243 lines
5.6 KiB
Fortran
243 lines
5.6 KiB
Fortran
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!=======================================================================
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MODULE UTILITIES_4
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!
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USE ACCURACY_REAL
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!
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! It contains the following functions/subroutines:
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!
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! * SUBROUTINE TAU_TO_D(TAU,DC)
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! * SUBROUTINE D_TO_TAU(DC,TAU)
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! * SUBROUTINE ETA_TO_D(ETA,DC,T,RD,D)
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! * SUBROUTINE D_TO_ETA(ETA,DC,T,RD,D)
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! * SUBROUTINE TAU_TO_ETA(TAU,RS,T,ETA)
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!
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!
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CONTAINS
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!
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!=======================================================================
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!
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SUBROUTINE TAU_TO_D(TAU,DC)
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!
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! This subroutine computes the diffusion coefficient from the
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! knowledge of the relaxation time using the relation:
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!
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!
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! v_F^2 * TAU
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! DC = ---------------- where d is the dimensionality
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! d
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!
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!
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! Input parameters:
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!
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! * TAU : relaxation time (in SI)
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!
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!
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! Output parameters:
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!
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! * DC : diffusion coefficient (in SI)
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!
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! Author : D. Sébilleau
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! Last modified : 25 Jun 2020
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USE MATERIAL_PROP, ONLY : DMN
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USE FERMI_SI, ONLY : VF_SI
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USE UTILITIES_1, ONLY : D
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: TAU
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REAL (WP) :: DC
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!
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DC=VF_SI*VF_SI*TAU/D(DMN) !
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!
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END SUBROUTINE TAU_TO_D
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!
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!=======================================================================
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!
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SUBROUTINE D_TO_TAU(DC,TAU)
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!
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! This subroutine computes the relaxation time from the
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! knowledge of the diffusion coefficient using the relation:
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!
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!
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! v_F^2 * TAU
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! DC = ---------------- where d is the dimensionality
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! d
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!
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!
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! Input parameters:
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!
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! * DC : diffusion coefficient (in SI)
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!
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!
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! Output parameters:
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!
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! * TAU : relaxation time (in SI)
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!
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!
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!
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! Author : D. Sébilleau
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! Last modified : 23 Oct 2020
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!
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USE MATERIAL_PROP, ONLY : DMN
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USE FERMI_SI, ONLY : VF_SI
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USE UTILITIES_1, ONLY : D
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: DC
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REAL (WP), INTENT(OUT) :: TAU
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!
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TAU = DC * D(DMN) / (VF_SI * VF_SI) !
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!
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END SUBROUTINE D_TO_TAU
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!
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!=======================================================================
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!
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SUBROUTINE ETA_TO_D(ETA,T,RD,DC)
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!
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! This subroutine computes the shear viscosity from the
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! knowledge of the diffusion coefficient using the relation:
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!
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!
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! k_B * T
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! DC = ----------------
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! 6*pi * ETA* RD
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!
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! Input parameters:
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!
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! * ETA : viscosity in SI
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! * T : temperature in SI
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! * RD : sphere radius in SI
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!
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!
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! Output parameters:
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!
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! * DC : diffusion coefficient (in SI)
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!
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!
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! Author : D. Sébilleau
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! Last modified : 25 Jun 2020
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!
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USE REAL_NUMBERS, ONLY : SIXTH
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USE CONSTANTS_P1, ONLY : K_B
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USE PI_ETC, ONLY : PI_INV
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!
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IMPLICIT NONE
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!
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REAL (WP), INTENT(IN) :: ETA,T,RD
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REAL (WP), INTENT(OUT) :: DC
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!
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DC = K_B * T * SIXTH * PI_INV / (ETA * RD) !
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!
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END SUBROUTINE ETA_TO_D
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!
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!=======================================================================
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!
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SUBROUTINE D_TO_ETA(DC,T,RD,ETA)
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!
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! This subroutine computes the diffusion coefficient from the
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! knowledge of the shear viscosity using the relation:
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!
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!
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! k_B * T
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! DC = ----------------
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! 6*pi * ETA* RD
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!
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!
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! Input parameters:
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!
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! * DC : diffusion coefficient (in SI)
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! * T : temperature in SI
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! * RD : sphere radius in SI
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!
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!
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! Output parameters:
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!
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! * ETA : viscosity in SI
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 25 Jun 2020
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!
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!
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USE REAL_NUMBERS, ONLY : SIXTH
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USE CONSTANTS_P1, ONLY : K_B
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USE PI_ETC, ONLY : PI_INV
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!
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IMPLICIT NONE
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!
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REAL (WP),INTENT(IN) :: DC,T,RD
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REAL (WP),INTENT(OUT) :: ETA
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!
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ETA = K_B * T * SIXTH * PI_INV / (DC * RD) !
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!
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END SUBROUTINE D_TO_ETA
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!
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!=======================================================================
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!
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SUBROUTINE TAU_TO_ETA(TAU,RS,T,ETA)
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!
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! This subroutine computes the shear viscosity from the
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! knowledge of the relaxation using the relation:
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!
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! References: (1) R. Kishore and K. N. Pathak,
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! Phys. Rev. 183, 672-674 (1069)
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!
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!
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! 2
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! ETA = --- * N0 * mu * TAU
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! 5
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!
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! This formula is valid in the low-temperature limit k_B*T << mu
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! for 3D systems
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!
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!
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! Input parameters:
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!
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! * TAU : relaxation time (in SI)
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! * RS : Wigner-Seitz radius (in units of a_0)
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! * T : temperature in SI
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!
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!
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! Output parameters:
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!
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! * ETA : shear viscosity (in SI)
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!
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!
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! Author : D. Sébilleau
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!
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! Last modified : 25 Jun 2020
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!
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!
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USE MATERIAL_PROP, ONLY : DMN
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USE REAL_NUMBERS, ONLY : TWO,FIFTH
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USE UTILITIES_1, ONLY : RS_TO_N0
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USE CHEMICAL_POTENTIAL, ONLY : MU
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!
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REAL (WP), INTENT(IN) :: TAU,RS,T
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REAL (WP), INTENT(OUT) :: ETA
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REAL (WP) :: N0,MU0
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!
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N0 = RS_TO_N0('3D',RS) !
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!
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MU0 = MU('3D',T) !
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!
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ETA = TWO * FIFTH * N0 * MU0 * TAU !
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!
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END SUBROUTINE TAU_TO_ETA
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!
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END MODULE UTILITIES_4
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