A New Principle for Measuring the Average Relative Humidity in Large Volumes of Non-Homogenous Gas

Abstract

Due to the current extent of arid regions, the pressure on available water resources is increasing. A suitable measure for water availability and dynamics in dry soil is the relative humidity of the soil air. Due to the heterogeneity of soil, water inputs, and root water uptake, the humidity of soil air will vary in space. Therefore, area-representative measurement methods are needed to find a representative measure of the soil water status. Existing sensors for the direct determination of relative humidity only represent a single location with a spatial extent of up to several cm. We introduce a new measuring principle that averages over a spatially heterogeneously distributed relative humidity. It is based on the selective diffusion of water vapor pressure through a tubular semipermeable membrane to/from a closed measurement chamber. A measured pressure change is sensitive to the water vapor pressure and enables, without any external calibration, to estimate an average of the relative humidity. The comparison of our first laboratory prototype of the new sensor with calibrated reference sensors for relative humidity in a range of approx. 4 to 100% proves the linearity of the measuring method and its high accuracy. For further optimization improved reference measurement techniques are necessary. A potential application is the improvement of water use efficiency in irrigated agriculture.

A Phase-Dependent Effect That Enables Multi-Scale Moisture Measurements in Heterogeneous Substrates Using Tubular RH Sensors

“…The gas transport properties of this non-porous rubber have been characterized in various studies [ 31 , 32 , 33 , 34 , 35 , 36 ]. PDMS has a high selectivity for H 2 O compared to other atmospheric gases, such as N 2 , O 2 , Ar, and CH 4 [ 25 ]. It is an order of magnitude more selective for water than it is for CO 2 , i.e., only for a substantial CO 2 concentration or a low temperature would a different membrane material be needed for the measurement.…”

“…To minimize the influence of this relaxation process on the measurement signal, an offset time of 0.1 s was applied between the closing of the pinch valves and the start of pressure registration. To control the cyclic measurement (i.e., to switch the pinch valves and register the pressure differences and ), the actuator unit described in [ 25 ] was used. The differential pressure changes and were calculated from the measured pressure–time curves and (for more detailed information, see [ 25 ]), where a correction of these pressure changes to the inner volume of the membrane tubes was carried out by multiplication with ( , and stored on a laptop.…”

“…Based on the assumptions of (i) the adsorption–desorption equilibria for the gas components in the air and the surfaces of the membrane, (ii) the applicability of the solution-diffusion model for gas transport through a non-porous membrane, and (iii) the validity of the superposition principle, the steady-state diffusive flow through the wall of the membrane can be expressed as the weighted sum [ 37 ] of the differences in the outer and inner partial pressures [hPa] of the ambient gas components (“ ”): where are the permeabilities (given in [m 2 /s] in Table 1 of [ 25 ]), is the universal gas constant, and [K] is the absolute temperature. The partial pressures depend on the mole fractions of the components of the air and its pressure in the surroundings of the membrane tube.…”

“…According to Table 1 in [ 25 ], the ratio is 0.008 and is 0.017. In terms of the mole fractions of the main components of dry air (N 2 , O 2 ), the weighted sum in Equation (5) is about .…”

“…and (iii) yields a representative mean over the heterogeneity of this substrate (iv) over a long period without the need to periodically calibrate the sensor. A membrane-based humidity sensor (MHS) [ 25 ] that works based on the selective diffusion of gases through tubular membranes should be capable of measuring the average relative humidity over an area on the order of to m 2 [ 26 , 27 , 28 ]. We demonstrated a suitable measurement range of up to nearly 100% for the MHS in our prior experiments and therefore believe that the MHS could function well in dry soils [ 3 ], i.e., below the vapor saturation of the soil air.…”