Numerical simulation of mass transfer in circulating drops

Numerical simulations of mass transfer are performed for a circulating liquid drop with applications in liquid–liquid extraction. Simulation parameters are chosen for a multi-component ternary system acetone–methanol–benzene. The drop circulation pattern is estimated via a truncated Galerkin representation of the drop streamfunction. Fickian diffusivities for multi-component mass transfer are obtained via Maxwell–Stefan theory with thermodynamic corrections. The advection–diffusion equations governing mass transfer are solved via two distinct numerical methods: a finite difference scheme (using the alternating direction implicit method) and a finite element scheme. Good agreement was obtained between both schemes. Simulation results are presented for a Reynolds number (Re=30) and for a selection of Peclet numbers (Pe=100, 1000 and 10 000, thereby giving insight into the effects of increasing Peclet number). The numerical simulations of the full advection–diffusion equations are compared against predictions of a rigid drop model (i.e. without circulation) and also against predictions of a semi-analytical boundary layer model developed by Uribe-Ramirez and Korchinsky. Results for bulk mass fractions reveal that the rigid drop model predictions evolve too slowly, while the boundary layer model predictions evolve much more quickly than the numerical simulations. Advection–diffusion simulation results for the evolution of mass fractions at selected individual locations in the drop show that points on streamlines nearest to the drop surface and/or drop axis evolve fastest, while those closest to the drop internal stagnation point evolve slowest. Corroborated by contour plots of component concentrations throughout the drop at selected times, this supports a picture whereby mass fractions become roughly uniform along individual streamlines, but mass is transferred diffusively from streamline to streamline

Merluccius hubbsi (Teleostei: Merlucciidae): stock identification based on reproductive biology in the south-southeast brazilian region

The Argentine hake, Merluccius hubbsi, a demersal-pelagic species found from Rio de Janeiro, Brazil to the Tierra del Fuego, Argentina, has become an important target of the Brazilian bottom-trawler fleet since 2001. Earlier studies focusing on the species have suggested that more than one stock might occur off the Brazilian coast, in accordance with environmental features. In order to evaluate this hypothesis, fish were collected from four different areas in the Brazilian waters in which the hake is distributed, during the summers and winters of 1996-2001 and 2004, the females being used to analyze and compare spatial-temporal variations in ovarian maturation. Gonad indexes were also applied for the same purpose. Results indicate a north-south spawning gradient occurring as from summer at around 21°S to winter near 34°S, leading to the identification of two distinct stocks: one located between 21°S and 29°S (Southeastern stock) and the other between 29°S and 34°S (Southern stock), this latter shared with Uruguay and Argentina. Brazilian stocks present clear signs of overexploitation, the situation calling for an urgent solution.<br>A merluza Merluccius hubbsi, espécie demerso-pelágica distribuída desde o Rio de Janeiro, Brasil, até a Terra do Fogo, Argentina, tornou-se alvo das frotas de arrasto de fundo da região Sudeste-Sul do Brasil desde 2001. Estudos anteriores sobre a biologia da espécie sugeriram a existência de mais de um estoque em águas brasileiras, relacionados a características ambientais. Para verificar esta hipótese, exemplares oriundos de quatro áreas em águas brasileiras foram coletados durante o verão e o inverno nos períodos 1996-2001 e 2004, sendo as fêmeas utilizadas para analisar variações espaço-temporais na maturação gonadal. Para corroborar estas análises também foram aplicados índices gonadais. Os resultados mostraram a ocorrência de um gradiente norte-sul para a desova, que é mais intenso no verão em 21°S e no inverno em 34°S. Foram identificados dois estoques: um denominado Sudeste, que se distribui entre 21°S-29°S, e outro Sul, entre 29°S-34°S, este último compartilhado com o Uruguai e a Argentina. Os estoques brasileiros apresentam sinais de sobrepesca, situação que merece atenção e medidas apropriadas de gestão