Computations based on mass transfer through pores.
Usage
rs_from_size(length, width = length, depth, num = 1, D)
gs_from_size(length, width = length, depth, num = 1, D)
gs_w_from_size(length, width = length, depth, num = 1, temperature)
gs_c_from_size(length, width = length, depth, num = 1, temperature)Arguments
- length, width
numeric "Length" and "width" of the stomatal opening, i.e., the major and minor diameters of the ellipse describing the stomatal pore's mean cross section [\(m\)].
- depth
numeric The depth (or diffusion path length) of the stomatal pore [\(m\)].
- num
numeric Number of stomata per unit area [\(mm^{-2}\)].
- D
numeric Diffusion coefficient of the gas [\(m^2\,s^{-1}\)].
- temperature
numeric Leaf temperature. Used to estimate the diffusion coefficient
D.
Value
A numeric vector of resistances expressed in \(s\,m^{-1}\)
or \(s\,mol^{-1}\), or of conductances expressed in \(m\,s^{-1}\) or in
\(mol\,m^{-2}\,s^{-1}\) when the density expressed in estomata per \(m^2\)
is passed as argument to n. With the default of n = 1 the
diffusive conductance per individual pore is returned expressed, e.g., for
molar conductance, in \(mol\,s-1\).
Details
The equation for \(r_s\) from Monteith and Unsworth (2008):
$$r_s = \frac{4(l + \pi\,d / 8)}{\pi\,n\,d^2\,D}$$
is used to compute diffusive resistance in function rs_from_size(),
which can be used to obtain diffusive resistance from a known size of a
pore with circular or elliptical cross section. The value of D, the
diffusion should match that of water vapour or \(CO_2\), and its unit
of expression determines the whether the returned value is expressed as the
inverse of a volume or molar flux rate.
Functions gs_from_size(), gs_w_from_size() and
gs_c_from_size() are convenience wrappers.
Note
This is an approximate computation as plant stomata have a section that varies with depth. The equation incorporates a single end correction and assumes no interference among the flows from neighbouring stomata crossing the bounday layer.
References
Monteith, J. L. and Unsworth M. H. (2008) Principles of Environmental Physics (3ed) Academic Press-Elsevier. ISBN: 978-0-12-505103-3. See Section 11.4 Mass transfer through pores.
See also
Functions D_water() and D_CO2() can be
used to compute the diffusion coefficients as a function of temperature. In
addition function molar_vol() computes the molar volume of an
ideal gas as a function of temperature and pressure. Functions
gs_mol2vol() and gs_vol2mol() interconvert
conductances between molar and volume bases of expression. These functions
are used internally in the functions described here.
Examples
# a single round stomatal pore
gs_from_size(length = 20e-6, depth = 5e-6, D = D_water(23))
#> [1] 6.016561e-10
# a single elliptical stomatal pore
gs_from_size(length = 30e-6, width = 10e-6, depth = 5e-6, D = D_water(23))
#> [1] 6.016561e-10
# 200 circular stomatal pores per mm^2
rs_from_size(length = 5e-6,
width = 5e-6,
depth = 10-6,
num = 200e6,
D = D_water(25))
#> Error in rs_from_size(length = 5e-06, width = 5e-06, depth = 10 - 6, num = 2e+08, D = D_water(25)): Dimensions of stomata are inconsistent, metres expected.
# 50 elliptical stomatal pores per mm^2
rs_from_size(length = 10-6,
width = 5-6,
depth = 20e-6,
num = 50e6,
D = D_water(23))
#> Error in rs_from_size(length = 10 - 6, width = 5 - 6, depth = 2e-05, num = 5e+07, D = D_water(23)): Dimensions of stomata are inconsistent, metres expected.
# a single round stomatal pore with dimensions in micrometers
gs_from_size(length = 20, depth = 5, D = D_water(23))
#> Assuming 'length', 'width' and 'depth' are expressed in micrometres (um)
#> [1] 6.016561e-10