TENSIOMETER AND METHOD FOR DETERMINING A SPATIALLY AVERAGED WATER POTENTIAL IN A TEST BODY

Description

[0001] The invention relates to a tensiometer and a method for determining a spatially averaged water potential in a test body. background

[0002] Plants must overcome the soil's water potential to extract water from it. This water potential comprises the gravimetric potential, the matrix potential, and the osmotic potential. Under humid, unsaturated conditions, the locally available water potential is generally considered to be equal to the matrix potential—the osmotic potential can generally be neglected. In arid soils, the concentration of dissolved salts, particularly due to the evaporation of soil water in the near-surface soil, can increase the contribution of the osmotic potential to the water potential to a level that can no longer be ignored.External conditions such as precipitation or irrigation, humidity, temperature, evaporation and locally varying internal source / sink phenomena in the soil, such as gravity-induced water removal, water uptake via plant roots or the binding of water to hygroscopic substances (often salts), constantly lead to local changes in water potential, which in turn cause water flows that vary over time. State of the art

[0003] Water potential is measured using tensiometers, which are categorized according to their measuring principle as either direct or indirect. Direct measurement is based on a water-filled cavity encapsulated by a porous filter cartridge in capillary contact with the soil and equipped with a pressure sensor. If the external water potential causes water to be drawn from the cavity, this leads to a drop in pressure within this type of tensiometer. The resulting pressure difference to atmospheric pressure (also known as soil suction) corresponds, at equilibrium, to the water or matrix potential. In indirect methods, the water potential in the soil is brought into equilibrium with a separate hygroscopic medium in which the water activity or water potential can be measured appropriately.Measurement methods are based, for example, on the change in the capacitance of a capacitor's dielectric material consisting of the medium, the electrical conductivity of the medium, the propagation of heat pulses through the medium, or the pressure in this medium.

[0004] Especially under dry conditions, where the demand for irrigation water reaches the limits of economically available water, irrigation strategies are needed that reliably supply plants with water before they reach the permanent wilting point (where plants are irreparably damaged). In the region of the permanent wilting point, water potentials can reach -1.5 MPa to -2.5 MPa in extreme cases. The roots then, figuratively speaking, draw water from a hanging column of water with a height Δ equivalent to this negative pressure. h = ρ wg ψ w (Waterproof) ρ w , gravitational constant g, water potential Ψ w ) of 15,000 to 25,000 cmWs (cm water column) on the remaining water still physically bound in capillaries and on surfaces (water films, gap fillings). In direct measuring tensiometers, the water would boil under these conditions, rendering them unusable in these ranges. Even at a suction tension of 700 to 800 cmWs, water vapor bubbles form in this type of tensiometer, making it impossible to measure the external water potential. Indirect measuring tensiometers, such as the polymer tensiometer, demonstrate their strength in this range. The measuring chamber of this type of tensiometer, equipped with a pressure sensor, is filled with a hygroscopic polymer that couples to the external water via a microporous membrane, such as microporous aluminum oxide, through a porous candle that is pressure-stable up to, for example, 15 bar.Hygroscopic polymers described in the literature include substances such as polyethylene glycol (PEG), polyacrylamide (Praestol 2500), and polysaccharide (Dextran 500). Due to their molecular size, these substances cannot penetrate the microporous membrane. However, they bind any water that enters the polymer, reducing its activity and thus drawing further water from the surrounding environment. This creates an overpressure (osmotic pressure) relative to the pressure of the water in the vicinity of the tensiometer. At the equilibrium of the chemical potentials of water within the polymer (determined by its osmotic potential) and in the soil (determined by its water potential), this overpressure shifts proportionally with the external water potential. If the external water potential decreases, the soil draws water from the polymer tensiometer, and the fluid pressure within the polymer decreases; vice versa.As long as the pressure in the polymer tensiometer is greater than the water vapor pressure, the formation of water vapor bubbles is prevented. This pressure, which limits the measuring range, is determined by the type of polymer and approximately coincides with the osmotic potential of the polymer supersaturated in water. US 5005403 discloses a method for determining a concentration in solutions by measuring a differential osmotic pressure across a permeable membrane. Problems of the polymer tensiometer

[0005] After calibrating the polymer tensiometer against a freely moving water phase at atmospheric pressure (hereinafter referred to as standard conditions) and taking temperature dependencies into account, the soil's water potential can be determined. By its very nature, this tensiometer principle is particularly suitable for deep (large in magnitude) water potentials and large measuring ranges, since the reference point of the measuring setup is defined by the polymer's osmotic potential. If this is approximately compensated by the water potential in the test specimen, the pressure in the tensiometer approaches zero (near the water vapor pressure).

[0006] The time required for equilibrium is limited by the volume of the polymer-filled measuring chamber. Therefore, polymer tensiometers with significantly minimized measuring chamber volume and maximized exchange surface area have been developed, for example, with chamber heights of 1.1 to 2.5 mm and a radius of 8.45 mm, and conical exchange surfaces in the range of 167 to 260 mm². While this is an important optimization step with regard to minimizing the settling time, it necessitates a local measurement from the perspective of field applications.

[0007] For efficient control of, for example, an irrigation system, a water potential sensor that averages over locally varying water potentials would be desirable. In particular, the ability to measure this average water potential over a lateral area would be advantageous, the size of which is sufficient, for instance, to average representatively across soil areas with varying root penetration. Such a spatial averaging area is characterized by the soil-dependent dimension of the so-called pedon, a soil section with a volume chosen to be sufficiently large so that the relevant soil properties are statistically averaged (representatively) in a site-specific manner. This pedon is often considered a soil section with a lateral extent of approximately 1 m, which is frequently used as a guide for the diameter of lysimeters.Depending on the soil type, but also on its vegetation, the actual required averaging length (pedon) for a representative determination of the water potential will lie particularly in a range from 1 dm to more than 10 m. Task

[0008] The invention is based on the objective of creating a robust, indirectly measuring tensiometer and a method that enables a representative determination of water potential or matrix potential in a heterogeneously composed test specimen, such as a pedon-scale section of a soil sample. The tensiometer and the method based on it should enable the representative, averaged determination of locally varying water potentials in both moist (humid) and dry soils (arid climates).To optimally adapt the measurement accuracy and the measuring range to the respective application, the following should also be implemented in particular: i) the reference point of the measuring arrangement should be moved to the water potential of the free water surface at atmospheric pressure (standard conditions), since naturally the greatest accuracy must be achieved here, ii) depending on the problem, other reference potentials should also be adjustable, and iii) the width of the measuring range should be adjustable by the user depending on the problem or be predefined depending on the use. Implementation according to the invention

[0009] The problem is solved by a tensiometer with the features of claim 1 and a method with the features of claim 15. Advantageous embodiments of the invention are set forth in the dependent claims.

[0010] The indirectly measuring tensiometer for measuring water potential or matrix potential, introduced below, is equipped with a reference system and is based on at least two non-porous, semipermeable membrane tubes made of suitable polymers, filled with osmotic solutions and sealed. Due to the nature of the membranes, substances can only cross them diffusively. A pressure difference between the osmotic solutions is measured using suitable pressure sensors. Furthermore, a method is introduced whereby the pressure difference detected by the tensiometer (according to one of the embodiments described in this disclosure) yields a measure averaged over the length of the membrane tube, which, with a suitable choice of reference potential and membrane material, corresponds to the spatially averaged water potential or the spatially averaged matrix potential of the water in the test specimen.Tensiometers and methods thus make it possible, as described below, to spatially average the water potential or the matrix potential in the test body, for example a pedon-scale soil body.

[0011] In particular, a tensiometer is provided, comprising a measuring cell of selectable length, referred to as a potential cell, which includes a sealable measuring chamber enclosed with a tubular semipermeable membrane and which can be installed in a test body; a reference system comprising a reference chamber and a measuring cell of selectable length, referred to as a reference cell, which includes a sealable measuring chamber enclosed with a tubular semipermeable membrane, wherein the reference cell is integrated into the reference chamber of the reference system, and wherein the reference chamber contains or is fillable with an osmotic reference solution, wherein the potential cell and the reference cell are filled or fillable with an osmotic solution; and a pressure measuring device configured to measure at least a pressure difference between the measuring chambers of the potential cell and the reference cell.

[0012] Furthermore, a method for determining a spatially averaged water potential in a test body is provided, wherein, by means of the tensiometer according to one of the described embodiments, at least the pressure difference between the measuring chambers of the potential cell and the reference cell is detected, which, due to its arrangement within the reference chamber of the reference system, allows reference to a selectable reference potential, wherein, starting from the detected pressure difference, the water and / or matrix potential in the test body averaged over the length of the potential cell is determined and provided as a measured value, depending on the semipermeable membrane used and the reference potential. Components of the tensiometer and their terms

[0013] The tensiometer comprises a potential cell and a reference system, and furthermore in particular a tensiometer board and suitable housing components depending on the design (the reference numerals are given with reference to the figures).

[0014] The potential cell comprises a membrane tube, the outer surface of which is in contact with a substrate in the test body for measuring the water potential, and the inner surface of which, in particular radially, defines a measuring chamber.

[0015] The reference system comprises a reference chamber filled with a reference solution, into which a reference cell is integrated.

[0016] The reference cell comprises a membrane tube, the outer surface of which is in contact with the reference solution for measuring a reference potential, and the inner surface of which, in particular radially, defines a further measuring chamber.

[0017] The measuring chambers are formed, or are formed, in particular by the respective membrane tubes.

[0018] The potential cell and reference cell are designed as radially symmetrical measuring cells, which may be equipped with suitable measuring devices and functional elements (for volume reduction and mechanical stabilization). The measuring chambers of both measuring cells, which can be closed, in particular with valves, are filled with identical osmotic solutions.

[0019] The tensiometer board contains integrated electronic circuitry for data acquisition, processing, evaluation, storage and / or output, as well as suitable connection options depending on the design.

[0020] The tensiometer is powered by an internal or external voltage source. Operating principle

[0021] The following section explains the operating principle of the tensiometer using an example based on structurally identical measuring cells. The potential cell is to be exposed externally to a test object, in particular the ground. The reference cell is to be located in the reference chamber filled with the reference substance, e.g., water, at atmospheric pressure (standard conditions). Both measuring cells are exposed to the same external temperature, sealed off from each other and from the outside environment, and initially contain the same concentration of a hygroscopic substance dissolved in water. A pressure measuring device records the differential pressure Δp between the measuring chambers of the potential cell and the reference cell. Alternatively, the pressure measuring device can also measure the differential pressures within the respective measuring chambers. Δp P and Δp R to measure atmospheric pressure (Index " P ", or " R " for potential or reference cell).

[0022] The measuring chambers are radially sealed by tubular, semipermeable, non-porous membranes that water can only cross diffusively. This exchange of water with the surrounding environment occurs until the difference in the chemical potentials of the water on either side of the respective membrane disappears. The chemical potential and the activity of water are analytically linked in equilibrium. Outside, the activity of the water is determined by the matrix potential Ψ prevailing around the potential cell. m and the osmotic potential of the pore solution ψ Π or the reference potential ψ 0 of the reference solution present as a reference system around the reference cell is determined, this is done within the two measuring chambers (index " MK ") through the osmotic potential ψ MK = ψ P = Ψ R of the initially identical osmotic solutions.

[0023] Aqueous solutions are approximately incompressible. Therefore, for an ideal, volume-constant measuring chamber of length L, water exchange results in a changing osmotic pressure, which would adjust itself locally within the chamber depending on the position of the external water potential. However, if the osmotic solution has a sufficiently low viscosity, it equalizes the local pressure differences in the measuring chamber quickly enough – an average pressure is established over the entire length of the measuring chamber. The differential pressure in the potential cell, relative to atmospheric pressure, is thus: Δ p P = Ψ ¯ w − Ψ MK , Ψ ¯ w = 1 L ∫ 0 L Ψ w x dx

[0024] Instead of going to a local place x 0 existing water potential Ψ w ( x 0 ), is the differential pressure Δ p P thus proportional to the soil water potential ψ averaged over the length of the potential cell w . Similarly, the differential pressure in the reference cell, relative to atmospheric pressure, yields Δ p R = ψ 0 - ψ MK and thus creates a simultaneous reference to the reference potential Ψ 0 , for example to ψ 0 = 0 for standard conditions.

[0025] The pressure difference between the two measuring cells, assumed to be ideal (constant volume) Δ p P - Δ p R = ψ w - ψ 0 approximately eliminates the osmotic potential present in the measuring chambers. Simultaneously, this coupling of the two measuring cells causes a rotation of the measuring range, thus defining the zero point of the pressure difference exactly by the reference potential. If the reference potential is defined for standard conditions, then the mean water potential present in the test specimen is given by ψ 0. w = Δ p P - Δ p R determined. The differential pressure Δp is calculated. = Δp P - Δ p RThe pressure between the two measuring chambers is determined directly using a differential pressure sensor, thus yielding the mean water potential according to ψ. w = Δ p directly from this measurement. Determination of water and matrix potential

[0026] The water potential can thus be measured, for example, for a reference potential defined under standard conditions. Suitable non-porous membrane materials for the measuring cells include membranes that are highly permeable to water, such as PEBAX 1074, PBT / PEO block copolymers, silicone, etc. In a variety of applications, especially under humid climatic conditions, this water potential also determines the matrix potential with sufficient accuracy, since the osmotic potential of the soil solution is often comparatively small (in magnitude).

[0027] Under arid climatic conditions (dry, warm soils), concentrated salts (electrolytes) can be present in the soil solution as a result of solvent evaporation, creating a non-negligible osmotic potential. To determine the matrix potential, the effect of this osmotic potential in the measured differential pressure must be eliminated or reduced. If permeable polymer membranes are used for water in the measuring chambers, but not for the electrolytes, the osmotic potential can be approximately compensated for by a suitable shift in the reference potential. This simply requires filling the reference system with a reference solution that is osmotically equivalent or similar to the soil solution. However, the electrolyte concentration in the soil solution varies depending on precipitation, evaporation, and the salt content.Tracking the reference potential, for example via conductivity measurements in the soil and reference solutions, would be possible, but would entail increased measurement and control effort. Without such tracking, the matrix potential measured with a tensiometer of this design will therefore vary depending on the difference in the osmotic potentials of the electrolytes in the soil and reference solutions.

[0028] In contrast, using an ionomer membrane to construct the measuring chambers would also allow ions to permeate the membrane. The osmotic effects of the electrolytes on both sides of the potential cell would then approximately cancel each other out. If the reference potential is defined by standard conditions, the matrix potential can now be determined precisely.

[0029] Potentially suitable ionomers include, for example, Nafion (DuPont), Flemion ™< (Asahi Glas Co. Ltd) and DowMembrane ®< (Dow Chemical).

[0030] Nafion ("General Information on Nafion® Membrane for Electrolysis", Product Information, Bulletin 97-01, Rev. 04 / 2006), a sulfonated tetrafluoroethylene (PTFE) polymer, is highly permeable to water (and other polar substances) as well as to cations, can be used at temperatures up to 190°C, and is chemically extremely stable. The only slightly elastic Nafion can withstand exceptionally high mechanical stresses, depending on its formulation (see product information), which is significant for the present application. Considering the pressure stability of Nafion membrane tubing up to 16 bar, a tensiometer constructed with this material has a wide possible measuring range within which the membrane tubing does not require mechanical support against the resulting overpressure.

[0031] For Nafion as a membrane material, cations would preferentially diffuse into the measuring chamber of the potential cell, followed by anions. Thus, appropriately designed measuring cells filled with a suitable osmotic solution can, albeit with a time lag, achieve the desired equalization of the external electrolyte concentration. During this concentration equalization, however, an osmotic pressure differential arises, which depends on the differences in electrolyte concentrations on either side of the membrane.

[0032] The preferential diffusion of cations through the Nafion membrane, on the other hand, leads to charge separation. As a result of the accumulation of cations in the measuring chamber, a positive charge excess builds up here, accompanied by a negative charge excess in the external environment of the membrane. The resulting electrochemical potential difference Δ φThis causes a migration of cations in the opposite direction to concentration-driven diffusion. According to the Nernst-Planck equation, the resulting mass flux density can be ṅ j ; through the membrane as a superposition of diffusion and migration ṅ j = -D j (∇c j - F zjcj / ( RT ) ∇φ) are described, where c j the concentration of the cation j the cargo zj is and D j whose diffusion coefficient in the membrane. F is the Faraday constant, R the universal gas constant and T the temperature. For negligibly small mass flows ( ṅ j → 0 ∀ j ), a relationship approximately proportional to the difference in cation concentration and electrochemical potential arises on both sides of the membrane Δ φ ~ ΣΔ cj / ( zjcj ) .

[0033] The totality of ions inside and outside the measuring chamber is subject to the condition of charge neutrality. Therefore, any positive excess charge built up inside the measuring chamber must be equal in magnitude to any negative excess charge resulting outside. These two excess charges thus generate an electrical voltage that depends on the type and concentration of the electrolytes. U via the membrane.

[0034] A suitable measurement of this voltage allows, firstly, the verification of balanced electrolyte concentrations on both sides of the membrane, since the voltage must then vanish. However, based on a calibration of the voltage against the resulting osmotic pressure in the potential cell, it is also possible to compensate for the effect of fluctuating osmotic potential differences on the measurement of the matrix potential by reducing or eliminating the voltage-dependent pressure from the measured differential pressure Δp. In one embodiment, therefore, the tensiometer is provided with a voltage measuring device for measuring an electrical voltage between the inside and outside of the membrane of the potential cell.

[0035] In one embodiment of the method, it is accordingly provided that the matrix potential ψ m The electrical potential U is determined in the test specimen in measuring cells equipped with ionomer membranes by measuring the electrical voltage U between the inside and outside of the membrane of the potential cell using the voltage measuring device, which, after calibration, makes it possible to determine a pressure that is caused by electrolyte concentration-dependent osmotic potential differences on both sides of the membrane, and to derive this from the measured pressure difference Δ. p to eliminate and thus the matrix potential ψ m to determine. Compensation for the pressure-dependent expansion of non-ideal measuring chambers

[0036] For non-ideal measuring chambers, the pressure-dependent elastic expansion of the chambers can lead to a dilution of the osmotic solution, resulting primarily from the pressure-dependent expansion of the membrane tubes. In the reversible range, this expansion is proportional to the pressure difference between the inside and outside of the respective membrane according to Hooke's law and can be taken into account in a reference-based measurement using a proportionality factor when determining the water or matrix potential. The influence of the elastic deformation can be approximated to a first approximation by a constant that needs to be calibrated. α take into account the water or matrix potential, which can be proportional to Δ p (1 + α) are calculated. In one embodiment of the method, it is therefore provided that a pressure-dependent elastic deformation of the measuring chambers of the measuring cells is taken into account when determining the water and / or matrix potential ψ. w / m is taken into account. Reference point and measuring range

[0037] By arranging the reference cell within the reference chamber, a defined reference potential ψ0 can be created, around which the measuring range can be adjusted depending on the problem. As described in the introduction to the operating principle, this reference potential defines the zero point of the measuring range, from which the measuring range rises with an adjustable width.

[0038] The composition of the reference solution and the pressure in the reference chamber determine this reference potential ψ₀. By appropriately selecting this reference system, contributions from components in the water potential can be eliminated from the measurement result in a design-specific manner. An osmotically adapted reference solution in the reference chamber, for example, one adapted to the measurement environment, can be used to determine the matrix potential in isolation from the osmotic potential. A pressure potential of interest can also be set in the reference chamber or imposed by the environment.

[0039] Depending on the problem, the measuring range can be determined by filling the measuring chambers with a suitable osmotic solution.

[0040] In embodiments of the method, it is therefore provided that the hygroscopic substance(s) and their concentrations within the osmotic solutions in the potential cell and in the reference cell and / or reference substance(s) as well as their concentrations in the reference solution are selected or have been selected depending on the properties of the test body and the type of membrane used.

[0041] In order to also be able to set a pressure in the reference chamber, one embodiment provides that the reference chamber has a device for setting a pressure. Osmotic solution

[0042] Osmotic solutions with a predetermined osmotic potential can be produced by dissolving suitable hygroscopic substances in defined concentrations in water. Besides salts (electrolytes), water-soluble polymers such as polyethylene glycols, polyacrylamides, and polysaccharides are suitable for this purpose, provided they cannot penetrate the membrane (diffusively) or can only do so at a negligible rate.

[0043] Polyethylene glycols (PEGs) are linearly linked polyethers available in different chain lengths (number of repeat units of the base molecule [-CH2-CH2-O-]). They are biodegradable and widely used in medicine and cosmetics. The solubility and osmotic activity of dissolved PEGs decrease with increasing chain length. Short-chain PEGs, e.g., PEG 400 or PEG 800 (400 or 800 repeat units, respectively), are miscible with water in almost any ratio, thus allowing for the design of various measurement ranges. Constructive variants of the tensiometer

[0044] The reference system (especially the reference chamber) can be encased, for example, in a suitable flexible plastic tube, such as one made of polyurethane (PU), polyvinyl chloride (PVC), etc. If pressure stability of the reference system is required, thin-walled capillaries made of stainless steel or suitable pressure-resistant plastics can be used. The tube / capillary ends are sealed externally or contain capillaries and valves for filling the reference chamber. To maintain the reference chamber at a defined pressure level, an external pressure (atmospheric pressure, hydrostatic water pressure) can be applied to the wall of the reference chamber or supplied to the interior of the chamber via a capillary. The reference cell is arranged appropriately within the reference chamber, for example, by passing it radially symmetrically through the chamber.

[0045] The measuring cells can be identical in construction. In particular, the measuring cells then have the same lengths, diameters, and membrane wall thicknesses, and the non-porous, semipermeable membranes are identical in type and manufacture.

[0046] At the same temperature within the tensiometer, the length or volume of the reference cell can be reduced. The same applies to the entire reference system, which can then be combined with the now comparatively larger potential cell at a suitable position. In one embodiment, therefore, the reference system is smaller than the potential cell and positioned at a suitable location within the tensiometer.

[0047] In one embodiment, the tensiometer comprises an element extending along a longitudinal axis of the measuring chambers of the measuring cells, which is inserted into the potential cell or into each potential and reference cell. This element is centrally located with respect to a cross-section of the measuring chambers oriented perpendicular to the longitudinal axis. The element can be, for example, cylindrical (round bar) or have a different cross-section, such as a profiled bar. This reduces the volume fraction of the measuring chambers containing the osmotic solutions. Given the unchanged geometry of the surrounding membrane, this volume reduction leads to faster pressure adjustment in the measuring chambers, thus shortening the tensiometer's response time.The rod-shaped element has a cross-section that allows it to be integrated into the respective measuring chamber in such a way that a volume remains between the element and the inner membrane surface, which can be filled with the osmotic solution and is distributed radially as evenly as possible around the element. Radially symmetrical integration of the element into the respective measuring chamber is optimal. The element is matched to the length and diameter of the respective measuring chamber to achieve a minimal response time of the tensiometer. The element is either flexible or rigid and can have ridges for position definition. These ridges are arranged spirally, linearly, or annularly on its surface and make linear or point contact with the membrane wall. Alternatively, a fleece or mesh-like stocking made of a suitable (incompressible) plastic can be used for position definition.

[0048] Integrating a volume-reducing element into the potential chamber as described above enables a further tensiometer design in which the reference system is integrated into the measuring chamber of the potential cell. In one embodiment, the reference system is integrated into the potential cell along its length. In a further developed embodiment, the reference system at least partially forms the element described above. Equal lengths for both measuring cells still allow measurements over areas with locally varying temperatures. The hollow cylindrical space remaining in the measuring chamber of the potential cell after the integration of the reference system achieves the desired reduction in the volume filled with the osmotic solution and thus reduces the tensiometer's response time.The chambers, membranes and the wall of the reference system can be manufactured in such a way that the volumes filled with the osmotic solution of the potential and reference cells are identical, or that a reproducible geometric relationship of membrane wall thicknesses, membrane areas and volumes of osmotic solutions ensures that the adjustment of the osmotic pressure, regardless of the membrane materials used (which may be different), occurs faster or at the same speed in the reference cell compared to the potential cell. Mechanical stabilization

[0049] The measuring chambers can be integrated into capillary tubes or, in particular, tubular braids, which are provided with water-permeable recesses and into which the respective measuring cells are flush-fitted / pressed. In one embodiment, therefore, the tensiometer is provided with capillary tubes featuring permeable cavities and / or pores, into which the membranes of the measuring cells are flush-fitted.

[0050] Alternatively, the membranes of the measuring cells can be at least partially integrated as filling material into the recesses of the capillary tubes or braids. Therefore, in a further embodiment, the tensiometer is provided with capillary tubes or, in particular, tubular braids containing cavities and / or pores, wherein the membranes of the measuring cells are at least partially integrated into the cavities.

[0051] Both methods reduce the elastic expansion of the measuring cells, allowing the volumes in the measuring chambers to be kept approximately constant even at high pressures. This type of stabilization also enables a reduction in the wall thickness of the membranes and the use of different polymers or ionomers while maintaining approximately the same expansion behavior. Furthermore, this protects the membranes from external mechanical influences.

[0052] The capillary tubes can, for example, have slotted recesses, be made of porous sintered metals or ceramics, or even be made of plastics. Braids can consist of or encompass metallic and / or non-metallic fibers and enclose and / or embed the membrane with a defined mesh size. Integrated temperature measurement

[0053] The tensiometer can be equipped with temperature sensors that, depending on the design, are integrated into the potential cell, the reference cell, or both measuring cells. In one embodiment, the tensiometer therefore has at least one temperature sensor in or on the potential cell and / or in or on the reference cell. This at least one temperature sensor allows, in particular, the measurement of at least the temperature in the potential cell or the reference cell. This provides temperature as an important parameter of the ambient conditions. Furthermore, measuring the temperature difference between the measuring cells makes it possible to compensate for temperature-dependent differential pressure dependencies between the measuring cells and / or to indicate corresponding uncertainties in the measurement result.The calibration of temperature-dependent dependencies of the differential pressure Δp is preferably carried out experimentally as a function of given temperatures and temperature differences.

[0054] The temperature sensor can, for example, be integrated as a wire-shaped resistance sensor along the longitudinal axis of the measuring cell.

[0055] The elements used for volume reduction can accommodate or form at least part of these temperature sensors. Therefore, in a further embodiment, it is provided that the element forms at least part of the temperature sensor. Integrated voltage measurement

[0056] The tensiometer can be equipped with a measuring arrangement comprising a voltage measuring device with appropriate contacts, which detects the electrical potential difference between the measuring chamber of the potential cell and its immediate surroundings as an electrical voltage. For a measuring cell constructed with an ionomer membrane, it is then possible to reduce or eliminate disturbances in the measurement of the matrix potential. This voltage can be calibrated as a function of the osmotic potential difference between both sides of the membrane caused by salts, e.g., as a pressure function, stored on the tensiometer board, and used to reduce or eliminate varying osmotic potential differences superimposed on the matrix potential.For calibration, the electrical voltage between the inside of the membrane (in the measuring chamber) and its outside (near the membrane surface) is preferably determined experimentally as a function of predetermined ion concentrations, and the associated osmotic pressure in the potential cell is determined.

[0057] The element used for volume reduction within the measuring chamber of the potential cell can form one of the electrical contacts for measuring the voltage. Therefore, in a further embodiment, the element forms at least part of an electrical contact with the osmotic solution in the potential cell, which is connected to the voltage measuring device. For this purpose, the surface of the element is at least partially electrically conductive.

[0058] The capillary tube or braid surrounding the potential cell can be (at least partially) electrically conductive and form at least part of the external electrical contact for voltage measurement. Therefore, in one embodiment, at least the capillary tube or braid in which the potential cell is arranged is at least partially electrically conductive and forms an electrical contact with the (moist) outer membrane surface, to which the voltage measuring device is connected. For this purpose, the braid can, for example, comprise metallic fibers through which the external potential can be tapped. Filling the measuring chambers

[0059] The measuring chambers can each have inlet and outlet valves at both ends. Therefore, in one embodiment, the measuring cells are provided with an inlet / outlet valve at each end. This allows the measuring chambers or cells to be filled, emptied, rinsed, and cleaned. In particular, this enables the exchange of the osmotic solution in a tubular tensiometer installed in the test specimen, e.g., in the ground, without removing the tensiometer and thus without disturbing the measuring environment during these maintenance operations. In this context, a pump device can be temporarily or permanently installed and / or used to empty and fill the measuring cells or to equalize concentration differences of the osmotic solutions between the measuring cells.

[0060] For adjustment, correction, and condition monitoring, the concentrations or corresponding concentration differences between the measuring cells can be temporarily or permanently recorded using a suitable measuring device. When using hygroscopic salts, for example, the conductivity can be measured to assess the concentration. In one embodiment, the tensiometer is therefore provided with a concentration measuring device configured to detect at least one concentration difference of a hygroscopic substance within the osmotic solutions in the measuring cells.

[0061] The hygroscopic substance(s) in the measuring chambers and / or the reference substance(s) can be selected or preset depending on the problem, taking into account the properties of the test specimen and the type of membrane used. This allows the measuring range to be defined in terms of position and size and adjusted during operation. The measuring range can be adjusted, for example, by changing the concentration(s) and type(s) of the hygroscopic substance(s), as this allows the osmotic potential of the solutions to be specifically influenced.

[0062] Furthermore, the reference solution can be used in a composition osmotically equivalent to that of the test specimen. If an ion-impermeable membrane is used as the membrane material, the osmotic potential can be eliminated for measurement purposes, whereby the pressure difference measured between the measuring chambers approximately determines the matrix potential. In one embodiment of the method, therefore, an aqueous solution with a composition osmotically approximately equivalent to that of the test specimen is used as the osmotic reference solution. Data processing

[0063] The pressure value determined by the pressure sensor is processed by a suitable electronic circuit into a data processing signal, for example as a data value or data packet, converted into the desired representation for the water or matrix potential, appropriately corrected, and, if necessary, stored, output, displayed, and / or made available via a data bus-compatible output together with other parameters (temperatures, system parameters). The necessary electronic components and program code are implemented in a tensiometer board. Installation-dependent variants

[0064] Because of the linear geometries of the potential cell and reference system, which can be flexibly designed, such a tensiometer can be guided as a common strand through the soil body, the substrate or medium.

[0065] If the tensiometer is to be designed to be inserted into the test specimen, the reference system can be mechanically stiffened externally, e.g., with a perforated hollow profile. The same applies in this case to the potential cell exposed to the test specimen.

[0066] Due to its linear, flexible or rigid design, the tensiometer can be adapted in type and length to a specific question, e.g., the heterogeneity of the site, the size of the peduncle, the root density distribution, etc., as well as to the type of installation in the test specimen, e.g., by laying it in suitable prepared areas of the test specimen accessible by slotting or pre-drilling, or by piercing it (possibly after pre-drilling to avoid local material compaction). scope

[0067] Besides its use in soils, the tensiometer can also be used in other substrates or media to determine the prevailing water content, for example, for the precise determination of relative humidity close to 100%, i.e., where conventional humidity sensors generally become inaccurate. Maintaining the highest possible humidity while simultaneously preventing condensation is necessary, for example, for storing fruit. Summary

[0068] The invention relates to a linear water potential sensor (tensiometer) of selectable length with adjustable measuring range for use in dry and moist, heterogeneously composed soils, substrates or media and a reference-based method for the representative determination of the water potential, e.g. along a horizon in this test body by spatially averaging the locally present water potentials along the tensiometer.

[0069] The tensiometer and the described method enable the determination of the water or matrix potential averaged over the test specimen, in particular a pedon-scale soil sample. Furthermore, by appropriately selecting the hygroscopic substance(s) and their concentration in the osmotic solution used, and / or the reference substance(s) and their concentration in the reference solution used, a measuring range can be set in terms of position and size that is optimally adapted to the dynamic range of the water potential in the test specimen.

[0070] In this way, a diffusion-based tensiometer is created, referenced via a definable internal standard, which can be adapted to the respective measurement problem in its spatial averaging behavior as well as in the size and position of the measuring range.

[0071] The invention is explained in more detail below with reference to preferred embodiments and the figures. These show: Fig. 1 a schematic representation of one embodiment of the tensiometer; Fig. 2 a schematic representation of a section of the tensiometer to illustrate another embodiment of the tensiometer; Fig. 3 a schematic representation of a section of the tensiometer to illustrate another embodiment of the tensiometer; Fig. 4 a schematic representation of another embodiment of the tensiometer; Fig. 5 a schematic flowchart of an embodiment of the method for determining a spatially averaged water potential in a test specimen.

[0072] In Fig. 1 Figure 1 shows a schematic representation of an embodiment of the tensiometer 1. The tensiometer 1 comprises a potential cell 2 and a reference system 40 with a reference cell 3 and a reference chamber 4 and a pressure measuring device 5.

[0073] The potential cell 2 comprises a sealable measuring chamber 2-1 enclosed by a tubular semipermeable membrane 12. The membrane 12 is a water-permeable polymer (for example, silicone) or an ionomer (for example, Nafion) or a material disclosed in the general description or functionally equivalent.

[0074] Reference cell 3 comprises a sealable measuring chamber 3-1 encased in a tubular semipermeable membrane 12. Reference cell 3 is structurally identical to potential cell 2. The diameter, length, and wall thickness of the membranes 12 of both measuring chambers 2-1 and 3-1, as well as the membrane material, are identical. Reference cell 3 is integrated into reference chamber 4.

[0075] Alternatively, it can also be provided that the reference system 40 is smaller compared to the potential cell 2 and is positioned at a suitable location in the tensiometer 1.

[0076] Potential cell 2 and reference cell 3 are filled with an osmotic solution 6, the solution 6 being the same in both measuring chambers 2-1 and 3-1. The osmotic solution 6 can be prepared with salts and / or water-soluble polymers, e.g., PEGs, with a suitable chain length.

[0077] The reference cell 3, integrated into the reference chamber 4, is surrounded by the reference solution 7. This reference solution 7, together with the reference potential, defines the reference point for measuring the water potential. The reference solution 7 can be, for example, water. The reference chamber 4 is formed, for example, by a liquid-tight tube or bag made of a suitable plastic, such as polyurethane (PU) or polyvinyl chloride (PVC), etc.

[0078] The pressure measuring device 5 makes it possible to detect at least the pressure difference Δp between the potential cell 2 and the reference cell 3, for example by means of a differential pressure sensor.

[0079] Potential cell 2 and reference system 40 (reference cell 3 and reference chamber 4) are exposed to the same environmental conditions. In particular, the same temperature should prevail in measuring cells 2 and 3. At least one temperature sensor 8 can be provided to measure a temperature T, with which at least one temperature of potential cell 2 is recorded.

[0080] The potential cell 2 and the reference system 40 (reference cell 3 and reference chamber 4) are arranged in a test body 20, in particular in soil 21, in which the water potential or the matrix potential is to be determined. It is specifically provided that the measuring chambers 2 and 3 are closely adjacent, for example, together as a single strand, and are guided through the test body 20 and 21. This is shown schematically in simplified form in the Fig. 1The diagram shows the positions of measuring cells 2, 3 and reference chamber 4 within test specimen 20 along a symbolic direction x. When using tensiometer 1 in the soil, measuring cells 2, 3 and reference chamber 4 can be oriented in any spatial direction, allowing the position of tensiometer 1 within test specimen 20 to be determined according to the specific research question, thus defining the area over which the averaged water or matrix potential is to be measured. Measuring cells 2, 3 and reference chamber 4 can have lengths L ranging from a few centimeters to many meters.

[0081] The tensiometer 1 can be used to determine the water or matrix potential ψ w / m in test specimen 20, whereby the pressure difference Δ pThe pressure difference Δp between potential cell 2 and reference cell 3 is measured by means of the pressure measuring device 5. Based on this pressure difference Δp, the water or matrix potential in the test body 20 – a soil 21 or other substrate – is measured and provided. This occurs in particular after equilibrium of water activities has been established between the osmotic solutions 6 in measuring cells 2, 3 on the one hand and the waters in their environment (test body 20, reference chamber 4) on the other.

[0082] To determine the water or matrix potential, the tensiometer 1 has a tensiometer board 30, which includes electronic components such as a programmed microcontroller and memory. The tensiometer board 30 is, in particular, part of the tensiometer 1. The tensiometer board 30 evaluates the signal from the pressure measuring device 5 and generates a measured value for the water or matrix potential ψ averaged over the length L. w / m .

[0083] It may be provided that the tensiometer 1 has a voltage measuring device 9 which measures an electrical voltage U The voltage is measured between an inner and an outer surface of the potential cell 2. It is then intended that the voltage be measured using the voltage measuring device 9. Uto correct electrolyte concentration-dependent osmotic potential differences between potential cell 2 and an external space, and is determined based on a calibration of the associative pressure in potential cell 2 from the determined differential pressure Δ p is reduced or eliminated in order to calculate the matrix potential ψ m averaged over the length L for the water state in the test body 20, in particular in the soil 21.

[0084] It can be provided that the tensiometer 1 has a rod-shaped element 10 inserted into the potential cell 2 and the reference cell 3, respectively, which extends along the measuring chambers 2-1 and 3-1 and is arranged centrally therein. This embodiment of the tensiometer 1 is shown schematically as an enlarged section in the Fig. 2This is illustrated. The element 10 can, for example, be designed as a profile or round bar and serves to reduce the volume of the measuring chamber containing the osmotic solution. In the illustrated embodiment, the volume of the measuring chamber is reduced to a hollow cylindrical annular space 11 between the element 10 and the inner surface of the membrane 12. For this purpose, the element 10 is arranged centrally with respect to the cross-section of the respective measuring cells 2 and 3. Positioning means can also be used to maintain the central arrangement of the element 10, as disclosed in the general description. By reducing the volume of the measuring chamber, the time required to adjust the pressure within the measuring cells 2 and 3 is reduced, allowing the water potential to be determined with greater temporal resolution. The element 10 is particularly flexible, so that the flexibility of the tubular measuring cells 2 and 3 is not restricted.

[0085] Furthermore, the element 10 may include at least part of a temperature sensor 8 and / or an electrical contact for the osmotic solution for the voltage measuring device 9. For this purpose, a temperature-dependent resistor is arranged in the element 10, for example in the profile or round bar, and / or the profile or round bar forms at least a partial electrically conductive electrode externally, which is in contact with a voltage measuring device 9.

[0086] It may also be further provided that the reference system 40 is integrated into the potential cell 2 along its length. In particular, it may then be provided that the reference system 40 at least partially forms the element 10.

[0087] The Fig. 3Figure 1 shows a schematic representation of a section of another embodiment of the tensiometer, in which the tensiometer has capillary tubes 17 with water-permeable perforated, slotted, or porous cavities 18. Instead of a rigid capillary tube 17, braids, particularly tubular ones, can also be provided. These braids can consist of or comprise metallic and / or non-metallic fibers. The membranes 12 of the measuring cells 2 and 3 are either flush integrated into the capillary tubes 17, fill the cavities in the wall of the capillary tubes 17, or are flush / force-fitted and / or embedded in a braid with a defined mesh size. The water from the surrounding environment is in contact with the membranes 12 of the measuring cells 2 and 3 via the cavities 18.This provides protection against mechanical influences and limits the varying elastic expansion of the membranes 12 caused by the changing pressure in the measuring cells 2, 3. The capillary tubes / mesh 17 can be made of plastic, metal, or ceramic. They can also be made of a suitable semipermeable membrane that is permeable to water.

[0088] Furthermore, it may be provided that the pressure-dependent elastic deformation of the measuring cells 2, 3 is calibrated in the manner described above and taken into account when determining the water or matrix potential.

[0089] Furthermore, it can be provided that at least the capillary tube / braid 17 in which the potential cell 2 is arranged is at least partially electrically conductive and forms an electrical contact with the (moist) outer membrane surface, to which the voltage measuring device 9 is connected. For this purpose, the braid can, for example, comprise one or more metallic fibers with which an external potential can be tapped.

[0090] It may be provided that the tensiometer 1 is a concentration measuring device 13 ( Fig. 1 ) exhibits the concentration difference Δ c The hygroscopic substance between measuring cells 2 and 3 is measured using the tensiometer board 30. This makes it possible to check, after filling or changing the osmotic solution 6, whether sufficiently similar concentrations are present in measuring cells 2 and 3.

[0091] It may be provided that the measuring cells 2 and 3 each have inlet and outlet valves 16 at both ends (14, 15). Fig. 1 This facilitates the filling and emptying of the measuring cells 2, 3. Furthermore, the reference chamber 4 may be provided with an inlet and outlet valve 16. In the Fig. 1 In the illustrated embodiment, measuring cells 2 and 3 can be connected to each other via the inlet and outlet valve 16. This allows for the equalization of the concentration of the osmotic solutions 6 between measuring cells 2 and 3 and facilitates their uniform filling.

[0092] In the Fig. 4 A schematic representation of another embodiment of the tensiometer 1 is shown. The embodiment is basically the same as that described in the Fig. 1The embodiment shown is configured as follows; the same reference numerals denote the same features and terms. In this embodiment, the pressure measuring device 5 comprises a first differential pressure sensor 5-1 and a second differential pressure sensor 5-2. The first differential pressure sensor 5-1 detects the pressure difference Δ p 1 between the potential cell 2 and the atmosphere. The second differential pressure sensor 5-2 detects a pressure difference Δ p 2 between reference cell 3 and the atmosphere. From the difference of the two differential pressures Δ p 1 , Δ p 2. The differential pressure Δ can be determined. p between the two measuring cells 2, 3, from which the water potential ψ averaged over the length L can be determined. w or determine the matrix potential ψm in the manner described above.

[0093] Furthermore, the tensiometer 1 may be provided with a pump device 22. This can be temporarily installed and / or used to equalize concentration differences between the two measuring chambers 2-1, 3-1, for example, after an exchange of the osmotic solution 6 located in the measuring chambers 2-1, 3-1.

[0094] Furthermore, it may be provided that the tensiometer 1 has a conductivity sensor 19 in order to determine the conductivity κ R to determine the ionic strength or concentration of reference solution 7. This makes it possible to check and adjust the ionic strength or concentration of reference solution 7 in reference chamber 4.

[0095] As a preparatory step, the hygroscopic substance(s) in the measuring chambers and / or the reference substance(s) in reference chamber 4 may be selected based on the properties of the test specimen. The same applies to the concentrations of the respective osmotic solutions. The selection of the hygroscopic substance(s) and / or the reference substance(s) may be based on empirical findings obtained through experimental series. For example, an aqueous solution with an osmotically equivalent composition to that of the test specimen may be prepared using suitable reference substance(s). In particular, this allows the matrix potential to be determined directly via the measured pressure difference if a suitable polymer is used as a membrane.

[0096] In the Fig. 5Figure 1 shows a schematic flowchart of an embodiment of the method for determining a spatially averaged water potential in a test body.

[0097] In measure 100, at least a pressure difference between the measuring chambers of the potential cell and the reference cell is detected by means of a tensiometer according to one of the embodiments described above.

[0098] In step 101, the water and / or matrix potential in the test body, averaged over the length of the potential cell, is determined based on the measured pressure difference, the type of semipermeable membrane used, and the reference potential, and provided as a measured value. This is done primarily using the tensiometer board.

[0099] In measure 100a, it may be provided that the matrix potential in the test specimen is determined in measuring cells equipped with ionomer membranes by measuring the electrical voltage between the inside and outside of the membrane of the potential cell using the voltage measuring device. After calibration, this device enables the determination of a pressure caused by electrolyte concentration-dependent osmotic potential differences on both sides of the membrane. This pressure is then eliminated from the measured pressure difference, thus determining the matrix potential. This is also done using the tensiometer board. The determined matrix potential is also provided.

[0100] In a preparatory measure 99, it may be provided that the hygroscopic substance(s) and their concentrations within the osmotic solutions in the potential cell and in the reference cell, as well as their concentrations in the reference solution, are selected or have been selected depending on the properties of the test specimen and the type of membrane used. The selection of the hygroscopic substance(s) may, for example, be based on empirical findings obtained in experimental series.

[0101] Measure 99 may, for example, stipulate that an aqueous solution with a composition approximately equivalent to that of the test specimen in terms of osmosis is used as the reference solution. In particular, this allows the matrix potential to be determined directly via the measured pressure difference, since the osmotic potential and the reference potential defined by the reference substance will have the same value.

[0102] Measure 101 may provide for the consideration of pressure-dependent elastic deformation of the measuring chambers of the measuring cells when determining the water and / or matrix potential.

[0103] The tensiometer and method described in this disclosure enable, in particular, the determination of a spatially averaged water potential over a test specimen. Furthermore, the matrix potential can also be determined using the described embodiments. In addition, a measuring range can be set by appropriately selecting the osmotic solution and / or the reference solution, so that the tensiometer can be adapted to the properties of the test specimen. Reference symbol list

[0104] 1 Tensiometer 2 Potential cell 2-1 Measuring chamber 3 Reference cell 3-1 Measuring chamber 4 Reference chamber 5 Pressure measuring device 5-1 Differential pressure sensor 5-2 Differential pressure sensor 6 Osmotic solution 7 Osmotic reference solution 8 Temperature sensor 9 Voltage measuring device 10 Element 11 Hollow cylindrical annular space 12 Membrane 13 Concentration measuring device 14 End 15 End 16 Inlet / outlet valve 17 Capillary tube (or braid) 18 Cavity 19 Conductivity sensor 20 Test specimen 21 Base 22 Pump device 30 Tensiometer board L Length of measuring chambers T Temperature U Electrical voltage x Mounting direction of the tensiometer Δ c concentration difference κ R Conductivity Δ p Pressure difference Δ p 1 Pressure difference Δ p 2 Pressure difference ψ m averaged matrix potential ψ w average water potential

Claims

1. A tensiometer (1), comprising: - a measuring cell of selectable length, referred to as a potential cell (2), which comprises a closable measuring chamber (2-1) sheathed in a tubular semi-permeable membrane (12) and can be installed in a test piece (20); - a reference system (40) comprising a reference chamber (4) and a measuring cell of selectable length, referred to as a reference cell (3), which comprises a closable measuring chamber (3-1) sheathed in a tubular semi-permeable membrane (12), wherein the reference cell (3) is integrated in the reference chamber (4) of the reference system (40), and wherein the reference chamber (4) contains an osmotic reference solution (7) or can be filled with such a solution, wherein the potential cell (2) and the reference cell (3) are or can be filled with an osmotic solution (6); and - a pressure-measuring apparatus (5), which is configured to measure at least one pressure difference (Δp) between the measuring chambers (2-1, 3-1) of the potential cell (2) and the reference cell (3).

2. The tensiometer (1) according to claim 1, characterized in that the reference cell (3) is structurally identical to the potential cell (2).

3. The tensiometer (1) according to claim 1, characterized in that the reference system (40) is smaller than the potential cell (2) and is positioned at a suitable point in the tensiometer (1).

4. The tensiometer (1) according to any one of the preceding claims, characterized in that the reference chamber (4) comprises a device for setting a pressure.

5. The tensiometer (1) according to any one of the preceding claims, characterized by a voltage-measuring apparatus (9) for measuring an electrical voltage (U) between the inner face and the outer face of the membrane (12) of the potential cell (2).

6. The tensiometer (1) according to any one of the preceding claims, characterized by an element (10) which is introduced into the potential cell (2) or into each of the potential and reference cells (2, 3), extends along a longitudinal axis of the measuring chambers (2-1, 3-1) of the measuring cells (2, 3), and is arranged centrally with respect to a cross section of the measuring chambers (2-1, 3-1) of the measuring cells (2, 3) oriented perpendicularly to the longitudinal axis.

7. The tensiometer (1) according to any one of the preceding claims, characterized in that the reference system (40) is integrated in the potential cell (2) over its length.

8. The tensiometer (1) according to claim 7, characterized in that the reference system (40) forms the element (10) according to claim 6 at least in part.

9. The tensiometer (1) according to any one of the preceding claims, characterized by capillary tubes (17) or braids, which are provided with permeable cavities and / or pores (18) and into which the membranes (12) of the measuring cells (2, 3) are each fitted to be flush or are integrated in the cavities at least in part.

10. The tensiometer (1) according to any one of the preceding claims, characterized by at least one temperature sensor (8) in or on the potential cell (2) and / or in or on the reference cell (3).

11. The tensiometer (1) according to any one of claims 6 to 10, characterized in that the element (10) forms at least a part of the temperature sensor (8) and / or of an electrical contact with the osmotic solution in the potential cell (2), which part is connected to the voltage-measuring apparatus (9).

12. The tensiometer (1) according to any one of claims 9 to 11, characterized in that at least the capillary tube (17) or the braid, in which the potential cell (2) is arranged, is electrically conductive at least in part and forms an electrical contact with the (moist) outer membrane surface, to which the voltage-measuring apparatus (9) is connected.

13. The tensiometer (1) according to any one of the preceding claims, characterized in that the measuring cells (2, 3) each have an inlet / outlet valve (16) at both ends (14, 15).

14. The tensiometer (1) according to any one of the preceding claims, characterized by a concentration-measuring apparatus (13), which is configured to measure at least one concentration difference (Δc) of a hygroscopic substance within the osmotic solutions (6) in the measuring cells (2, 3).

15. A method for determining a spatially averaged water potential (ψw) in a test piece (20), wherein at least the pressure difference (Δp) between the measuring chambers (2-1, 3-1) of the potential cell (2) and the reference cell (3), which, due to its arrangement inside the reference chamber (4) of the reference system (40), permits the reference to a selectable reference potential, is measured by means of the tensiometer (1) according to any one of claims 1 to 15, wherein the water and / or matrix potential (ψw / m) in the test piece (20), averaged over the length of the potential cell (2), is determined on the basis of the measured pressure difference (Δp) depending on the semi-permeable membrane used and on the reference potential, and is provided as a measured value.