tests/binary_diffusion.R

In chapensk: Estimation of Gas Properties from the Lennard-Jones Potential

library(chapensk)

# graphics parameters
width <- 10
height <- 10
mar <- c(5.1, 4.6, 0.2, 0.6)
mai <- c(1.02, 0.82, 0.04, 0.04)
family <- "Helvetica"
pointsize <- 12
lwd <- 1

Diffusion <- function(T, D0, b) {
  return <- D0 * (T / pkg.env$T0)^b
}

helium <- Gas("helium")
hydrogen <- Gas("hydrogen")
nitrogen <- Gas("nitrogen")
argon <- Gas("argon")
methane <- Gas("methane")
ethane <- Gas("ethane")
propane <- Gas("propane")
butane <- Gas("n-butane")
sulfurdioxide <- Gas("sulfur dioxide")
fluoromethane <- Gas("fluoromethane")
difluoromethane <- Gas("difluoromethane")
trifluoromethane <- Gas("trifluoromethane")

if (interactive()) {
  if (exists("outputDevice")) {
    if (outputDevice == "pdf") pdf(file = "man/figures/binary_diffusion.pdf", width = width, height = height, family = family, pointsize = pointsize)
    if (outputDevice == "svg") svg(file = "man/figures/binary_diffusion.svg", width = width, height = height, family = family, pointsize = pointsize)
  }
  split.screen(figs = c(2, 2))
}

nitrogen_in_helium <- subset(binary_diffusion, (gas == "nitrogen" & bath_gas == "helium"))
argon_in_helium <- subset(binary_diffusion, (gas == "argon" & bath_gas == "helium"))

if (interactive()) {
  screen(1)
}
par(mai = mai, mar = mar)

plot(nitrogen_in_helium$T, nitrogen_in_helium$D,
  log = "xy",
  xlab = expression(paste(italic(T), " / [K]")),
  ylab = expression(paste(italic(D), "/ [cm2/s]")),
  pch = 0, col = "blue"
)
Dcalc <- nitrogen$binary_diffusion(T = nitrogen_in_helium$T, bathGas = helium)
nitrogen_in_helium$Dcalc <- 1E4 * Dcalc
lines(nitrogen_in_helium$T, 1E4 * Dcalc, col = "blue")
nls_n2_he <- nls(D ~ Diffusion(T, D0, b), data = nitrogen_in_helium, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_n2_he))
points(argon_in_helium$T, argon_in_helium$D, pch = 1, col = "red")
Dcalc <- argon$binary_diffusion(T = argon_in_helium$T, bathGas = helium)
argon_in_helium$Dcalc <- 1E4 * Dcalc
lines(argon_in_helium$T, 1E4 * Dcalc, col = "red")
nls_ar_he <- nls(D ~ Diffusion(T, D0, b), data = argon_in_helium, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_ar_he))
legend("bottomright",
  legend = c("nitrogen", "argon"),
  col = c("blue", "red"),
  pch = c(0, 1)
)
if (interactive()) {
  legend("top", bty = "n", legend = "(a)")
  close.screen()
}

methane_in_helium <- subset(binary_diffusion, (gas == "methane" & bath_gas == "helium"))
ethane_in_helium <- subset(binary_diffusion, (gas == "ethane" & bath_gas == "helium"))
propane_in_helium <- subset(binary_diffusion, (gas == "propane" & bath_gas == "helium"))
butane_in_helium <- subset(binary_diffusion, (gas == "butane" & bath_gas == "helium"))

if (interactive()) {
  screen(2)
}
par(mai = mai, mar = mar)

plot(methane_in_helium$T, methane_in_helium$D,
  log = "xy",
  xlab = expression(paste(italic(T), " / [K]")),
  ylab = expression(paste(italic(D), "/ [cm2/s]")),
  pch = 0, col = "blue",
  ylim = c(0.3, 3)
)
Dcalc <- methane$binary_diffusion(T = nitrogen_in_helium$T, bathGas = helium)
lines(methane_in_helium$T, 1E4 * Dcalc, col = "blue")
methane_in_helium$Dcalc <- 1E4 * Dcalc
nls_ch4_he <- nls(D ~ Diffusion(T, D0, b), data = methane_in_helium, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_ch4_he))
points(ethane_in_helium$T, ethane_in_helium$D, pch = 1, col = "red")
Dcalc <- ethane$binary_diffusion(T = nitrogen_in_helium$T, bathGas = helium)
lines(ethane_in_helium$T, 1E4 * Dcalc, col = "red")
ethane_in_helium$Dcalc <- 1E4 * Dcalc
nls_c2h6_he <- nls(D ~ Diffusion(T, D0, b), data = ethane_in_helium, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_c2h6_he))
points(propane_in_helium$T, propane_in_helium$D, pch = 2, col = "dark green")
Dcalc <- propane$binary_diffusion(T = propane_in_helium$T, bathGas = helium)
lines(propane_in_helium$T, 1E4 * Dcalc, col = "dark green")
propane_in_helium$Dcalc <- 1E4 * Dcalc
nls_c3h8_he <- nls(D ~ Diffusion(T, D0, b), data = propane_in_helium, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_c3h8_he))
points(butane_in_helium$T, butane_in_helium$D, pch = 3, col = "orange")
Dcalc <- butane$binary_diffusion(T = butane_in_helium$T, bathGas = helium)
lines(butane_in_helium$T, 1E4 * Dcalc, col = "orange")
butane_in_helium$Dcalc <- 1E4 * Dcalc
nls_c4h10_he <- nls(D ~ Diffusion(T, D0, b), data = butane_in_helium, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_c4h10_he))
legend("bottomright",
  legend = c("methane", "ethane", "propane", "butane"),
  col = c("blue", "red", "dark green", "orange"),
  pch = c(0, 1, 2, 3)
)
if (interactive()) {
  legend("top", bty = "n", legend = "(b)")
  close.screen()
}

if (interactive()) {
  screen(3)
}
par(mai = mai, mar = mar)
methane_in_nitrogen <- subset(binary_diffusion, (gas == "methane" & bath_gas == "nitrogen"))
ethane_in_nitrogen <- subset(binary_diffusion, (gas == "ethane" & bath_gas == "nitrogen"))
propane_in_nitrogen <- subset(binary_diffusion, (gas == "propane" & bath_gas == "nitrogen"))
butane_in_nitrogen <- subset(binary_diffusion, (gas == "butane" & bath_gas == "nitrogen"))
plot(methane_in_nitrogen$T, methane_in_nitrogen$D,
  log = "xy",
  xlab = expression(paste(italic(T), " / [K]")),
  ylab = expression(paste(italic(D), "/ [cm2/s]")),
  pch = 0, col = "blue",
  ylim = c(0.1, 1)
)
Dcalc <- methane$binary_diffusion(T = methane_in_nitrogen$T, bathGas = nitrogen)
methane_in_nitrogen$Dcalc <- 1E4 * Dcalc
lines(methane_in_nitrogen$T, 1E4 * Dcalc, col = "blue")
nls_ch4_n2 <- nls(D ~ Diffusion(T, D0, b), data = methane_in_nitrogen, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_ch4_n2))
points(ethane_in_nitrogen$T, ethane_in_nitrogen$D, pch = 1, col = "red")
Dcalc <- ethane$binary_diffusion(T = ethane_in_nitrogen$T, bathGas = nitrogen)
lines(ethane_in_nitrogen$T, 1E4 * Dcalc, col = "red")
ethane_in_nitrogen$Dcalc <- 1E4 * Dcalc
nls_c2h6_n2 <- nls(D ~ Diffusion(T, D0, b), data = ethane_in_nitrogen, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_c2h6_n2))
points(propane_in_nitrogen$T, propane_in_nitrogen$D, pch = 2, col = "dark green")
Dcalc <- propane$binary_diffusion(T = propane_in_nitrogen$T, bathGas = nitrogen)
lines(propane_in_nitrogen$T, 1E4 * Dcalc, col = "dark green")
propane_in_nitrogen$Dcalc <- 1E4 * Dcalc
nls_c3h8_n2 <- nls(D ~ Diffusion(T, D0, b), data = propane_in_nitrogen, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_c3h8_n2))
points(butane_in_nitrogen$T, butane_in_nitrogen$D, pch = 3, col = "orange")
Dcalc <- butane$binary_diffusion(T = butane_in_nitrogen$T, bathGas = nitrogen)
lines(butane_in_nitrogen$T, 1E4 * Dcalc, col = "orange")
butane_in_nitrogen$Dcalc <- 1E4 * Dcalc
nls_c4h10_n2 <- nls(D ~ Diffusion(T, D0, b), data = butane_in_nitrogen, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_c4h10_n2))
legend("topleft",
  legend = c("methane", "ethane", "propane", "butane"),
  col = c("blue", "red", "dark green", "orange"),
  pch = c(0, 1, 2, 3)
)
if (interactive()) {
  legend("top", bty = "n", legend = "(c)")
  close.screen()
}

if (interactive()) {
  screen(4)
}
par(mai = mai, mar = mar)
sulfurdioxide_in_helium <- subset(binary_diffusion, (gas == "sulfur dioxide" & bath_gas == "helium"))
sulfurdioxide_in_hydrogen <- subset(binary_diffusion, (gas == "sulfur dioxide" & bath_gas == "hydrogen"))
sulfurdioxide_in_nitrogen <- subset(binary_diffusion, (gas == "sulfur dioxide" & bath_gas == "nitrogen"))
plot(sulfurdioxide_in_nitrogen$T, sulfurdioxide_in_nitrogen$D,
  log = "xy",
  xlab = expression(paste(italic(T), " / [K]")),
  ylab = expression(paste(italic(D), "/ [cm2/s]")),
  pch = 2, col = "dark green",
  ylim = c(0.1, 2)
)
Dcalc <- sulfurdioxide$binary_diffusion(T = sulfurdioxide_in_nitrogen$T, bathGas = nitrogen)
sulfurdioxide_in_nitrogen$Dcalc <- 1E4 * Dcalc
points(sulfurdioxide_in_hydrogen$T, sulfurdioxide_in_hydrogen$D,
  pch = 0, col = "blue"
)
points(sulfurdioxide_in_helium$T, sulfurdioxide_in_helium$D,
  pch = 1, col = "red"
)
lines(sulfurdioxide_in_nitrogen$T, 1E4 * Dcalc, col = "dark green")
nls_sulfurdioxide_in_nitrogen <- nls(D ~ Diffusion(T, D0, b), data = sulfurdioxide_in_nitrogen, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_sulfurdioxide_in_nitrogen))
Dcalc <- sulfurdioxide$binary_diffusion(T = sulfurdioxide_in_helium$T, bathGas = helium)
sulfurdioxide_in_helium$Dcalc <- 1E4 * Dcalc
lines(sulfurdioxide_in_helium$T, 1E4 * Dcalc, col = "red")
nls_sulfurdioxide_in_helium <- nls(D ~ Diffusion(T, D0, b), data = sulfurdioxide_in_helium, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_sulfurdioxide_in_helium))
Dcalc <- sulfurdioxide$binary_diffusion(T = sulfurdioxide_in_hydrogen$T, bathGas = hydrogen)
sulfurdioxide_in_hydrogen$Dcalc = 1E4 * Dcalc
lines(sulfurdioxide_in_hydrogen$T, 1E4 * Dcalc, col = "blue")
nls_sulfurdioxide_in_hydrogen <- nls(D ~ Diffusion(T, D0, b), data = sulfurdioxide_in_hydrogen, weights = 1 / U_D, start = list(D0 = 0.62, b = 1.7), trace = TRUE)
print(summary(nls_sulfurdioxide_in_hydrogen))
if (interactive()) {
  legend("top", bty = "n", legend = "(d)")
  close.screen()
}
legend("bottomright",
  legend = c("hydrogen", "helium", "nitrogen"),
  col = c("blue", "red", "dark green"),
  pch = c(0, 1, 2)
)
dev.off()
width <- 5
height <- 5
if (interactive()) {
  if (exists("outputDevice")) {
    if (outputDevice == "pdf") pdf(file = "man/figures/fluoromethane.pdf", width = width, height = height, family = family, pointsize = pointsize)
    if (outputDevice == "svg") svg(file = "man/figures/fluoromethane.svg", width = width, height = height, family = family, pointsize = pointsize)
  }
}
fluoromethane_in_nitrogen <- subset(binary_diffusion, (gas == "fluoromethane" & bath_gas == "nitrogen"))
difluoromethane_in_nitrogen <- subset(binary_diffusion, (gas == "difluoromethane" & bath_gas == "nitrogen"))
trifluoromethane_in_nitrogen <- subset(binary_diffusion, (gas == "trifluoromethane" & bath_gas == "nitrogen"))
par(mai = mai, mar = mar)
plot(fluoromethane_in_nitrogen$T, fluoromethane_in_nitrogen$D,
  log = "xy",
  xlab = expression(paste(italic(T), " / [K]")),
  ylab = expression(paste(italic(D), "/ [cm2/s]")),
  pch = 0, col = "blue",
  ylim = c(0.1, 0.6)
)
fluoromethane_chisq <- function(p) {
  fluoromethane$sigma <- p[1]
  fluoromethane$zeta <- 0
  fluoromethane$epsk <- p[2]
  Dcalc <- 1E4 * fluoromethane$binary_diffusion(T = fluoromethane_in_nitrogen$T, bathGas = nitrogen)
  return <- sum(((fluoromethane_in_nitrogen$D - Dcalc) / fluoromethane_in_nitrogen$U_D)^2)
}
optim_fluoromethane <- optim(par = c(4, 180), fluoromethane_chisq, method = "L-BFGS-B", control = list(trace = 1, parscale = c(1, 100)))
print(optim_fluoromethane$par[1])
print(optim_fluoromethane$par[2])
fluoromethane$sigma <- optim_fluoromethane$par[1]
fluoromethane$zeta <- 0
fluoromethane$epsk <- optim_fluoromethane$par[2]
Dcalc <- fluoromethane$binary_diffusion(T = fluoromethane_in_nitrogen$T, bathGas = nitrogen)
lines(fluoromethane_in_nitrogen$T, 1E4 * Dcalc, col = "blue")
fluoromethane_in_nitrogen$Dcalc <- 1E4 * Dcalc

points(difluoromethane_in_nitrogen$T, difluoromethane_in_nitrogen$D, pch = 1, col = "red")
difluoromethane_chisq <- function(p) {
  difluoromethane$sigma <- p[1]
  difluoromethane$zeta <- 0
  difluoromethane$epsk <- p[2]
  Dcalc <- 1E4 * difluoromethane$binary_diffusion(T = difluoromethane_in_nitrogen$T, bathGas = nitrogen)
  return <- sum(((difluoromethane_in_nitrogen$D - Dcalc) / difluoromethane_in_nitrogen$U_D)^2)
}
optim_difluoromethane <- optim(par = c(4, 180), difluoromethane_chisq, method = "L-BFGS-B", control = list(trace = 1, parscale = c(1, 100)))
print(optim_difluoromethane$par[1])
print(optim_difluoromethane$par[2])
difluoromethane$sigma <- optim_difluoromethane$par[1]
difluoromethane$zeta <- 0
difluoromethane$epsk <- optim_difluoromethane$par[2]
Dcalc <- difluoromethane$binary_diffusion(T = difluoromethane_in_nitrogen$T, bathGas = nitrogen)
lines(difluoromethane_in_nitrogen$T, 1E4 * Dcalc, col = "red")
difluoromethane_in_nitrogen$Dcalc <- 1E4 * Dcalc

points(trifluoromethane_in_nitrogen$T, trifluoromethane_in_nitrogen$D, pch = 2, col = "dark green")
trifluoromethane_chisq <- function(p) {
  trifluoromethane$sigma <- p[1]
  trifluoromethane$zeta <- 0
  trifluoromethane$epsk <- p[2]
  Dcalc <- 1E4 * trifluoromethane$binary_diffusion(T = trifluoromethane_in_nitrogen$T, bathGas = nitrogen)
  return <- sum(((trifluoromethane_in_nitrogen$D - Dcalc) / trifluoromethane_in_nitrogen$U_D)^2)
}
optim_trifluoromethane <- optim(par = c(4, 180), trifluoromethane_chisq, method = "L-BFGS-B", control = list(trace = 1, parscale = c(1, 100)))
print(optim_trifluoromethane$par[1])
print(optim_trifluoromethane$par[2])
trifluoromethane$sigma <- optim_trifluoromethane$par[1]
trifluoromethane$zeta <- 0
trifluoromethane$epsk <- optim_trifluoromethane$par[2]
Dcalc <- trifluoromethane$binary_diffusion(T = trifluoromethane_in_nitrogen$T, bathGas = nitrogen)
lines(trifluoromethane_in_nitrogen$T, 1E4 * Dcalc, col = "dark green")
trifluoromethane_in_nitrogen$Dcalc <- 1E4 * Dcalc
legend("bottomright",
  legend = c("fluoromethane", "difluoromethane", "trifluoromethane"),
  col = c("blue", "red", "dark green"),
  pch = c(0, 1, 2)
)
dev.off()