.
             */
            static FP lagrangianMultiplier(const FP rootMeanSquareBondLength, const FP shearRate, const FP zeroShearRelaxationTime);
 
            /**
             * Returns the zero-shear relaxation time \f$ \tau_0 \f$ of the dumbbell.
             * @param[in] rootMeanSquareBondLength    The root mean square bond length \f$ l \f$ of the dumbbell.
             * @param[in] mpcSelfDiffusionCoefficient The self-diffusion coefficient \f$ D \f$ of the bare MPC fluid
             *                                        particle.
             * @param[in] mpcHydrodynamicRadius       The hydrodynamic (Stokes-Einstein) radius \f$ R_H \f$ of the bare
             *                                        MPC fluid particle.
             */
            static FP zeroShearRelaxationTime(const FP rootMeanSquareBondLength, const FP mpcSelfDiffusionCoefficient,
                                              const FP mpcHydrodynamicRadius);
 
            /**
             * Returns the Weissenberg number \f$ \mathrm{Wi} \f$.
             * @param[in] shearRate               The shear rate \f$ \dot{\gamma} \f$.
             * @param[in] zeroShearRelaxationTime The zero-shear relaxation time \f$ \tau_0 \f$ of the dumbbell.
             */
            static FP weissenbergNumber(const FP shearRate, const FP zeroShearRelaxationTime)
            {
                return shearRate * zeroShearRelaxationTime;
            }
 
            /**
             * Returns the ratio \f$ \mu = \frac{\lambda}{\lambda_0} \f$ of the Lagrangian multipliers with and without shear flow.
             * @param[in] weissenbergNumber The Weissenberg number \f$ \mathrm{Wi} \f$.
             */
            static FP lagrangianMultiplierRatio(const FP weissenbergNumber);
    };
}
 
#endif