The simplest expressions for the rate of removal of particulate soil from fabrics, including those for first-order kinetics, are described. Two factors militate against obtaining proportionality constants between a time function and a residual soil function which remain constant for long washing times, namely: redeposition, and heterogeneities in soil and fabric. Soil redeposition tends to lower the observed soil-removal rate. This effect can be eliminated by suitable experimental procedures. However, the inhomogeneities inherent in fabrics (fiber surface irregularities, variation in spaces between fibers and yarns) cause them to have sorption sites with a broad range of soil binding strengths. Variations in the size and shape of particles on artificial test fabrics and, for natural soil, in chemical composition as well, cause the particles to adhere to fabric substrates with bonds of different strengths. These heterogeneities produce a broad range of specific soil-removal rates whose values depend on the energies of adhesion of the particle-fabric complex. The most loosely held soil, with the highest removal rate constants, is washed off early so that the soil remaining on the fabric becomes progressively richer in the most tightly bound soil, with the smallest removal rate constants. Hence the average or observed rate constant for soil removal decreases during the washing process.
