透過壁を持つ血管中の血液の流動の理論的研究

抄録

When blood flows through capillaries, exchanges of various substances, particularly of water, take place across the capillary wall. It is interesting to consider the influence of the exchange of the fluid across the wall upon the motion of the fluid within the capillary. A hydrodynamical theory of steady slow motion of blood through capillaries with permeable walls is hereunder presented. It is assumed that the exchange of fluid across the capillary wall obeys Starling's hypothesis, M=k(p-α), that is, the rate of flow M per unit area of the wall surface is proportional to the difference between the pressure of the fluid within and that outside the capillary. It is further assumed that the filtration constant k is very small, that is, ε=kη/R<<1, where η represents the coefficient of the viscosity of blood and R the radius of the capillary. Blood is regarded as homogeneous Newtonian fluid.
The following expressions have been obtained for the velocity and pressure distributions within the capillary and the volume of the fluid flowing per unit time across the cross section of the capillary.
with
where u and v represent respectively the longitudinal and the radial component of the velocity and L the length of the capillary. The constants p_a and p_v represent respectively the arterial and the venous pressure.