RESUMEN
Sufficient conditions to control solute transport across the cap responsible for the formation, development, and final shape of the lotus-type pores for different spatial variations of the partition coefficient, and the ratio between concentration in solid at the solidification front and concentration at a reference state near the top free surface during unidirectional solidification are presented in this study. Lotus-type porous material contemporarily used in micro-or nano-technologies strongly depend on distributions, orientations, and shapes of pores in solid. The model accounts for solute pressure in the pore affected by solute transport and balance of gas, capillary and hydrostatic pressures, and Sieverts' law or Henry's law at the bubble cap and top free surface. Solute transport across the cap accounts for rejection and convection-affected concentration at solidification front, and convection based on the reference state deviated from that at the top free surface. The resulting simultaneous systems of unsteady first-order ordinary differential equations are solved by MATLAB code. Changing rate of solute pressure in the pore responsible for entrapment and final length of lotus-type pores affected by volume expansion, and solute transport due to diffusion and rejection by the solidification front at the cap is also analyzed. The predicted shapes of lotus-type pores agree with algebraic expression confirmed by available experimental data.
RESUMEN
Mechanisms of the length and maximum radius of lotus-type or single pores in ice or nonmetals satisfied by Henry's law at gas-liquid interfaces dissolved by a gas during unidirectional solidification are rigorously investigated and supported by a Table from algebraic predictions involving different dimensionless working parameters. Lotus-type porous materials characterized by directional properties have been often used as functional materials in food, biomedical, and micro- and nano-technologies. Following previous work taking into account solute amount and transport within the pore, and concentration boundary layers on the advancing solid-liquid interface and bubble cap, and the Young-Laplace equation and Henry's law at liquid-gas interfaces, the algebraic study further provides a Table for a quantitative and extensive understanding of different mechanisms of length and maximum radius. Dimensionless parameters include solute transport parameters of Henry's law constant, mass transfer coefficient, partition coefficient, solute gas amount in imposed ambient, and solute transport parameter, and fluid and thermal parameters of solidification rate, imposed gas pressure, hydrostatic pressure, and geometrical parameter of inter-pore spacing. The controlling of the shapes of lotus-type pores is achieved by a good comparison between predicted maximum diameter and inter-pore spacing during freezing of water dissolved by oxygen gas.
RESUMEN
Patients with deep brain stimulation (DBS) implants may be subject to heating during MRI due to interaction with excitatory radiofrequency (RF) fields. Parallel RF transmit (pTx) has been proposed to minimize such RF-induced heating in preliminary proof-of-concept studies. The present work evaluates the efficacy of pTx technique on realistic lead trajectories obtained from nine DBS patients. Electromagnetic simulations were performed using 4- and 8-element pTx coils compared with a standard birdcage coil excitation using patient models and lead trajectories obtained by segmentation of computed tomography data. Numerical optimization was performed to minimize local specific absorption rate (SAR) surrounding the implant tip while maintaining spatial homogeneity of the transmitted RF magnetic field (B1+), by varying the input amplitude and phase for each coil element. Local SAR was significantly reduced at the lead tip with both 4-element and 8-element pTx (median decrease of 94% and 97%, respectively), whereas the median coefficient of spatial variation of B1+ inhomogeneity was moderately increased (30% for 4-element pTx and 20% for 8-element pTx) compared to that of the birdcage coil (17%). Furthermore, the efficacy of optimized 4-element pTx was verified experimentally by imaging a head phantom that included a wire implanted to approximate the worst-case lead trajectory for localized heating, based on the simulations. Negligible temperature elevation was observed at the lead tip, with reasonable image uniformity in the surrounding region. From this experiment and the simulations based on nine DBS patient models, optimized pTx provides a robust approach to minimizing local SAR with respect to lead trajectory.