# Mitigating Electrochemical Effects in Resistive Frost-Detection Sensors
### Working Principles of a Resistive Frost-Detection Sensor  
Resistive frost-detection sensors function based on the principle of electrical resistance variation between two electrodes. In previous research, copper electrodes were arranged in a configuration where their resistance changes depending on the medium present between them. This operating principle is illustrated in Figure 1.  
The resistivity of the medium between the electrodes is influenced by the presence of air, water, or frost. As condensation or frost forms, the medium's electrical properties change, altering the overall sensor resistance. By measuring these variations, it becomes possible to infer the presence of moisture or frost accumulation on the surface of a heat exchanger (HX). Prior studies [16] have shown that a copper wire electrode sensor with a fabric medium provided superior performance in frost detection compared to other resistive sensor designs. A visualization of this sensor is presented in Figure 2.  
Sensor resistance measurements were obtained using a voltage divider circuit, as shown in Figure 3, which converts variations in the sensor's resistance into a measurable output voltage. The variable resistance of the sensor (\(R_{s}\)) results from changes in the electrical properties of the medium between the electrodes, which may consist of air, water, or frost/ice. These variations can be further influenced by factors such as frost density, water purity (distilled or ion-rich), and the presence of other impurities. This affects the output voltage as given by Equation (1):  
\[V_{out}=V_{in}\frac{R_{s}}{R_{s}+R_{f}} \tag{1}\]  
where \(V_{out}\) is the output voltage \([\mathrm{V}]\), \(V_{in}\) is the input voltage \([\mathrm{V}]\), \(R_{s}\) is the variable resistance of the frost measuring sensor \([\Omega]\), and \(R_{f}\) is a fixed resistance \([\Omega]\). Figure 1: Simplified diagram of the resistive frost-detection sensor (**a**) and overlaid equivalent circuit representation highlighting the sensor’s variable resistance \(R_{s}\) (**b**) [17]. Figure 3: Voltage divider circuit, with \(R_{f}\) as the fixed resistor, \(R_{s}\) as the sensor’s variable resistance, and \(V_{in}\) and \(V_{out}\) as input and output voltages, respectively. Figure 2: Resistive frost-detection sensor with a fabric medium between the electrodes (**a**) and a rendered model (**b**) of this sensor as developed in [16]. By measuring \(V_{out}\), the value of \(R_{s}\) can be calculated by solving Equation (1) for \(R_{s}\), as shown in Equation (2):  
\[R_{s}=\frac{V_{out}\times R_{f}}{V_{in}-V_{out}} \tag{2}\]  
The voltage divider was powered by a 5 V supply, connected between VCC and GND, with \(V_{out}\) fed into a 10-bit analog-to-digital converter (ADC) for data acquisition. Since \(V_{in}\) is continuously supplied, an electric field is always present across the sensor electrodes, regardless of whether the ADC is actively reading. As a result, the negatively charged electrode acts as a cathode, while the positively charged electrode functions as the anode. In the presence of an electric field, water molecules that are condensed between the sensor electrodes dissociate, initiating electrochemical reactions at each electrode. At the cathode, a reduction reaction occurs, where water molecules gain electrons, producing hydrogen gas (H\({}_{2}\)) and hydroxide ions (OH\({}^{-}\)), as described by Equation (3):  
\[4\mathrm{H}_{2}\mathrm{O}(l)+4e^{-}\to 2\mathrm{H}_{2}(g)+4\mathrm{OH}^{-}( aq) \tag{3}\]  
Simultaneously, at the anode, an oxidation reaction takes place, where water molecules lose electrons, leading to the formation of oxygen gas (O\({}_{2}\)) and hydrogen ions (H\({}^{+}\)), as shown in Equation (4):  
\[2\mathrm{H}_{2}\mathrm{O}(l)\rightarrow\mathrm{O}_{2}(g)+4\mathrm{H}^{+}(aq) +4e^{-} \tag{4}\]  
These electrochemical reactions generate ions that increase the conductivity of the water and lead to the production of hydrogen and oxygen gases at the electrodes.