The trajectory model of dispersed phase drops and distribution model of drop diameters were derived.By numerical simulation,the analytical results indicate that a large number of dispersed phase drops accumulate on th...The trajectory model of dispersed phase drops and distribution model of drop diameters were derived.By numerical simulation,the analytical results indicate that a large number of dispersed phase drops accumulate on the upper plate in different directions and form a hydrodynamic area with the stream-wise location in the range of 0—0.4m,where the flow of trickling film obtains kinetic drive from flowing field.The flowing field of trickling film exhibits an unstable state if the stream-wise location is less than 0.02m,and a stable state otherwise.Moreover,different velocity vectors of drops in the x-y plane result in different interactions between the trickling film and drops.For the non-uniform distribution of drop diameters,there is a stronger interaction between the trickling film and drop if the stream-wise location is less than 0.02m,because the amplitudes of velocity vectors are higher than those in the range of 0.02—1.0m.The result reveals a complexity and diversity of stratified two-phase flowing field.On the other hand,both the basic flowing field and distributions of drop diameters have a great influence on the distributions of comparable kinetic energy of drops.The complicated motions of larger drops are helpful to coalescence because they will consume much more kinetic energy on the trickling film than those of smaller drops.The change of comparable kinetic energy of smaller drops is continuous and steady.The smaller drops are easily entrained by the liquid-liquid flowing field.展开更多
We develop a two-stage （four component） model for youths with serious drinking prob- lems and their treatment. The youths with alcohol problems are split into two classes, namely those who admit to having a problem ...We develop a two-stage （four component） model for youths with serious drinking prob- lems and their treatment. The youths with alcohol problems are split into two classes, namely those who admit to having a problem and those who do not. It is shown that the model possesses two steady states, one where people have no alcohol problems and one where there is an endemic state involving those with an alcohol problem. The stability of these states is analyzed and a threshold established such that each state will be stable depending on whether the incidence rate is above or below the threshold. The model is analyzed in the context of actual data.展开更多
基金Supported by Natural Science Foundation of Tianjin (No.09JCYBJC06400,No.10 JCZDJC23300)
文摘The trajectory model of dispersed phase drops and distribution model of drop diameters were derived.By numerical simulation,the analytical results indicate that a large number of dispersed phase drops accumulate on the upper plate in different directions and form a hydrodynamic area with the stream-wise location in the range of 0—0.4m,where the flow of trickling film obtains kinetic drive from flowing field.The flowing field of trickling film exhibits an unstable state if the stream-wise location is less than 0.02m,and a stable state otherwise.Moreover,different velocity vectors of drops in the x-y plane result in different interactions between the trickling film and drops.For the non-uniform distribution of drop diameters,there is a stronger interaction between the trickling film and drop if the stream-wise location is less than 0.02m,because the amplitudes of velocity vectors are higher than those in the range of 0.02—1.0m.The result reveals a complexity and diversity of stratified two-phase flowing field.On the other hand,both the basic flowing field and distributions of drop diameters have a great influence on the distributions of comparable kinetic energy of drops.The complicated motions of larger drops are helpful to coalescence because they will consume much more kinetic energy on the trickling film than those of smaller drops.The change of comparable kinetic energy of smaller drops is continuous and steady.The smaller drops are easily entrained by the liquid-liquid flowing field.
文摘We develop a two-stage （four component） model for youths with serious drinking prob- lems and their treatment. The youths with alcohol problems are split into two classes, namely those who admit to having a problem and those who do not. It is shown that the model possesses two steady states, one where people have no alcohol problems and one where there is an endemic state involving those with an alcohol problem. The stability of these states is analyzed and a threshold established such that each state will be stable depending on whether the incidence rate is above or below the threshold. The model is analyzed in the context of actual data.
