The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Ex vivo evaluation of a Taylor-Couette flow, immobilized heparinase I device for clinical application

Efficient and safe heparin anticoagulation has remained a problem for continuous renal replacement therapies and intermittent hemodialysis for patients with acute renal failure. To make heparin therapy safer for the patient with acute renal failure at high risk of bleeding, we have proposed regional heparinization of the circuit via an immobilized heparinase I filter. This study tested a device based on Taylor-Couette flow and simultaneous separation/reaction for efficacy and safety of heparin removal in a sheep model. Heparinase I was immobilized onto agarose beads via cyanogen bromide activation. The device, referred to as a vortex flow plasmapheretic reactor, consisted of two concentric cylinders, a priming volume of 45 ml, a microporous membrane for plasma separation, and an outer compartment where the immobilized heparinase I was fluidized separately from the blood cells. Manual white cell and platelet counts, hematocrit, total protein, and fibrinogen assays were performed. Heparin levels were indirectly measured via whole-blood recalcification times (WBRTs). The vortex flow plasmapheretic reactor maintained significantly higher heparin levels in the extracorporeal circuit than in the sheep (device inlet WBRTs were 1.5 times the device outlet WBRTs) with no hemolysis. The reactor treatment did not effect any physiologically significant changes in complete blood cell counts, platelets, and protein levels for up to 2 hr of operation. Furthermore, gross necropsy and histopathology did not show any significant abnormalities in the kidney, liver, heart, brain, and spleen.