By COMSOL, Inc.
Simulate MEMS Devices and a Variety of Multiphysics Interactions The MEMS Module is used for simulating piezoelectric and capacitive devices. Simulations can include prestress and nonlinear effects. With the MEMS Module, thermal expansion in actuators and sensors can also be modeled. In addition to common multiphysics phenomena, the MEMS Module can model a number of intricate multiphysics interactions that are important for accurate simulation of MEMS devices. This includes hygroscopic swelling, thermoelastic and squeeze-film damping, bidirectional fluid–structure interaction (FSI), and piezoresistive, electrostrictive, and ferroelectroelastic effects (including hysteresis). The MEMS Module can be used with other COMSOL Multiphysics add-on modules. For instance, when it is combined with the AC/DC Module, magnetostrictive devices can be analyzed. Adding the Structural Mechanics Module enables shell modeling in MEMS devices, and adding the Microfluidics Module will provide additional tools for analyzing biomedical MEMS devices involving fluid flow. What Can Be Modeled with the MEMS Module Analyze a variety of MEMS devices subject to interactions between multiple physical phenomena. Actuators: Simulate a wide range of actuators, including electrothermal, electrostatic, and piezoelectric actuators. Sensors: Predict the behavior of capacitive, piezoelectric, and piezoresistive sensors. Gyroscopes and Accelerometers: Analyze the electrostatic–mechanical or piezoelectric performance of gyroscope and accelerometer designs. Piezoelectric Devices: Model piezoelectric devices such as RF filters, energy harvesters, transducers, actuators, and gyroscopes. Quartz Oscillators: Compute the frequency response of piezoelectric crystal oscillators with arbitrary cuts and include thermal dissipation. Electrostatically Actuated Resonators: Compute the resonant frequencies, pull-in voltage, Q factor, and the effects of different damping modes of MEMS resonators. Fluidic Devices: Explore designs of micropumps, microvalves, and microfluidic sensors. Bulk Acoustic Wave (BAW) Resonators: Compute the frequency response and dispersion diagrams of BAW devices. Run a Variety of Structural Analyses The MEMS Module inherits the solid mechanics capabilities of the Structural Mechanics Module, with options for modeling solid mechanics in 3D, 2D, and 2D axial symmetry. Analyze virtually any phenomenon related to mechanics on the microscale, including contact, friction, centrifugal, Coriolis, and Euler forces. To model nonlinear materials, including hyperelastic materials, the MEMS Module can be combined with the Nonlinear Structural Materials Module. Solid Mechanics Analyses in the MEMS Module - Static - Eigenfrequency - Undamped - Damped - Prestressed - Transient - Direct or mode superposition - Frequency response - Direct or mode superposition - Prestressed - Geometric nonlinearity and large deformations - Mechanical contact - Buckling - Response spectrum - Random vibration - Component mode synthesis Features and Functionality in the MEMS Module The MEMS Module contains specialized features and functionality for modeling MEMS devices. Built-In User Interfaces and Results The MEMS Module provides built-in user interfaces that are tailored to the type of device and multiphysics interaction being analyzed. These interfaces define sets of domain equations, boundary conditions, initial conditions, predefined meshes, and predefined studies with solver settings as well as predefined plots and derived values. All of these features can be accessed within the COMSOL Multiphysics environment. Values for the electric field, stress, strain, quality factors, damping, resonant frequencies, dissipation, and scattering parameter (S-parameter), as well as values for capacitance, admittance, and impedance matrices, can be calculated and exported to the Touchstone file format. Any mathematical expression can be plotted or evaluated in terms of the computed quantities. Electrostatics The capacitive effects in MEMS devices can be analyzed with electrostatics computations where the fields are determined by the electric potential and charge distribution. Both the finite element method (FEM) and boundary element method (BEM) are available for solving the electric potential and can be combined for a hybrid boundary-element–finite-element method (BEM–FEM). Based on the computed potential field, a number of quantities can be calculated, such as the capacitance matrices, electric fields, charge density, and electrostatic energy. The electrostatics functionality can be extended with built-in options for multiphysics effects like piezoelectricity, electrostriction, and ferroelectricity. Debye dispersion and dielectric loss material models are available for both frequency-domain and time-dependent analysis. Fluid–Structure Interaction (FSI) The Fluid-Structure Interaction (FSI) multiphysics interface of the MEMS Module combines fluid flow with solid mechanics to capture the bidirectional interactions between fluids and solid structures. The flow can be either laminar or turbulent. For including specific microfluidic phenomena, the MEMS Module can be combined with the Microfluidics Module. Turbulent flow requires the CFD Module or Heat Transfer Module. The CFD Module also allows two-phase and three-phase flow to be coupled with solid mechanics. Piezoresistivity The piezoresistive effect refers to the change in a material’s conductivity in response to an applied stress. The ease of integration of small piezoresistors with standard semiconductor processes, along with the reasonably linear response of the sensor, has made this technology particularly important in the pressure sensor industry. For modeling piezoresistive sensors, the MEMS Module provides several dedicated interfaces for piezoresistivity in solids or shells. When combining the MEMS Module with the Structural Mechanics Module, a piezoresistivity user interface for thin shells is available. Thermomechanical Couplings The Thermoelasticity interface combines the Solid Mechanics and Heat Transfer in Solids interfaces, which includes coupling terms for thermoelastic damping. Thermoelastic damping is particularly important in smaller MEMS structures, in which regions of compression and expansion are in close proximity. The cyclic deformation of resonators creates local temperature variations and thermal expansion of the material, which appears as damping. The thermoelastic coupling terms result in the material being cooled when under tension and heated when under compression. The resulting irreversible heat transfer between warm and cool regions of the solid produces mechanical losses that may be important at the microscopic level. Damping in MEMS Resonators A number of different damping phenomena can be modeled using the MEMS Module, including squeeze-film damping; isotropic and anisotropic loss-factors for dielectric, elastic, and piezoelectric materials; and thermoelastic damping. For computing anchor damping, perfectly matched layers (PMLs) provide state-of-the-art absorption of outgoing elastic waves for both elastic and piezoelectric solids. A fully coupled eigenfrequency, frequency-response, or transient analysis can be performed. By combining the MEMS Module with the Acoustics Module, the effects of acoustic damping from a surrounding fluid, including pressure acoustic and thermoviscous damping, can be included. Prestressed and Biased Devices The MEMS Module can be used to study devices that are prestressed with mechanical and thermal loads. The built-in harmonic perturbation analysis allows for computing the frequency response as well as the eigenfrequencies and eigenmodes of such models. In a similar way, electrostatically biased MEMS resonators, including micromechanical filters, can be analyzed. For instance, since these devices are biased by a DC voltage and driven by an alternating current, it is possible to analyze how damping and biasing effects cause the resonance frequencies to shift. Joule Heating and Thermal Stress Thermal, electric, and structural effects can be easily combined. Predefined multiphysics couplings for Joule heating and thermal expansion enable modeling of electric current conduction in a structure, the subsequent electric heating caused by the ohmic losses, and the thermal stresses induced by the temperature field. Typical applications include thermal actuators and fuses. All material properties can be nonlinear and temperature dependent. Modeling of mechanical contact can be extended to include contact resistance for both heat and electric currents. Thin conducting layers can be modeled using specialized tools for layered shells. Piezoelectricity Uniquely advanced piezoelectric modeling tools allow for static, frequency-domain, coupled eigenfrequency, and time-domain simulations. Designs are allowed to have materials combined in any imaginable configuration and can easily include coupled piezoelectric, metallic, dielectric, and fluid parts. Both the direct and inverse piezoelectric effects can be modeled, and the piezoelectric coupling can be formulated using the strain-charge or stress-charge forms. The MEMS Module includes a library of common piezoelectric material properties, including lead zirconate titanate (PZT) and quartz. Many piezoelectric materials exhibit nonlinear ferroelectroelastic behavior at large applied electric fields. It is also possible to model thin-layered dielectric and piezoelectric structures with shells, which can be accessed by combining the MEMS Module and Composite Materials Module. Damping in piezoelectric devices can be represented with loss factors for the piezoelectric as well as the elastic and dielectric domains. Dielectric heating can be computed and coupled with heat transfer analysis to investigate the effects of dispersion. When analyzing piezoelectric behavior using the Piezoelectricity interface, results can be obtained for the electric potential and electric field, displacement, strain, stress, capacitance, losses, admittance, impedance, and S-parameters. Wave Dynamics in Elastic and Piezoelectric Materials Vibrations and propagation of elastic and piezoelectric waves can be modeled in the frequency domain as well as in the time domain. This enables analysis of, for example, acoustic transducers and resonators, including bulk acoustic wave (BAW) and surface acoustic wave (SAW) devices. For time-domain simulations, a choice between implicit and explicit methods is available. In all cases, different material types can be combined in the same model, including functionally graded materials. The frequency-domain and implicit time-domain simulations are based on the finite element method, whereas the explicit time-domain simulations are based on the discontinuous Galerkin (dG or dG-FEM) method. The dG-FEM method uses a time-explicit solver to ensure a computationally efficient hybrid method that can solve very large models with many millions of degrees of freedom (DOFs). This method shows excellent parallel computing performance, including when running it on clusters. For modeling waves leaving the computational domain, a variety of boundary conditions and absorbing layers are available, including nonreflecting boundary conditions, sponge layers, perfectly matched layers (PMLs), and elastic port boundary conditions. Electromagnetic–Structure Interaction The Electromechanics multiphysics interface combines solid mechanics and electrostatics with a moving mesh to model the deformation of electrostatically actuated structures, such as inertial sensors. The interface is also compatible with ferroelectroelastic and electrostrictive materials and has options for both FEM and BEM. A similar multiphysics interface for magnetomechanics is available when the MEMS Module is combined with the AC/DC Module. Electrostrictive and Ferroelectroelastic Materials Electrostriction is a form of electromechanical interaction where an electric field applied to an electrostrictive material generates a deformation of the material (direct effect), and a stress applied to the material changes its polarization (inverse effect). To model this phenomenon, the Electrostriction interface can be used, which includes a multiphysics coupling between the Solid Mechanics and Electrostatics interfaces. The Ferroelectroelasticity interface can be used for modeling the coupling of Solid Mechanics and Electrostatics. This enables modeling of nonlinear electromechanical interactions in ferroelectric and piezoelectric materials. Electric polarization in such materials, including possible hysteresis and saturation effects, depends nonlinearly on the applied electric field. In addition, the polarization and mechanical deformations in such materials can be strongly coupled. Electrical Circuits The MEMS Module enables the combination of 2D and 3D models with SPICE circuits. In the combined simulation, parts of the model will have circuit representation. This can be used to evaluate the effect of a series capacitor on a quartz crystal oscillator, for example. For any model or combination of models, the Electrical Circuit interface can be used to solve for the voltages, currents, and charges associated with the circuit elements. Circuit models can contain passive elements like resistors, capacitors, and inductors as well as active elements such as diodes and transistors. Circuit topologies can be imported or exported in the SPICE netlist format. Create and Import MEMS Designs Geometric models can be created directly in COMSOL Multiphysics using the built-in CAD tools or imported from files created in other software.
The Microfluidics Module is designed specifically for handling momentum, heat, and mass transport with special considerations for fluid flow at the microscale. What Can Be Modeled with the Microfluidics Module: Perform various microfluidics analyses with the COMSOL® software. - Lab-on-a-Chip Devices: Compute the radial pressure distribution and flow rate through a rotating lab-on-a-chip platform. - Microfluidic Channels: Infuse and flush connected pieces of equipment with a fluid. - Micropumps: Model microfluidic systems with applications ranging from biological fluid handling to microelectronic cooling. - Micromixers: Simulate rapid mixing of different fluid streams. - Inkjet Printing: Model the fluid flow in an inkjet to predict optimal inkjet design. - Drug Delivery: Describe the operation of a drug delivery system. - Fuel Cells: Study proton exchange membrane (PEM) fuel cell designs and construction challenges. - Electrowetting Optical Devices: Modify a contact angle by changing the voltage applied to the conducting liquid. - Electrokinetic Valves: Analyze pressure-driven flow and electrophoresis in a 3D microchannel system. - Detection Tests: Study possible symmetries in the spreading of a liquid sample in a test strip. Features and Functionality in the Microfluidics Module: The capabilities of the Microfluidics Module can address multiple simulation problems. - Single-Phase Flow: The Fluid Flow interfaces use physical quantities, such as pressure and flow rate, and physical properties, such as viscosity and density, to define a fluid flow problem. The Laminar Flow interface covers incompressible and weakly compressible flows. This interface also allows for the simulation of non-Newtonian fluid flow. An interface for creeping flow is used when the Reynolds number is significantly smaller than one. This is often referred to as Stokes flow and is appropriate for use when viscous flow is dominant. It is usually applicable to microfluidic devices. - Three-Phase Flow: The Laminar Three-Phase Flow, Phase Field interface is designed to track the interfaces between three immiscible and incompressible fluids. This multiphysics interface couples a Laminar Flow interface to a Ternary Phase Field interface. The flow is assumed to be laminar; that is, the Reynolds number is low to moderate, and the density of each phase is constant. The interface solves the Navier–Stokes equations for the conservation of momentum as well as the continuity equation for the conservation of mass. The interface position is tracked by solving four additional transport equations, two for the phase field variables and two for the generalized chemical potentials. The movement of the surface is determined by the minimization of free energy. - Transport of Species: The Microfluidics Module provides a dedicated interface for transport of diluted species. It is used to simulate chemical species transport through diffusion, convection (when coupled with fluid flow), and migration in electric fields for mixtures where one component — a solvent — is present in excess (90 mol% or greater). It is typically employed to model the performance of mixers and Marangoni effects driven by concentration gradients. For modeling of chemical reactions in microfluidic devices, the Microfluidics Module can be combined with the Chemical Reaction Engineering Module, which also makes available transport of concentrated species with binary diffusion. - Electrokinetic Flow: When modeling the transport of diluted species, the electromigration of ions in a static electric field can be included according to the Nernst–Planck equation. Applications of this functionality include electrophoretic mobility and electroosmotic flow. The Microfluidics Module can be combined with the Chemical Reaction Engineering Module to access the Nernst–Planck interface and Electrophoretic Transport interface, which are dedicated to the modeling of electrolytes and can include the formulations of Poisson’s equation or the electroneutrality condition for the charge balance. The combination of Nernst–Planck and Poisson's equations can be used for modeling charged double layers and electroosmotic flow. - Two-Phase Flow: Three different methods are available in the Microfluidics Module for modeling two-phase flow: level set, phase field, and moving mesh methods. These are used to model two fluids separated by a moving fluid interface, where the interface is tracked in detail, including surface curvature and surface tension forces. The level set and phase field methods use a fixed background mesh and solve additional equations to track the interface location. The moving mesh method solves the flow equation on a moving mesh, and boundary conditions representing the fluid interface are directly applied at the surface. In this case, additional equations are solved for the mesh deformation by means of the arbitrary Lagrangian–Eulerian (ALE) method. All of these methods and their interfaces support both compressible and incompressible laminar flows, where one or both fluids can be non-Newtonian. - Porous Media Flow: Porous media flow can also occur in microscale geometries. When the pore size is in the micron range, the flow is often friction-dominated; in such cases, Darcy’s law can be used to solve the flow. The Microfluidics Module features a dedicated interface for porous media flow based on Darcy's law. In this case, shear stresses perpendicular to the flow are neglected. For intermediate flows, an interface for the Brinkman equations is available. This interface models flow through a porous medium where shear stresses cannot be neglected. There is support for both the Stokes–Brinkman formulation, suitable for very low flow velocities, and Forchheimer drag, which is used to account for effects at higher velocities. The fluid can either be incompressible or compressible, provided that the Mach number is less than 0.3. The formulation allows for free and porous media models, including porous media using the Brinkman equations or laminar flow. These interfaces are appropriate for microfluidic porous media flow. Example applications include paper microfluidics and transport in biological tissue. - Rarefied and Slip Flow: Rarefied gas flow occurs when the mean free path of the molecules becomes comparable with the length scale of the flow. The Knudsen number, Kn, characterizes the importance of rarefaction effects on the flow. As the gas becomes more rarefied (corresponding to how high the Knudsen number is), the Knudsen layer — which is present within one mean free path of the wall — begins to have a significant effect on the flow. For Knudsen numbers below 0.01, rarefaction can be neglected, and the laminar flow interfaces of the Microfluidics Module can be used with nonslip boundary conditions. For slightly rarefied gases (0.01 < Kn < 0.1), the Knudsen layer can be modeled by appropriate boundary conditions at the walls together with the continuum Navier–Stokes equations in the domain. In this instance, a Slip Flow interface is available in the Microfluidics Module. To model higher Knudsen numbers, the Molecular Flow Module is required. Expanded Modeling with the Microfluidics Module: As with the other products in the COMSOL product suite, when the Microfluidics Module is added to COMSOL Multiphysics®, the features and functionality are fully integrated into the modeling workflow and are ready to be used with other modules. For instance, the Microfluidics Module can be combined with the: - Heat Transfer Module to model thermal flows as well as conduction, natural and forced convection, Joule heating, thermophoresis, and Marangoni effects - AC/DC Module to study the effects of magnetophoresis and magnetohydrodynamics - Structural Mechanics Module to perform fluid–structure interaction simulations for fixed and deforming geometries with single-phase or multiphase flow - Chemical Reaction Engineering Module to model chemical reactions and transport of concentrated species and to access advanced capabilities for modeling transport of electrolytes and ions with electric fields as driving forces
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Model transport phenomena and chemical reactions relevant to various industries with the COMSOL® software. What Can Be Modeled with the Chemical Reaction Engineering Module: - Bulk Chemicals: Simulate space-dependent continuous stirred mixers and tank reactors for high flow rates. - Specialty Chemicals: Study reaction kinetics and mass transport to design processes for the fine chemicals industry, such as extraction and distillation processes. - Biotechnology and Pharmaceuticals: Optimize designs and processes for biotech and pharmaceutical applications by modeling the transport and reactions of drugs in tissue and across membranes. - Food Processing: Investigate heat transfer and reactions during pasteurization or study other processes in the food industry, such as drying, cooking, and fermentation. - Petrochemical: Model catalyst deactivation and pressure losses in packed bed reactors. - Environmental Technology: Investigate the elimination of pollutants in effluent streams using separation processes such as adsorption, membrane filtration, and crystallization. - Semiconductors: Study the rate of chemical vapor deposition (CVD) as a function of fluid flow and reaction kinetics in a CVD boat reactor. - Consumer Products: Design static mixers for laminar flow —such as mixers for epoxies, silicones, and acrylic resins — that achieve the desired emulsion properties. - Polymers: Study different aspects of polymer production processes, such as the dissolution of reactants, polymerization reactions, curing reactions, and filtration of the product stream. - Agricultural Chemicals: Investigate optimal process conditions and reactor design for the production of fertilizers, pesticides, and herbicides. Overview of the Modeling Strategy and Workflow: Realistic descriptions of reacting systems in scientific and engineering studies often need to incorporate both transport phenomena and chemical reactions. The Chemical Reaction Engineering Module includes features for following the typical workflow in chemical and chemical engineering investigations, which involves the following incremental steps: - Study reaction mechanisms in ideal, perfectly mixed systems - Calculate kinetic, thermodynamic, and transport properties - Extend the investigations to space-dependent system components that include: Transport of chemical species, Heat transfer, Fluid flow, Electrokinetic effects This workflow can be applied in many different fields that involve chemical reactions and for modeling at different scales, such as for the modeling of nanotechnology and microreactors as well as for environmental studies and geochemistry. The entire process, from defining models to the presentation of the results, is documented in the software for transparency and reproducibility. Features and Functionality in the Chemical Reaction Engineering Module: The Chemical Reaction Engineering Module provides a built-in workflow for simulating perfectly mixed systems in 0D followed by transport phenomena in 2D and 3D. Defining Reaction Kinetics: The first step in modeling any system is to establish the material balances. With the Reaction Engineering interface, chemical equations can be input in order to automatically obtain the material balance equations for the chemical species in the system and the energy balance equations for the system. When a reaction mechanism is added, the kinetic expressions as a function of the species concentrations are derived automatically from the mass action law for elementary steps. Users can also input their own analytical expressions for the reaction rate as a function of the species concentrations and temperature. The material balances and the reaction kinetic expressions give the ordinary differential equations that are formulated automatically by the software. For a perfectly mixed batch reactor, the solution to the equations gives the composition of the reacting mixture over time. Generating Space-Dependent Models: A working model for a perfectly mixed system can be used to automatically define material, energy, and momentum balances for space-dependent systems. The transport properties calculated in the Reaction Engineering interface (for example, heat capacity, thermal conductivity, viscosity, and binary diffusivity) automatically transfer to the physics interfaces for chemical species transport, heat transfer, and fluid flow. This functionality allows for refining kinetics and thermodynamics expressions of chemical reactions before moving to 2D, 2D axisymmetric, and 3D models. Chemical Species Transport: Modeling transport phenomena in reacting systems involves the description of the chemical species in so-called multicomponent transport models. The Chemical Reaction Engineering Module includes sophisticated models for multicomponent transport in the Transport of Concentrated Species interface, which offers the Maxwell–Stefan formulation and the mixture-averaged models for multicomponent transport. For diluted solutions, the Transport of Diluted Species interface is available, which treats cases where the interactions in the solution are dominated by solute–solvent interactions. The Dispersed Two-Phase Flow with Species Transport interface can be used to describe chemical species transfer between two immiscible fluid phases. The chemical species transport equations are also available for including Knudsen diffusion in, for example, porous media. The dusty gas diffusion model is also included. The formulation of the mass balance model as well as the transport properties can be obtained directly from chemical equations when generating a space-dependent model from the Reaction Engineering interface. Electrokinetic Effects: When modeling the transport of diluted or concentrated species, electric fields can be included as driving forces for transport for the modeling of electrolytes and ions. The Nernst-Planck and Electrophoretic Transport interfaces are dedicated to the modeling of electrolytes and can include the formulations of Poisson’s equation or the electroneutrality condition for the charge balance in the electrolyte. Applications of this functionality include electrokinetic valves, electroosmotic flow, and electrophoresis. Thermodynamic Properties Database: The Chemical Reaction Engineering Module contains a thermodynamic properties database, which can be used to calculate properties for gas mixtures, liquid mixtures, gas–liquid systems at equilibrium (flash calculations), liquid–liquid systems, and gas–liquid–liquid systems at equilibrium. There is a variety of thermodynamic models that can be used to calculate density, heat capacity, enthalpy of formation, enthalpy of reaction, viscosity, thermal conductivity, binary diffusivity, activity, and fugacity. Read more about this functionality on the Liquid & Gas Properties Module page, which is included in the Chemical Reaction Engineering Module. The thermodynamic properties database can be used to create a so-called property package for a specific reacting system by selecting the chemical species present in the system, the desired properties, and the thermodynamic model. When defining reaction mechanisms, the reactants and products can be matched with the chemical species in the property package defined by the thermodynamic properties database. This matching automatically links the functions and equations generated by the property package to the model of the reacting system. Parameter Estimation: Analysis of systems of chemical reactions and reaction mechanisms usually rely on parameter estimation of frequency factors, activation energies, and other parameters that may quantitatively describe experimental observations. The Chemical Reaction Engineering Module includes dedicated features for parameter estimation, designed to optimize these parameters using data from multiple experiments. The typical workflow for the estimation of model parameters is as follows: First, the model parameters to estimate (such as the rate constants) are selected, and the initial values and scales for the parameters are defined. Then, the experimental data is imported and data columns are correlated with model variables by entering the proper variable names or expressions. Next, an optimization method is chosen and computed. The progress of the optimization can be inspected during computation. Once the optimal parameter values have been found, the results can be compared with experimental measurements. Fluid Flow: The fluid flow functionality included the Chemical Reaction Engineering Module can handle laminar and porous media flow. Additionally, when combined with the CFD Module, there are ready-made couplings for the modeling of chemical species transfer in turbulent flow. The formulation of the fluid flow model as well as the viscosity and density can be obtained directly from chemical equations when generating a space-dependent model from the Reaction Engineering interface. Heat Transfer: The heat transfer functionality included in the Chemical Reaction Engineering Module can account for heat transfer by conduction, convection, and radiation. The radiation term is given by surface-to-ambient radiation, while the Heat Transfer Module is required for surface-to-surface radiation and radiation in participating media. The heat transfer capabilities of the Chemical Reaction Engineering Module include heat transfer in fluids, solids, and porous media. The formulation of the heat transfer model, as well as the thermodynamic and transport properties, can be obtained directly from chemical equations when generating a space-dependent model from the Reaction Engineering interface. Surface Reactions and Heterogeneous Catalysis: Surface reactions are typical for heterogeneous catalysis as well as for surface deposition processes such as chemical vapor deposition. They are found in the bulk chemicals industry, such as in the Haber–Bosch process for the production of ammonia and in microsensors for the detection of very low amounts of tracers that can adsorb on surfaces and be detected by, for example, a change in electrical properties. In transport-reaction models, surface reactions can be treated as boundary equations coupled to the boundary conditions for the transport and reaction equations in the bulk. This would be typical for models below or up to the microscopic scale. Alternatively, in porous media, these reactions are treated in a similar fashion as homogeneous reactions but include the specific surface area (area per unit volume of the porous material) and the effective transport properties. This would be typical for models both in the microscopic scale and the macroscopic scale — so-called multiscale models. The Chemical Reaction Engineering Module includes ready-made formulations for heterogeneous catalysis for surface reactions on boundary faces as well as surface reactions distributed over a homogenized porous catalyst. For porous catalysts, multiscale models are predefined to describe bimodal pore structures. Such structures may consist of microporous pellets packed to form a macroporous pellet bed.
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Model Low-Temperature Plasma Sources with the Plasma Module What Can Be Modeled with the Plasma Module Simulate the behavior of plasmas subject to a variety of electromagnetic excitations. Inductively Coupled Plasmas Investigate how power couples to the plasma in an ICP reactor. Capacitively Coupled Plasmas Model CCP reactors using a dedicated interface that directly solves the time-periodic steady state. Inductively Coupled Plasmas with RF Bias Investigate how an inductively coupled RF bias influences an ICP reactor. Nonisothermal Plasma Flow Couple a plasma model with fluid flow and heat transfer. Electron Cyclotron Resonance (ECR) Plasma Sources Couple a plasma model with magnetic fields and electromagnetic waves to model an ECR plasma source. Microwave-Excited Plasmas Investigate the effects of microwave heating in a plasma. Direct Current Discharges Simulate discharges sustained by a DC voltage or current. Corona Discharges Compute the spatial distribution of charged species in corona discharges. Electric Breakdown Detect if a high-voltage DC system can cause gas breakdown. Electrostatic Precipitators Track charged particle trajectories and compute the transmission probability of an electrostatic precipitator. Plasma Arcs Simulate the temperature distribution in a plasma arc and surrounding materials. ICP Torches Investigate the electrical and thermal characteristics of an ICP torch at atmospheric pressure. Plasma Global Models Model plasma reactors using global models for fast parameterizations and complex chemistries, including the Boltzmann equation. Electron Energy Distribution Functions (EEDFs) Compute EEDFs and obtain electron transport parameters and source terms for use in fluid plasma models. Optimization for Plasma Uniformity Optimize the coil design and positioning of an ICP reactor to obtain plasma uniformity. Ion Energy Distribution Function Compute the ion energy distribution function at surfaces. Etching and Deposition Simulate etching and growth rates along a surface. Features and Functionality in the Plasma Module The Plasma Module provides specialized tools for modeling low-temperature and thermal plasmas. Nonequilibrium Plasmas The Plasma Module provides built-in interfaces for modeling low-temperature plasma reactors that are sustained by a static or time-varying electric field. These interfaces each define sets of domain equations, boundary conditions, initial conditions, predefined meshes, and predefined studies with solver settings for steady and transient analyses, as well as predefined plots and derived values. Transport equations for all species (electrons, ions, and neutrals) are solved self-consistently with Poisson's equation. The electrons' mean energy equation can also be solved by modeling how the electrons gain energy from the electric field and lose energy in collisions with the background gas. Plasma Chemistry Reactions The plasma chemistry is extremely important for obtaining realistic simulation results. The Plasma Module can be used to define electron impact reactions, reactions between heavy species, and surface reactions. The plasma chemistry dictates how electrons lose or gain energy in collisions with the background gas. The Plasma Module offers dedicated features for modeling electron impact reactions that can result in ionization, excitation, and attachment. Electron impact reactions can be defined from cross-section data, and source terms can be obtained by suitable integration over electron energy distribution functions. Multiphysics Interface for Modeling ICP Reactors The Inductively Coupled Plasma multiphysics interface is used to study discharges that are sustained by induction currents. This multiphysics interface connects the plasma conductivity from the Plasma interface to the Magnetic Fields interface and couples the resulting electron heating due to the induction currents back to the Plasma interface. The magnetic field is solved for in the frequency domain and the plasma is solved for in the time domain. Multiphysics Interfaces for Modeling Equilibrium Discharges The Plasma Module includes interfaces for modeling plasmas in thermodynamic equilibrium. In thermodynamic equilibrium, electrons and heavy species have the same temperature, and the plasma can be characterized by a single temperature. To model plasmas in such conditions, the Plasma Module offers several Equilibrium Discharges interfaces that couple electromagnetics, fluid flow, and heat transfer, incorporating Lorentz force, electromotive force, enthalpy transport, Joule heating, and radiation loss. Multiphysics Interface for Modeling Microwave Plasmas The Microwave Plasma multiphysics interface is used to study discharges that are sustained by electromagnetic waves (wave-heated discharge). When this interface is selected, a Plasma interface and an Electromagnetic Waves interface are automatically generated, as well as multiphysics couplings. The Plasma Conductivity Coupling feature couples the plasma conductivity to the Electromagnetic Waves interface, and the Electron Heat Source feature couples the resulting electron heating back to the Plasma interface. The electromagnetic waves are solved for in the frequency domain and the plasma is solved for in the time domain. Boundary Conditions for Plasma–Surface Interactions As a part of the built-in interfaces within the Plasma Module, there are a variety of boundary conditions to describe how a plasma interacts with a surface. For example, electron density and energy fluxes at a surface are easily defined by applying the Wall feature. This feature introduces losses by transport to the electron transport equations. Additional flux sources can be included, such as secondary electron emission and generic electron fluxes at a surface. Fluxes of charged particles are automatically computed at electrodes and can be added to model external circuits. If a dielectric is in contact with the plasma, the surface charge accumulation can be computed from the fluxes of charged species at the surface. Surface Chemistry Reactions The Plasma Module includes a range of functionality for modeling etching and deposition processes in semiconductor fabrication processes. It solves plasma transport equations fully coupled with surface reaction kinetics, enabling the dynamic exchange of species between the surface and the gas phase. Surface site occupancy models can be used to accurately capture self-limiting reaction mechanisms. Furthermore, surface reaction rates can be specified with energy-dependent reaction yield models, facilitating detailed simulation of mechanisms such as ion-enhanced etching and energy-selective surface modifications. Multiphysics Interfaces for Modeling ICP Reactors with RF Bias The Inductively Coupled Plasma with RF Bias interface is used to study discharges that are sustained by induction currents and by an RF bias. This multiphysics interface connects the plasma conductivity from the Plasma, Time Periodic interface to the Magnetic Fields interface and couples the electron heating resulting from the induction currents back to the Plasma, Time Periodic interface. The magnetic field is solved for in the frequency domain and the plasma is solved for in the time domain. Multiphysics Interfaces for Modeling Fluid Flow and Heat Transfer of Background Gases The Nonisothermal Plasma Flow interfaces combine plasma, fluid flow, and heat transfer interfaces to model background gas flow and heating in a plasma reactor. The heat transfer in the materials surrounding a plasma can also be simulated. The Nonisothermal Plasma Flow multiphysics feature automatically computes the heat source resulting from plasma reactions and inputs it into heat transfer interfaces as a volume heat source. Fluid and thermodynamic properties like viscosity and thermal conductivity are computed in the Plasma interface and passed automatically to fluid flow and heat transfer interfaces. Physics Interface for Modeling CCP Reactors The Plasma Module includes a specialized numerical method for modeling CCP with significantly faster computation times than traditional methods. Instead of solving in the time domain, the periodic steady-state solution is computed by adding an extra dimension to the underlying mathematical equations. This extra dimensional equation represents one RF cycle and enforces periodic boundary conditions. This avoids having to solve for tens or hundreds of thousands of RF cycles, which typically takes a long time before the plasma reaches the periodic steady-state solution. This approach maintains all the nonlinearity of the model while dramatically reducing computation time.
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LiveLink™ for MATLAB® provides the necessary tools for maximizing the use of COMSOL Multiphysics® and MATLAB® in combination. Run Multiphysics Simulations from MATLAB® LiveLink™ for MATLAB® provides commands in the MATLAB® scripting language, sent from MATLAB® to COMSOL Multiphysics®, that initiate simulations in COMSOL Multiphysics®. This can be used for automating modeling steps as well as integrating COMSOL Multiphysics® models with calculations performed in MATLAB®. LiveLink™ for MATLAB® uses the COMSOL application programming interface (API), which has all the necessary functions and methods for implementing models from scratch or updating settings in existing models. All aspects of COMSOL Multiphysics® modeling can be controlled using MATLAB® through the API, which is tightly integrated with the MATLAB® environment. LiveLink™ for MATLAB® enables users to perform geometry and mesh operations, change physics settings, run parametric studies, control solvers, and postprocess the results. Results can be extracted as numerical data and MATLAB® figures. Utility Tools for Managing Models from MATLAB® All COMSOL® model settings are available from the command line in MATLAB®. To help get acquainted with the model data structure and the model settings, LiveLink™ for MATLAB® comes with two utility tools for navigating and searching the model contents: the Model Navigator and Model Search tools. The Model Navigator provides an overview of the model structure in a model tree together with the model settings and the commands that can be executed for each part of the model. Using this tool, it is easy to extract commands for setting and finding model properties to use in custom scripts. The Model Search tool will search the COMSOL Multiphysics® model from the MATLAB® interface, helping to find expressions and variables used in a model. Several filters and search settings are provided to narrow the search. Furthermore, a model from MATLAB® and the COMSOL Desktop® can be accessed simultaneously. This way, the workflow that is best suited for the task at hand can be used. It may be preferable to perform some tasks using the command line and scripting, while other tasks may be more convenient to perform using the COMSOL Multiphysics® user interface. Manage and Create Geometry Models and Meshes from MATLAB® Running COMSOL Multiphysics® from MATLAB® provides a lot of flexibility when handling geometry models and meshes. From MATLAB® programs and the MATLAB® command-line interface, it is possible to: - Generate geometry objects with inputs from MATLAB® - Import and export CAD models in a range of industry-leading file formats 1 - Run simulations based on imported CAD models - Create, import, and export surfaces on the STL, 3MF, and PLY file formats - Plot geometry objects in MATLAB® figures - Obtain geometry information for points, edges, surfaces, and domains, e.g., for adjacency, curvature, distances, etc. - Convert an image to a 2D geometry - Generate meshes - Plot meshes in MATLAB® figures - Retrieve mesh information such as mesh statistics and other mesh data - Import and export mesh data Call MATLAB® Functions from the COMSOL Desktop® LiveLink™ for MATLAB® provides a direct connection to MATLAB® while running COMSOL Multiphysics®. It is possible to call MATLAB® functions from the COMSOL Multiphysics® user interface to define material properties, boundary conditions, and more. These MATLAB® functions can be evaluated while the model is solving. Additionally, a COMSOL simulation app can contain MATLAB® calls, in which case MATLAB® will automatically start when called during runtime. Integrate with Existing MATLAB® Programs For MATLAB® users, COMSOL Multiphysics® simulations can easily be integrated into existing code bases. A model that has been set up in the COMSOL Multiphysics® user interface can be saved to an M-file. This M-file then contains COMSOL® API calls, in MATLAB® syntax, for running COMSOL Multiphysics® functionality. This provides a quick and convenient way of automatically generating COMSOL® modeling code, which can be used as a starting point for further integration into MATLAB® programs. Using the automatic code generation tools provides a quick way to learn the COMSOL® API for MATLAB®, which is included in LiveLink™ for MATLAB®. The COMSOL® API is easy to learn and has an intuitive structure similar to the steps used when setting up models in the COMSOL Multiphysics® user interface using the Model Builder. Existing code that is based on MATLAB® toolboxes or custom code integrates easily with COMSOL Multiphysics® simulations. Users can even call COMSOL Multiphysics® from user interfaces that have been created using MATLAB®. This makes it possible to, for example, use MATLAB® for data preparation and postprocessing and COMSOL Multiphysics® for structural, fluid, electromagnetics, or other physics or multiphysics modeling. Simulations can then be carried out using a mix of programs and models created with MATLAB®, COMSOL Multiphysics®, and even other tools. Generate Plots in MATLAB® and Extract Data from COMSOL Multiphysics® All COMSOL Multiphysics® plots can be recreated in MATLAB®. All plot types can be generated as regular MATLAB® plots and can be saved or exported and manipulated like any other MATLAB® plot. From MATLAB® programs, COMSOL Multiphysics® expressions can be evaluated either locally at a few points or for larger portions of a model, such as along the edges, on surfaces, or in volumes. Users can access the raw solution data or processed data based on arbitrary expressions, including maximum, minimum, average, and integral values. The COMSOL Multiphysics® unit handling is fully supported for any type of extracted data, which means that it is possible, for example, to use unit handling in custom programs for unit conversion. Any numerical data from COMSOL Multiphysics® simulations can be retrieved and assigned to MATLAB® variables for further analysis. Low-level information that is directly related to mesh and shape function data can be extracted, as well as sensitivities and time and spatial derivatives. 1. Requires one of the following add-on products: the CAD Import Module, the Design Module, LiveLink™ for SOLIDWORKS®, LiveLink™ for Inventor®, LiveLink™ for Solid Edge®, LiveLink™ for AutoCAD®, or LiveLink™ for Revit®
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