Fig. 6

The effects of eccentricity on hydraulic resistance of elliptical annuli modeling PASs surrounding pial arteries. Hydraulic resistance \(\mathcal {R}\) as a function of a \(\epsilon _x\) or b \(\epsilon _y\) for several values of \(\alpha \). Color maps of the velocity profiles for c \(\alpha =2\), \(\epsilon _x=0.4\), \(\epsilon _y=0\) and d \(\alpha =2\), \(\epsilon _x=0\), \(\epsilon _y=-0.4\). \(K=1.4\) for all plots shown here. Circular annuli have \(\alpha = \sqrt{2.4}\), and annuli with \(\alpha > \sqrt{2.4}\) have \(r_2 > r_3\). For a fixed value of \(\alpha \), any non-zero eccentricity increases the flow rate and reduces the hydraulic resistance