Mass Balance Equation

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David D. Y. Chen - One of the best experts on this subject based on the ideXlab platform.

  • Behavior of interacting species in vacancy affinity capillary electrophoresis described by Mass Balance Equation
    Electrophoresis, 2008
    Co-Authors: Ying Sun, Ning Fang, David D. Y. Chen
    Abstract:

    Vacancy ACE (VACE) is one of the ACE methods, and has been used to study binding interactions between different biomolecules. Thermodynamic binding constants can be estimated with nonlinear regression methods. With a highly efficient computer simulation program (SimDCCE), it is possible to demonstrate the detailed behaviors of each species during the interaction process under different conditions. In this work, thirteen scenarios in four different combinations of migration orders of the free protein, free drug, and complex formed are studied. The detailed interaction process between protein and ligand is discussed and illustrated based on the Mass Balance Equation, also called Mass transfer Equation. By properly setting the parameters in the simulation model, the influence of different factors during the interaction process can be well understood.

  • recent developments towards a unified theory for separation science minireview
    Electrophoresis, 1998
    Co-Authors: Michael T Bowser, David D. Y. Chen
    Abstract:

    : Various techniques for chemical separation can be described using a generally applicable theory. There are several schools of thought on how a unified separation science should be developed. The theories described include the Mass Balance Equation (i.e. moving boundary), virtual migration distances, and the use of individual capacity factors.

Joachim Ulrich - One of the best experts on this subject based on the ideXlab platform.

  • Impurity distribution in a solid-liquid interface during static layer crystallization.
    Journal of colloid and interface science, 2002
    Co-Authors: Kwang-joo Kim, Joachim Ulrich
    Abstract:

    The impurity distribution inside crystalline layers in static layer crystallizations was explored theoretically and experimentally for a binary eutectic mixture of caprolactam and water. The impurity distribution in the layer is modeled by a Mass Balance Equation coupled with an energy Balance Equation. The Mass Balance Equation is established with a combination of the growth of the layer and the diffusional movement of impurity. The mathematical model was solved by a numerical method. The predictions are discussed with respect to the interfacial distribution coefficient, concentration, and temperature at the solid-liquid interface, crystalline layer thickness, and concentration of the layer. The impurity distribution obtained by the model was appropriately verified with the results obtained by the experiments.

  • Theoretical and experimental studies on the behaviour of liquid impurity in solid layer melt crystallizations
    Journal of Physics D: Applied Physics, 2001
    Co-Authors: Kwang-joo Kim, Joachim Ulrich
    Abstract:

    The concentration inside a crystalline layer was explored theoretically and experimentally for solid layer melt crystallizations. The distribution of the purity in the crystalline layer is modelled by a Mass Balance Equation coupled with an energy Balance Equation. The Mass Balance Equation is established with the combination of the growth of the layer, the inclusion of the impurity and the migration of the impurity. The concentration profiles were obtained by considering both the migration of inclusions after the layer build-up and the entrapment of inclusion during the growth. The mathematical model established is solved by a numerical method. The predictions are discussed with respect to the interfacial distribution coefficient, the migration effect for removing the inclusion, the concentration and temperature at the solid-liquid interface, crystalline layer thickness, the concentration of the layer, the crystal growth rate and the migration rate. The purity distribution obtained by the model was appropriately verified with that obtained by the experiments.

  • Purification of crystalline layers by controlling the temperature gradient
    Powder Technology, 2001
    Co-Authors: Kwang-joo Kim, Joachim Ulrich
    Abstract:

    The purification of the crystalline layers obtained in layer crystallization has been carried out by a temperature gradient method. The effect of temperature gradients on the migration of inclusions was studied. The effect of the structural configuration of the layers on the migration of inclusions was also explored. Impurity concentrations in the layers were obtained under variation of operating conditions such as the temperature gradient and cooling rate. The migration rate of inclusions and the impurity distribution obtained in the layer are modeled by a Mass Balance Equation coupled with an energy Balance Equation. The impurity distribution obtained by the model was verified with that which was obtained by the experiments.

Adam Zielonka - One of the best experts on this subject based on the ideXlab platform.

  • inverse alloy solidification problem including the material shrinkage phenomenon solved by using the bee algorithm
    International Communications in Heat and Mass Transfer, 2017
    Co-Authors: Adam Zielonka, Edyta Hetmaniok, Damian Slota
    Abstract:

    Abstract In the paper we solve the one-phase inverse problem of alloy solidifying within the casting mould, including the shrinkage of metal which results from the difference between densities of the liquid and solid phases. The process is modeled by means of the solidification in the temperature interval basing on the heat conduction Equation with the source element enclosed, whereas the shrinkage of metal is modeled by the proper application of the Mass Balance Equation. The investigated inverse problem consists in reconstruction of the heat transfer coefficient on the boundary of the casting mould on the basis of measurements of temperature read from the sensor placed in the middle of the mould. Functional expressing the error of approximate solution is minimized with the aid of Artificial Bee Colony Optimization algorithm.

  • Solution of the direct alloy solidification problem including the phenomenon of material shrinkage
    Thermal Science, 2017
    Co-Authors: Edyta Hetmaniok, Damian Słota, Adam Zielonka
    Abstract:

    In the paper we describe the solution technique for solving the direct problem of the alloy solidifying within the casting mould with the phenomenon of material shrinkage taken into account. Due to the difference between densities of the liquid and solid phases, the shrinkage of metal often appears during the solidification. The investigated process is modeled by means of the solidification in the temperature interval basing on the heat conduction Equation with the source element enclosed which includes the latent heat of fusion and the volume contribution of solid phase. Whereas the shrinkage of metal is modeled by the proper application of the Mass Balance Equation.

Eli Grushka - One of the best experts on this subject based on the ideXlab platform.

  • Numerical Solution of the Complete Mass Balance Equation in Chromatography
    Analytical chemistry, 1996
    Co-Authors: Gitti L. Frey, Eli Grushka
    Abstract:

    A new approach to simulate the movement of bands through a chromatographic column is presented. Similar to the Craig distribution model, the Mass Balance Equation is divided into two Equations describing two successive processes. The first Equation includes two effects:  solute diffusion in the mobile phase and migration of the solute band with the mobile phase. The second Equation deals with the distribution of the solute between phases, i.e., the adsorption isotherm. The partial differential Equations are integrated numerically over time and space using two methods. The first approach is a finite difference method. In the second approach, the propagation operator is expanded in a Chebyshev series, where large time steps can be used. The rate of adsorption and desorption is determined by the size of the time increment. By varying the size of the time step, it is possible to study kinetic effects. The influences of sample size, injection width, rate of Mass transfer, and mobile phase velocity on the eluti...

Damian Slota - One of the best experts on this subject based on the ideXlab platform.

  • inverse alloy solidification problem including the material shrinkage phenomenon solved by using the bee algorithm
    International Communications in Heat and Mass Transfer, 2017
    Co-Authors: Adam Zielonka, Edyta Hetmaniok, Damian Slota
    Abstract:

    Abstract In the paper we solve the one-phase inverse problem of alloy solidifying within the casting mould, including the shrinkage of metal which results from the difference between densities of the liquid and solid phases. The process is modeled by means of the solidification in the temperature interval basing on the heat conduction Equation with the source element enclosed, whereas the shrinkage of metal is modeled by the proper application of the Mass Balance Equation. The investigated inverse problem consists in reconstruction of the heat transfer coefficient on the boundary of the casting mould on the basis of measurements of temperature read from the sensor placed in the middle of the mould. Functional expressing the error of approximate solution is minimized with the aid of Artificial Bee Colony Optimization algorithm.