Here, they are applied to two regimes of fluid transport in porous media where conductance depends on the radius or on the cube of the radius representing diffusion in slit-like pores and dilute gas flow in cylindrical pores, respectively.
Above this size, since the mass of the droplet increases according to the cube of its radius, further increases by condensational growth are very slow.
Open image in new window Fig. 6 Cube of SNP radius (r3) plotted against growth time for Xa-mediated synthesis Open image in new window Fig. 7 Cube of SNP radius (r3) plotted against growth time for Pg-mediated synthesis.
Open image in new window Fig. 9 Cube of SNP radius (r3) plotted against growth time for Va-mediated synthesis (note that initial 10 min growth time is linear and the remaining 15 min is non-linear).
Open image in new window Fig. 8 Cube of SNP radius (r3) plotted against growth time for Og mediated synthesis (note that initial 10 min growth time is linear and the remaining 15 min is non linear).
In Proposition 44 of his Principia, he showed that the difference is proportional to the inverse cube of the radius, specifically by the formula given above, which Newtons writes in terms of the two constant areal velocities, h1 and h2 F_2(r) - F_1(r) = m \frac{h_1^2 - h_2^2}{r^3} ; Proposition 45; Problem 31 To find the motion of the apsides in orbits approaching very near to circles.
By increasing the internal radius (r) of the catheter (that is, by replacing a 20-gauge with an 18-gauge catheter), the damping coefficient decreases significantly as it varies inversely to the cube of the radius.
If cell growth represents simply an increase in the perikaryal area, the ratio of membrane protein to total protein would fall in parallel with the decline in the surface/volume ratio (volume increases with the cube of the perikaryal radius, whereas surface area increases with the square of the radius).
Unimodal ideal suspensions showed viscoelasticity with relaxation times proportional to the cube of the particulate radius.
Furthermore, use of the groups ˆβ and ˆkc implies that for scale-up, the ratio of the radius to the average vertical velocity in the reactor remains constant, so the reactor output is proportional to the cube of the reactor radius.
