Entropy generation in heat conduction and engineering embolic micro-particles with electrospray

Abstract

The present work contains two distinct parts: entropy generation in heat conduction and engineering embolic micro-particles with electrospray. Energy is conserved by the first law of thermodynamics; its quality degrades constantly due to entropy generation. It’s thus important to examine the entropy generation regarding the way to reduce its magnitude and the limit of entropy generation as time tends to infinity regarding whether it’s bounded or not. In present work, entropy generation was examined regarding its magnitude and the limit and the increase of entropy principle was applied to develop mathematical inequalities with heat conduction in both adiabatic systems and systems with heat exchange across boundaries. For adiabatic systems, entropy generation was investigated for heat conduction processes under different coordinate systems. The results show a bounded entropy generation if the heat conduction is initiated by the initial temperature distribution, but unbounded if the heat conduction involves a heat source with a positive average over the heat conduction domain. By applying the increase of entropy principle, some mathematical inequalities were developed. For systems with heat exchange across boundaries, variation of boundedness of entropy generation was examined and the consequence of the increase of entropy principle was exploited with heat conduction in cuboid, cylinders and spheres. The former focuses on the limit of the entropy generation as time tends to infinity and uncovers an unbounded limit if the system boundary involves the heat exchange with the surrounding. The latter yields various innovative mathematical relations. Part one of the present work has shed light on the ways of making entropy generation well-controlled and offered some fundamental insights into universe and our future. The work also builds up the relation between the second law of thermodynamics and mathematical inequalities, which are useful both for studying differential equations and for examining accuracy of analytical, numerical and experimental results. Part two of the present work is on engineering embolic micro-particles with electrospray. Therapeutic embolization is a minimally invasive, nonsurgical interventional therapeutic technique for the treatment of various diseases, including tumors, vascular lesions and hemorrhages. The micro-particles with the right size are infused through a catheter into the desired artery, obstructing the blood flow and thus the delivery of oxygen and nutrients, eventually leading to the necrosis of the tissue. Embolic particles uniform in shape and size are essential for obtaining good clinical outcomes and minimize complications. Therefore, the effective generation of uniform and size-controlled micro-particles in large quantity is of paramount importance. In the present work, embolic micro-particles were engineered from an electrified meniscus of the precursor alginate solution. A micro-dripping regime was identified with electric Bond number BE ~ 0.3-1 and Weber number We <1, where the conical tip of the charged meniscus emits periodically a single yet fine droplet. The dependence of droplet size and generation frequency on the dimensionless controlling parameters in this regime was obtained to be 〖 d〗_d~q^0.5,f~q^(-0.15) B_E^0.67. These form the useful guideline for effective production of therapeutic micro-particles from precursor solution of similar physical properties on a commercial scale.