What does "detergent is the last to leave the equipment surface" after rinsing mean? This seems like a broad statement, can it be supported by literature/documentation?
The only source of "detergent last to rinse" that I am aware of is based on the physical behavior of surface active agents and the interchangeable use of the word detergent and surfactant in common usage. More properly you should say the surfactant is the last to rinse. Surfactants or surface active agents are made of molecules that have one end that is hydrophilic (water loving) and the other end is hydrophobic (water hating). Surface active agents in aqueous solutions are attracted to solution surface interfaces because the hydrophobic end of the surfactant molecule is repelled from the bulk water solution while the hydrophilic end of the molecule is attracted to the water solution.
In theory the surfactant is most stable when arranged in a film. The film's structure is made up of one side where the hydrophobic tails are facing outwards towards the solution/surface interface and the hydrophilic ends of the molecules are facing inward towards the water solution. By increasing the concentration of surfactants by adding detergent to a water, a monolayer surfactant film will form in the solution until a critical micelle concentration is achieved (micelles are balls of surfactants arranged with their hydrophobic ends facing inwards and their hydrophilic ends facing outwards - micelles are responsible for emulsifying because the inner regions of micelle can hold hydrophobic oily molecules emulsified in the water solution). Cleaning is typically done with surfactant concentrations above the critical micelle concentration. As the cleaning solution is rinsed away, you drop below the critical micelle concentration of surfactant, promoting mass displacement of the micelles as well as the remaining surfactant molecules (either individual or monolayer) by rinsing. Continued rinsing further dilutes the monolayer and removal of the surfactants, thereby essentially being the last molecules from the cleaning system to rinse away.
As a practical matter with the limits of quantitation in the analytical methods used for cleaning validation studies and crude successive rinse studies, Alconox, Inc technical support has never heard of detecting different rates of rinsing among highly water soluble detergent ingredients. As a practical matter with highly water soluble detergent ingredients, all ingredients seem to rinse at the same rate in dip rinsing studies. Over 4 rinses, in the 3rd rinse all ingredients were detected, and by the 4th rinse they were all gone. Successive rinse methods were not fine enough to detect the subtle effect of the last to rinse away surfactant.
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