Relation between mechanism of soil removal from fabrics and a parameter derived from probability density functional method for washing force analysis

Abstract

The probability density functional method is one of the washing force analysis methods that combines the classical kinetic analysis of detergency method and risk calculation method using probability density function. This paper discusses the relation between soil removal mechanisms and the value of σ rl, which is one of the two parameters used in the probability density functional method. Four repetitive washing tests were conducted using test fabrics soiled with iron(III) oxide, carbon black, four kinds of water-soluble dyes and three kinds of oily dyes, and the removal (%) was analyzed with the probability density functional method. The results show that the range of σ rl varied with removal mechanisms; mechanical removal of particle soil (0.01–0.6), dissolution into water of water-soluble soil (0.3–1.4), solubilization of oily soil into surfactant micelle (1.0–2.0) and emulsification or dispersion of oily soil (≥3.0). This tendency can be used for estimating the removal mechanism of any washing system where the soil type is unknown.

Kinetic analysis of hemoglobin detergency by probability density functional method

“…Based on the analysis of the washing test results with respect to the probability density function method, σ rl in the range of 0.39–0.70 was obtained ( Table 1 ). Moreover, a direct relationship was found between σ rl and the cleaning mechanism, and the cleaning mechanism varied in accordance with an increase in σ rl in the following order: the detachment of the solid particle soil ( σ rl : 0.01–0.6), the dissolution of water-soluble soil (limited to substances that have a chemical binding force with fiber) ( σ rl : 0.3–1.4), the removal by solubilization of oily soil with aqueous surfactant solution ( σ rl : 1.0–2.0), the emulsification of oily soil with aqueous surfactant solution, and the removal by oily substance dispersion ( σ rl : 3.0-) ( Fig 3 ) [ 39 ]. Given that the experimental value of σ rl was in the range of dissolution of the water-soluble soil, the hemoglobin was assumed to be removed by dissolution.…”

“…In the probability density functional method [ 35 – 39 ], the adhesion force of soil and the removal force of soil are assumed to be in accordance with a normal distribution, and the cleaning efficiency is determined based on both distributions. Further assumptions are that the adhesion force of soil is in accordance with a normal distribution with an average value of 0 and a standard deviation of 1 ( Eq 3 ), and the cleaning power is in accordance with a normal distribution with an average value of μ rl and a standard deviation of σ rl ( Eq 4 ).…”

“…The washing results of an oily dye stain [35], iron oxide particle dirt [36], and commercially available washing test cloth soiled with a mixed stain [37] were analyzed with respect to two parameters of the probability density functional method, the mean μ rl and standard deviation σ rl of the removal load distribution, assuming that the cleaning power follows a normal distribution. It was recently demonstrated that one of the two parameters (σ rl ) is related to the soil type [38] and the soil removal mechanism [39].…”

Analysis of interaction between mechanical force and chemical effect in cleaning phenomenon by probability density functional method

“…It has been clarified that σ rl is related to the dirt type and cleaning mechanism (Fujimoto et al, 2017; Oya, 2019), and the value of μ rl represent the removal force if σ rl is constant. Assuming that the difference in μ rl increased by improving condition X is Δ X , the difference in μ rl increased by improving condition Y is Δ Y , and the difference in μ rl obtained by improving both conditions X and Y is Δ( X + Y ), then, the interaction between the two factors can be expressed as follows: …”

“…It has been demonstrated that the parameter σ rl is related to the type of dirt and the dirt removal mechanism (Fujimoto et al, 2017; Oya, 2019). Whereas, μ rl was used to determine the interaction between two different cleaning elements, and additive effect for protein soil (Oya et al, 2020) and synergistic effect for fatty acid soil (Oya‐Hasegawa et al, 2021), were observed with respect to temperature and pH effects.…”