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MassConcentrationCondition [pred,vars,pars]

represents a mass concentration boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.

MassConcentrationCondition [pred,vars,pars,lkey]

represents a thermal surface boundary condition with local parameters specified in pars[lkey].

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Basic Examples  
1D  
2D  
3D  
Material Regions  
Nonlinear Time Dependent  
Applications  
See Also
Tech Notes
Related Guides
History
Cite this Page

MassConcentrationCondition [pred,vars,pars]

represents a mass concentration boundary condition for PDEs with predicate pred indicating where it applies, with model variables vars and global parameters pars.

MassConcentrationCondition [pred,vars,pars,lkey]

represents a thermal surface boundary condition with local parameters specified in pars[lkey].

Details

  • MassConcentrationCondition specifies a boundary condition for MassTransportPDEComponent .
  • MassConcentrationCondition is typically used to set a mass species concentration on the boundary. Common examples include a mass species inflow condition.
  • MassConcentrationCondition sets a specific mass species concentration on the boundary with dependent variable in [TemplateBox[{InterpretationBox[, 1], {"mol", , "/", , {"m", ^, 3}}, moles per meter cubed, {{(, "Moles", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]], independent variables in [TemplateBox[{InterpretationBox[, 1], "m", meters, "Meters"}, QuantityTF]] and time variable in [TemplateBox[{InterpretationBox[, 1], "s", seconds, "Seconds"}, QuantityTF]].
  • Stationary variables vars are vars={c[x1,,xn],{x1,,xn}}.
  • Time-dependent variables vars are vars={c[t,x1,,xn],t,{x1,,xn}}.
  • The mass concentration condition MassConcentrationCondition models .
  • Model parameters pars as specified for MassTransportPDEComponent .
  • The following additional model parameters pars can be given:
  • parameter default symbol
    "MassConcentration"
  • 0
  • , mass concentration [TemplateBox[{InterpretationBox[, 1], {"mol", , "/", , {"m", ^, 3}}, moles per meter cubed, {{(, "Moles", )}, /, {(, {"Meters", ^, 3}, )}}}, QuantityTF]]
  • MassConcentrationCondition evaluates to a DirichletCondition .
  • The boundary predicate pred can be specified as in DirichletCondition .
  • If the MassConcentrationCondition depends on parameters that are specified in the association pars as ,keypi,pivi,, the parameters are replaced with .
  • Examples

    open all close all

    Basic Examples  (3)

    Set up a mass concentration boundary condition:

    Compute the mass concentration with model variables vars and parameters pars with a mass concentration of at the left boundary:

    Set up the equation:

    Solve the PDE:

    Visualize the solution and note the sinusoidal mass change on the left:

    Set up a system of mass concentration boundary conditions:

    Scope  (7)

    Basic Examples  (2)

    Define model variables vars for a transient species field with model parameters pars and a specific boundary condition parameter:

    Define model variables vars for a transient species field with model parameters pars and multiple specific parameter boundary conditions:

    1D  (1)

    Model a 1D chemical species field in an incompressible fluid whose right side and left side are subjected to a mass concentration and inflow condition, respectively:

    [画像: del .(-d del c(x))+v^->.del c(x)^(︷^( mass transport model )) =|_(Gamma_(x=0))q(x)^(︷^( mass flux value ))]

    Set up the stationary mass transport model variables vars:

    Set up a region :

    Specify the mass transport model parameters species diffusivity and fluid flow velocity :

    Specify a species flux boundary condition:

    Specify a mass concentration boundary condition:

    Set up the equation:

    Solve the PDE:

    Visualize the solution:

    2D  (1)

    Model mass transport of a pollutant in a 2D rectangular region in an isotropic homogeneous medium. Initially, the pollutant concentration is zero throughout the region of interest. A concentration of 3000 is maintained at a strip with dimension 0.2 located at center of the left boundary, while the right boundary is subject to a parallel species flow with constant concentration of 1500 , allowing for mass transfer. A pollutant outflow of 100 is applied at both the top and bottom boundaries. A diffusion coefficient of 0.833 is distributed uniformly with a uniform horizontal velocity of 0.01 :

    [画像: del .(-d del c(x,y))+v^->.del c(x,y)^(︷^( mass transport model )) =|_(Gamma_(y=0, y=10))q(x,y)^(︷^( mass flux value ))+|_(Gamma_(x=20))h (c_(ext)(x,y)-c(x,y))^(︷^( mass transfer value ))]

    Set up the mass transport model variables vars:

    Set up a rectangular domain with a width of and a height of :

    Specify model parameters species diffusivity and fluid flow velocity :

    Set up a species concentration source of 0.2 in length at the center of the left surface:

    Set up a mass transfer boundary on the right surface:

    Set up an outflow flux q of on the top and bottom surfaces:

    Set up the equation:

    Solve the PDE:

    Visualize the solution:

    3D  (1)

    Model a non-conservative chemical species field in a unit cubic domain, with two mass conditions at two lateral surfaces and a mass inflow through a circle with radius 0.2 at the center of the top surface, as well as an orthotropic mass diffusivity :

    [画像: del .(-d del c(x,y,z))+v^->.del c(x,y,z)^(︷^( mass transport model )) =|_(Gamma_(z=1& (x-0.5)^2+(y-0.5)^2<=0.04))q(x,y,z)^(︷^( mass flux value ))]

    Set up the mass transport model variables vars:

    Set up a region :

    Specify a diffusivity and a flow velocity field :

    Specify mass concentrations:

    Specify a flux condition of through a regional circle on the top surface:

    Set up the equation:

    Solve the PDE:

    Visualize the solution:

    Material Regions  (1)

    Model a 1D chemical species transport through different material with a reaction rate in one. The right side and left side are subjected to a mass concentration and inflow condition, respectively:

    [画像: del .(-d del c(x))+a c(x)^(︷^( mass transport model )) =|_(Gamma_(x=0))q(x)^(︷^( mass flux value ))]

    Set up the stationary mass transport model variables vars:

    Set up a region :

    Specify the mass transport model parameters species diffusivity and a reaction rate active in the region :

    Specify a species flux boundary condition:

    Specify a mass concentration boundary condition:

    Set up the equation:

    Solve the PDE:

    Visualize the solution:

    Nonlinear Time Dependent  (1)

    Model a 1D non-conservative chemical species field with a nonlinear diffusivity coefficient and an outflow condition through part of the boundary, which is expressed as follows:

    [画像: (partialc(t,x))/(partialt)+del .(-d del c(t,x))^(︷^( diffusion term )) +v^->.del c(t,x))^(︷^( convection term)) =|_(Gamma_(x=0.2))q(t,x)^(︷^( mass flux boundary ))]

    Set up the mass transport model variables vars:

    Set up a region :

    Specify a nonlinear species diffusivity and fluid flow velocity :

    Specify an outflow flux of applied at the right end:

    Specify a time-dependent mass concentration surface condition:

    Set up an initial condition:

    Set up the equation:

    Solve the PDE:

    Visualize the solution:

    Applications  (1)

    Model mass transport of a pollutant in a 2D rectangular region in an isotropic homogeneous medium. Initially, the pollutant concentration is zero throughout the region of interest. A concentration of 3000 is maintained at a strip with dimension 0.2 located at center of left boundary, while a pollutant outflow of 100 is applied at both the top and bottom boundaries. A diffusion coefficient of 0.833 is distributed uniformly, but both horizontal and vertical velocity are spatial dependent:

    [画像: del .(-d del c(x,y))+v^->.del c(x,y)^(︷^( mass transport model )) =|_(Gamma_(y=0, y=10))q(x,y)^(︷^( mass flux value ))]

    Set up the mass transport model variables vars:

    Set up a rectangular domain with a width of and a height of :

    Specify model parameters species diffusivity and fluid flow velocity :

    Set up a species concentration source of 0.2 in length at the center of the left surface:

    Set up an outflow flux of on the top and bottom surfaces:

    Set up the equation:

    Solve the PDE:

    Visualize the solution:

    See Also

    MassFluxValue   MassImpermeableBoundaryValue   MassOutflowValue   MassSymmetryValue   MassTransferValue   MassTransportPDEComponent

    Tech Notes

    History

    Introduced in 2020 (12.2)

    Wolfram Research (2020), MassConcentrationCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/MassConcentrationCondition.html.

    Text

    Wolfram Research (2020), MassConcentrationCondition, Wolfram Language function, https://reference.wolfram.com/language/ref/MassConcentrationCondition.html.

    CMS

    Wolfram Language. 2020. "MassConcentrationCondition." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MassConcentrationCondition.html.

    APA

    Wolfram Language. (2020). MassConcentrationCondition. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MassConcentrationCondition.html

    BibTeX

    @misc{reference.wolfram_2025_massconcentrationcondition, author="Wolfram Research", title="{MassConcentrationCondition}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/MassConcentrationCondition.html}", note=[Accessed: 09-January-2026]}

    BibLaTeX

    @online{reference.wolfram_2025_massconcentrationcondition, organization={Wolfram Research}, title={MassConcentrationCondition}, year={2020}, url={https://reference.wolfram.com/language/ref/MassConcentrationCondition.html}, note=[Accessed: 09-January-2026]}

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