Mathematical Problems in Engineering

Volume 2015, Article ID 215758, 7 pages

http://dx.doi.org/10.1155/2015/215758

## The Influence of Specimen Size and Distance to a Surface on Resistive Moisture Content Measurements in Wood

^{1}Division of Building Materials, Lund University, Box 118, 221 00 Lund, Sweden^{2}Division of Building Physics, Lund University, Box 118, 221 00 Lund, Sweden

Received 14 November 2014; Revised 3 February 2015; Accepted 3 February 2015

Academic Editor: Carla Roque

Copyright © 2015 Maria Fredriksson et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The moisture content of wood is commonly determined by measuring the electrical resistance between two electrodes inserted in the wood. However, problems using this method close to wood surfaces were reported in a previous study. In the present study, the effect of the distance to a surface and the specimen size on the measured electrical resistance was studied analytically as follows. The two electrodes create an electrical potential in the wood specimen. The boundary condition for the electrical potential is that the electrical current across all specimen surfaces is zero, which is achieved by using a suitable array of mirror sources. The analytical solution for the electrical potential was used to analyse the influence of the distance from the electrodes to the specimen surface as well as the size of the specimen. In addition, the error in moisture content was evaluated. The effect of the distance to a surface and the specimen size depended on the equivalent radius of the electrodes; if large electrodes are used in small specimens or close to surfaces, there is a risk that a higher resistance is measured which results in slightly lower measured moisture content than the actual moisture content of the specimen.

#### 1. Introduction

Wood is a hygroscopic material and the moisture content of the wood thus changes with the relative humidity of the surrounding air. The moisture content affects wood properties such as strength and dimensional stability and, in addition, biological degradation is also closely related to the moisture content (see, e.g., [1]). The moisture content is defined as mass of water divided by the mass of the dry wood and is usually determined by the gravimetric method, that is, by mass determination of both the wet piece of wood and after drying at 103°C. Another common method for moisture content determination is to use a moisture content meter. This method is less accurate than the gravimetric method but is convenient since it enables in situ measurements in wood structures and gives an instant value of the moisture content. The most common moisture content meters determine the moisture content by measuring the electrical resistance or electrical conductance between two electrodes that are inserted in the wood. Since the electrical resistance decreases when the moisture content increases (see, e.g., [2]), the moisture content can be calculated from the measured electrical resistance if the relationship between the resistance and the moisture content is known. The design of the electrodes varies, but usually pin-type electrodes with tapered ends are used (see, e.g., [3]), but there are also examples of other electrode designs (e.g., [4–7]). The electrodes are often insulated so that the electrical conductance is measured between the tips of the electrodes. Apart from resistance-type moisture content meters, there are also capacitance moisture content meters that measure the dielectric constant and power-loss type moisture contents meters that measure the dielectric loss factor, but these types are much less common than the resistance-type moisture content meters [1].

Various factors, both wood properties and experimental variables, can affect the electrical conductance of wood and thus moisture content measurements. Examples of such factors are temperature, wood species, structural orientation, density, chemical constituents, and extractives [8]. Among these factors, the temperature affects the electrical resistance the most [9] and temperature correction is therefore necessary. The electrical resistance is also affected by wood species to a large extent since different species contain different amount of extractives and have different densities and different lignin content [8]. The relationship between electrical resistance and moisture content has therefore been determined for different wood species, see, for example, [3]. Preservative treatment of wood with salts generally decreases the electrical resistance and the use of a moisture content meter thus results in a moisture content reading that is higher than the actual moisture content [3]. Moisture content meters are therefore generally not used for preservative treated wood since it is not possible to correct for these errors [3]. Due to polarization effects, the measured electrical resistance is affected by the time during which the voltage is applied [9]. Therefore, the polarity is switched when measuring the electrical conductivity for moisture content determination; see, for example, [7]. The measurements in the verification experiments in the present study were made by applying a voltage of 2 V during 0.5 s after which a first reading was made during 0.5 s. The polarity was then switched and after 0.5 s a second reading was made during 0.5 s. This is similar to how most wood moisture meters work. It is thus a simple measurement with the only aim of acquiring a resistance value that can be related to the moisture content of the wood. These types of devices work with voltage steps which contain both high and low frequency components, but as each step is rather long (0.5 s) a measurement can be considered to be quasi-stationary (DC electrical resistance moisture measurement).

Skaar [8] claimed that the size of the sample is of little importance since the resistance is concentrated on the vicinity of the electrodes. However, Nore and Thue [10] reported problems using resistive moisture content measurements close to a surface. They found that the moisture content measured by the resistive method was lower 3 mm below the surface than in the middle of a 23 mm thick board even though the board should have a uniform moisture content. Their results thus indicate that the measured moisture content is affected if measurements are made close to a surface.

This paper presents an analytical study on the influence of the distance to a surface and specimen size on the measured electrical resistance between two electrodes inserted in a specimen. The error in resistance was also translated to error in moisture content by using a relationship between electrical resistance and moisture content from the literature.

#### 2. Theory

The electrical current obeys Ohm’s law: where is the difference in electrical potential and is the electrical resistance. The electrical resistance is the inverse of the electrical conductance : The electrical potential from a point source at a distance from the source is where is the electrical conductivity which is the inverse of the electrical resistivity : The distance is where are the Cartesian coordinates of the point source.

In the following sections, we will derive equations for the electrical potential in limited size specimens with two electrodes. We will first do this for the one-dimensional case and then extend this solution to the three-dimensional case. It should be noted that the potential differences between the two electrodes are dependent on the size of the electrodes, which we assume to be spherical with a certain equivalent radius.

##### 2.1. Two Electrodes on the -Axis

The electrical potential from the positive and negative electrodes at and is The rectangular cuboidal wood sample occupies the region , , . The electrical current in any point is equal to the gradient of the electrical potential times the electrical conductivity . The boundary conditions at the six wood surfaces are that the electrical current perpendicular to the surfaces is zero. The boundary condition at the surfaces and is There are corresponding conditions in the and directions. These conditions are achieved by putting suitable arrays of mirror sources outside the wood sample as described below.

Figure 1(a) shows the electrodes placed at and . To obtain zero gradient at , two mirror sources are placed at and (Figure 1(b)). This element from to is symmetric around zero and is considered a unit cell. The gradient at is zero due to symmetry. To achieve zero gradient at , this unit cell is repeated to both the left and the right (Figure 1(c)). If more unit cells are placed next to each other in both directions, the gradient at converges towards zero. The gradient at from all sources but the last two at the far left is zero due to symmetry. The gradient from the last two plus and minus sources tends to zero as increases. The coordinates of the positive point source and its mirror sources are and the coordinates for the negative point source and its mirror sources are where is the number of repetitions of the unit cell to the left and right, respectively.