6.7 Jar tests are used to study flocculation in laboratories. A jar test apparatus is a 4.0 liter batch reactor in which a water sample is placed, coagulant is initially added, and it is stirred at a constant rate. Samples are taken of the water over time, and the total number of particles (singlets plus aggregates) are counted. (a) Draw a picture of the setup, and write a mass balance describing the total particle number concentration (N) as a function of time in the batch reactor. (b) If the stirrer imparts 6.5 x 10-5 W/kgm-5-3) of power at a given stirring speed and 15C, what is the mean velocity gradient (G) in the reactor? (c) There are 1.0 x 10' particles initially in the 4.00 L of water put in the jar apparatus. All of the particles are initially 50 micrometers (5 x 10^8 m) diameter. Assuming the stirring speed in part (b), how many particles per liter will there be after 30 minutes of stirring, if the particles are completely destabilized? (d) What is the average number of singlet particles in an aggregate after the 30 minutes of stirring? (e) What would the particle concentration be after 30 minutes based on part (c), but for the case where the particles are partially destabilized and only one in every five colli- sions between particles results in the colliding particles adhering