Results
We performed 50 simulations for various degrees then averaged the clogging time over the 50 simulations to get an estimate of the average clogging time. Ideally, we would've like to see a global maximum (i.e. $f'(x) = 0$ and $f''(x) < 0$) in our results to definitively conclude that that include is indeed the optimal angle. However from figures (6) we don't observe that characteristic, however the slope near the origin decreases as we increase resistance which agrees with previous research. We increased resistance once more time to 15 and successfully observed the characteristic global maximum in addition to the angle which agrees with research on the angle considered the "optimal angle". Only tentatively a success, we significantly increased the number of simulations to 3500 and refined the interval of degrees to search over $[0,20]$ and plotted the standard error bars. For a pore profile with initial resistance 15, we have statistically significant results (no overlap in 3 times the standard error bars) to conclude that the optimal linear profile is with an inclination angle of 13 degrees.
