Water rise mathematical model in simple curvilinear capillaries

Side shoots and plant branches unlike trunks are often not rectilinear — they can be compared with various mathematical curves. Xylem of such branches copies their curvilinearity. It motivates the spatial curvature of the chains of its tracheids and vessels. A mathematical model of water lifting and distribution caused by the surface tension forces in the symmetrical curved capillary branches of various configurations is considered. The process analysis shows that with the expansion in number of branches, water advancing in the curvilinear capillary system increases. Water volume rising in the side curvilinear capillary branches, other factors being equal, is greater than in rectilinear ones. It is found that the total water rise height in the vertical (rectilinear) capillary — if there are side curvilinear capillaries — increases, and it does not depend on the type of the function that describes the curvature of the lateral curvilinear capillaries.