Fluid Dynamics

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An interesting example of a fluid transport system that grows from a low to high Re system is the vertebrate embryonic heart. In mammals and birds, the developing heart grows from a simple valveless pump to a four chambered heart over a range of Re of about 0.02 to 1000. The flow within the heart influences its growth, and it is possible that stages in development from the valveless tube to the chambered heart correspond to fluid dynamic changes related to scaling effects. We constructed physical models of the embryonic heart in order to study vortex formation in the atrium, ventricle, and bulbus arteriosus. Several chamber depths and endocardial cushion heights were considered, and Reynolds numbers were varied from about 10^{−2} (corresponding to the case of the embryonic heart after the formation of the tube) to 10^3 (corresponding to the case of the adult heart). We found that the transition to vortical flow occurred around a Re of 30, and this transition depends upon the chamber depth and the cushion height.

Contraction kinematics and data from electrocardiograms taken when the embryonic heart tube first forms suggest that the blood is pumped by peristaltic contractions of the heart; however, recent work based on particle image velocimetry suggests that the heart uses a valveless suction pump mechanism, whereby active pumping occurs only in the anterior region of the heart and the posterior waves of contraction are passive. Several physical and numerical models of this pumping mechanism have been described, but none of them have driven the fluid at the either the same Re or Womersley number as that of the embryonic heart. To determine the actual pumping mechanism of the heart tube, we use a combination of in vivo measurements, experiments with physical models, and numerical simulations. We plan to obtain spatially and temporally resolved intracardial flow fields in vivo using the sea squirt Clavelina intestinalis. Simplified physical and numerical models of the heart tube will then be used to determine which mechanism could produce flow velocities similar to those measured in vivo. A key component of this project will be to create a coupled model of cardiac mechanics and electrophysiology for the embryonic heart tube.

Experimental Movies

Flow visualization in a channel with chambers at Re = 0.12

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Flow visualization in a channel with chambers at Re ~ 1000

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Computation Movies
Immersed boundary method used to simulate peristalsis and dynamic suction pumping for Womersley number=0.2 and Womersley number=10. Computational experiments are done to show the efficacy of the pumping mechanisms for small and large scale fluid dynamics. The Womersley is changed by varying the viscosity of the fluid.
Dynamic suction pumping for Womersley=10, 40 micron tube diameter:
Peristalsic pumping for Womersley=10, 40 micron tube diameter:
Dynamic suction pumping for Womersley=0.2, 40 micron tube diameter:
Peristaltic pumping for Womersley=0.2, 40 micron tube diameter: