http://hdl.handle.net/10174/14410 2026-06-09T00:03:42Z http://hdl.handle.net/10174/42143 Title: Numerical investigation of a concentration divider for ultrasound calibration using constructal design. Authors: Machado, K.V.; Pepe, V.R.; Miguel, A.F.; Rocha, L.A.O.; Haeberle, F. Abstract: This study applies the Constructal Design method to the geometric optimization of a branched symmetric concentration divider for calibrating ultrasound devices used to monitor tumor response with dynamic contrast. Accurate calibration ensures image quality and diagnostic reliability. The geometry consists of a three-dimensional, tree-shaped flow network with two inlets and three outlets, where inlet 1 carries water containing contrast particles, while inlet 2 carries only water. Laminar flow simulations are performed using Computational Fluid Dynamics (CFD) with Ansys Fluent, assuming no-slip wall conditions and zero-pressure outlets. The analysis investigates the effects of the inlet velocity ratio, the diameter ratio, and the vertical positions of the central outlet and inlet tubes, while keeping the total volume and inlet diameter constant. Additionally, velocity, pressure, particle distributions, flow partition ratio, and hydraulic resistance are evaluated. Results show nearly linear concentration responses among the outlets (100%, 50%, and 0%) when the device approaches geometric symmetry with equal inlet velocities, demonstrating efficient control of flow splitting. Although the diameter ratio imposes a trade-off with hydraulic resistance, geometric symmetry combined with Constructal Design promotes improved flow uniformity and enhanced performance, with potential applications in microfluidic mixers that require precise intermediate concentrations. 2026-01-01T00:00:00Z http://hdl.handle.net/10174/42119 Title: Non-equilibrium transport dynamics and macroscopic thermodynamic efficiency of binary Knudsen flow in tapered semipermeable channels Authors: Miguel, Antonio Abstract: This study investigates the non-equilibrium transport dynamics and macroscopic thermodynamic efficiency of a binary gas mixture traversing a tapering, selectively permeable cascade operating strictly within the Knudsen regime. By employing a Lagrangian test particle Monte Carlo framework alongside a Fokker-Planck formalism, discrete stochastic trajectories driven by particle-boundary interactions are coupled with ensemble macroscopic concentration profiles. The separation process is thermodynamically evaluated by balancing the separation work gain against two primary costs: the microscopic entropic penalty of momentum erasure via diffuse wall colli­sions, and the macroscopic transport penalty induced by geometric backscattering. To formalize this, the specific separation thermodynamic efficiency is introduced, a metric that normalizes overall performance against the intrinsic material transmission probability. The results reveal a critical morphological transition in optimal cascade architecture. It is demonstrated that low-affinity membranes fundamentally require moderate geometric constriction to mechanically force boundary collisions and maximize the integrated probability of permeation, optimally balancing permeation against induced backscattering. On the other hand, in high-affinity systems, the active species is rapidly extracted near the inlet, localizing maximum thermodynamic dissipation and rendering severe tapering physically detrimental. Consequently, highly selective membranes strictly favor uniform channel geometries to mitigate irreversible transport losses. Finally, this framework establishes that optimal geometric design is not static but must be dynamically tailored to the intrinsic surface affinity to maximize macroscopic thermodynamic efficiency. 2026-01-01T00:00:00Z http://hdl.handle.net/10174/42110 Title: The evolutionary success of angiosperms: a foundation of bioenergetic surplus Authors: Miguel, Antonio Abstract: The global ecological dominance of angiosperms represents a major evolutionary success. This study suggests that their ascendance is not due to a single trait but to a deeply integrated hydraulic design that maximizes performance and resilience. A model is developed, and based on the constructal law, the leaf vascular archi­tecture of three major plant lineages, angiosperms, gymnosperms, and ferns is compared. The model evaluates performance based on two foundational parameters: the branching exponent which accounts for the supply efficiency, and the vein placement ratio, which controls water distribution. The results demonstrate that the angiosperm architecture is superior across all modeled metrics. This design minimizes the energetic cost of water transport, ensures uniform water distribution, and enables rapid hydraulic responsiveness. Significantly, the model reveals that this profound efficiency generates a bioenergetic surplus that funds a resilient, redundant vascular network. This fault-tolerant design provides a decisive advantage against physical damage, ensuring that high photosynthetic capacity is a sustained reality rather than a fragile state. It is this synergistic system that provides a quantitative explanation for the enduring global supremacy of angiosperms. 2026-01-01T00:00:00Z http://hdl.handle.net/10174/42104 Title: Field-Theoretic Derivation of the Constructal Law from Non-Equilibrium Thermodynamics Authors: Miguel, Antonio Abstract: Traditional analyses of transport phenomena rely on prescribed geometric boundaries, yet natural flow systems dynamically evolve their architecture to maximize access to currents. To address this disparity, we propose a field-theoretic framework for the constructal law that treats physical geometry as a dynamic state variable, represented by a time-dependent conductivity tensor. Using a variational approach grounded in non-equilibrium thermody-namics, we derive a general tensor evolution equation. Within this framework, macroscopic flow architecture emerges deterministically from the continuous competition between non-linear flux-induced accretion, linear entropic relaxation, and spatial smoothing. Scaling analysis reduces this dynamic to a tri-parameter dimensionless phase space: a morphogenic number driving structural growth, a structural diffusion number governing spatial coherence, and a stochastic intensity number providing the microscopic seeds for symmetry breaking. Our principal result is the analytical prediction of a critical bifurcation. When the local morphogenic number strictly exceeds unity, the system escapes its stable, isotropic configuration and branches into highly conductive, anisotropic architectures. We demonstrate the predictive validity and trans-scalar applicability of this continuum theory by mapping it to highly diverse phase transitions, successfully capturing phenomena ranging from microscopic aerosol agglomeration and microbial resistance, to macroscopic coral plasticity and crystal growth instabilities, and finally to the astrophysical launching of relativistic jets from black holes. 2026-01-01T00:00:00Z