Development of a mathematical model for physical disintegration of flushable consumer products in wastewater systems

The processes that flushable solid products may undergo after discharge to wastewater systems are (1) physical disintegration of solids resulting from turbulence, (2) direct dissolution of water-soluble components, (3) hydrolysis of solids to form soluble components, and (4) biodegradation of soluble and insoluble components. We develop a mathematical model for physical disintegration of flushable solid consumer products and test it with two different flushable products - product A, which has 40% water soluble-content, and product B, which has no water-soluble components. We present our modeling analysis of experimental results, from which we computed disintegration rate constants and fractional distribution coefficients for the disintegration of larger solids. The rate constants for solids of product A in units of (hour ^-1) are 0.45 for >8-mm, 2.25 x 10^-2 for 4- to 8-mm, 0.9 x 10^-2 for 2- to 4-mm, and 1.26 x 10^-2 for 1- to 2-mm solids. The rate constants for solids of product B in units of hour^-1 are 1.8 for >8-mm, 1.8 for 4- to 8-mm, 3.6 x 10^-1 for 2- to 4-mm, and 2.25 x 10^-3 for 1- to 2-mm solids. As indicated by the rate constants, larger solids disintegrate at a faster rate than smaller solids. In addition, product B disintegrated much faster and went mostly to the smallest size range, while product A disintegrated more slowly and was transferred to a range of intermediate solid sizes.