Numerical study of flow in a constricted curved annulus: An application toflow in a catheterised artery

The flow of an incompressible Newtonian fluid in a curved annulus with a lo cal constriction at the outer wall is investigated numerically. The three-d imensional nonlinear elliptic partial differential equations governing the flow are simplified by use of small curvature and mild constriction approxi mations. The simplified equations of motion, which are locally two-dimensio nal elliptic in nature at each cross-section, are solved numerically by mea ns of the finite-difference method described by Collins and Dennis [Quart. Jour. Mech. Appl. Math. 28 (1975) 133-156]. Although the results are restri cted to small curvature and mild constriction, these are valid for all Dean numbers D in the entire laminar flow regime. The numerical results show th at, for higher values of radii ratio k, the pressure gradient, pressure dro p, and frictional resistance increase considerably and they vary markedly a cross the constricted length. These results are used to estimate the increa se in frictional resistance in an artery when a catheter is inserted into i t. In the absence of constriction (delta (1)=0) and depending on the value of k ranging from 0.1 to 0.7, the frictional resistance increases by a fact or ranging from 1.32 to 23.91 for D=500 and 1.20 to 16.56 for D=2000. But, in the presence of constriction (delta (1) = 0.1) with the same range for k , the increase in frictional resistance is by a factor ranging from 1.34 to 42.32 for D=500 and 1.18 to 29.5 for D=2000. In a straight annulus, the in creased factor ranges from 1.74 to 32.61 for delta (1)=0 and 1.78 to 58.27 for delta (1) = 0.1 (for all Dean numbers D).