Introduction to COMSOL Multiphysics

Siófok, Hungary, March, 2018 Henrik Ekström

General Outline • Introduction to COMSOL Multiphysics

– Microconnector Bump Demo • COMSOL Simulations Lecture 1: Electroanalysis

– Cyclic Voltammetry Demo • COMSOL Hands-on Exercise 1

– Chronoamperometry (Cottrell Equation) • COMSOL Simulations Lecture 2 : Current Distribtions

– Wire Electrode Demo • COMSOL Hands-on Exercise 2

– Decorative Plating

About COMSOL • HQ in Stockholm • 22 offices • 500 employees • 20 000 licenses, 100 000 users

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Why Simulate? • Conception and understanding

– Enables innovation

• Design and optimization – Achieve the highest possible

performance

• Testing and verification – Virtual testing is much faster

than testing physical prototypes

Simulation of current density in a chlor-alkali cell, showing variation across the surfaces of each electrode.

Simulating with COMSOL Multiphysics® • Electrical, mechanical, fluid, and

chemical simulations

• Multiphysics – include and couple all relevant physical effects

• Single physics in one integrated environment

• Cross-disciplinary product development

Complete Simulation Environment

Model Builder Provides instant access to any part of the model settings • CAD/Geometry • Materials • Physics • Mesh • Solve • Results

Graphics

COMSOL Desktop® Straightforward to use, the Desktop gives insight and full control over the modeling process

Some Terms • Module

– Add-on to the license you buy – contains additional functionality such as Physics Interfaces, Solvers and Material Libraries • Physics Interface

– Taylor made user-interface for setting up equations (related to a specific physics field) • Application

– The file (xxx.mph) that contains your model tree, defined using: • Global definitions • Components (the actual model, with geometry, local defintitions, physics interfaces, and mesh) • Studies (the numerical solvers) • Results (post processing)

• Materials – For linking parameters used in physics interfaces to data from the Material Library

• Application Library – Library of solved tutorial and benchmark examples.

• App – A user-interface, wrapped around your Application, that you create yourself for sharing your work to less experienced modelers

Under the Hood • Most physics interfaces use the Finite Element Method (FEM) for discretizing and

solving the problems • Boundary Element and other formulations also available for certain physics • Finite Element formulations use an open weak-form syntax, visible (and hackable)

for the user • Various different solvers are available:

– Stationary, Time-Dependend and Frequency Domain – Fully Coupled vs Segragated approaches for coupled probles – Iterative (Multigrid) or Direct – Parametric Sweeps – Adaptive Mesh Refinement – Cluster computing

COMSOL Multiphysics®

The COMSOL Product Suite

Electrochemistry Products • batteries • fuel cells

• electroplating • other related surface processes

• corrosion analysis • corrosion prevention

• electrolysis • electrodialysis • electroanalysis

• All products rest on the same physics, but the user interfaces are tailored to the requirements of particular applications.

The Electrochemistry Interfaces • Current Distribution interfaces

– Generic electrochemical cell modeling – Nernst-Planck equations – Flat or porous electrodes – Arbitrary number of reactions – Double-layer effect

• Electroanalysis • Nernst-Planck-Poisson Equations • Battery Interfaces • Corrosion interfaces • Electrodeposition interfaces

The Battery Interfaces • Concentrated electrolyte theory used in all battery

interfaces (except Single Particle Battery) • Lithium-Ion Battery

– Charge balances in the electrodes and electrolyte – Material balances for the salt – Energy balance including electrochemical reactions – Material balance of intercalating species in electrode

particles – Solid electrolyte interface (SEI) on electrode particles

Settings for electrode reactions in the lithium-ion battery interface

The Battery Interfaces • Battery with Binary Electrolyte

– Similar to the Lithium-Ion Battery interface – Generic interface for batteries with concentrated binary

electrolytes • Lead-Acid Battery

– Porosity variation within electrodes coupled to electrode reactions and material balances

– Material balance for the salt in the electrolyte • Single Particle Battery

– Simplified generic battery interface – Each electrode is treated as a single ”particle” – For larger geometries, battery packs, or shorter

simulation times

Typical set of nodes of the Lead-Acid Battery interface for creating a model

The Batteries & Fuel Cells Material Library • Literature data for the most common electrode

and electrolyte materials: – Electrolyte conductivities – Equilibrium potentials – Diffusion coefficients – Activity coefficients – Transport numbers – Densities – Heat capacities*

*All listed properties not available for all listed materials

The Corrosion/Electrodeposition Interfaces • Dissolving/Depositing Electrode Species

– Keep track of reacted material per m2 of electrode surface in time-dependent simulations

• Predefined couplings to geometry deformations

Specifying the deposition of copper on an electrode surface in the user interface

Initial and corroded geometry due to galvanic corrosion of a magnesium alloy. Modeled using a deforming geometry (moving mesh/ale).

The Chemical Species Transport Interfaces • Transport of Diluted Species

– Diffusion, migration, and convection – Fick’s law/Nernst-Planck equations – Multiple species

• Transport of Diluted Species in Porous Media • Electrophoretic Transport • Nernst-Planck-Poisson Equations • Batteries & Fuel Cells:

– Transport of Concentrated Species • Maxwell-Stefan equations • Typically used for gas phase diffusion

– Reacting flow interfaces • Use Surface Reactions to model intermediate species on

electrode surfaces • Coupling features to electrochemistry

– Flat electrodes (molar fluxes) – Porous electrodes (molar sources/sinks)

Heat Transfer and Fluid Flow • Laminar flow • Porous media flow • Heat transfer

– Solids, fluids, and porous media • Coupling features

– Joule heating and heat from electrochemical reactions

– All Electrochemistry interfaces contain predefined heat source variables to be used for coupling to Heat Transfer interfaces

– Predefined mass sources and fluxes for coupling Electrochemistry to Fluid Flow

Demo: Microconnector Bump • Electrolyte flows over electrolyte

surface • Electrode covered by photoresist with

holes • Cell working at high overpotentials

and under diffusion control

• The goal is a well shaped, uniform bump

• What is the impact of the convective flow?

Model Details • Geometry

– 2D, includes hole in photoresist, and diffusion layer

• Mass transport – Transport of Diluted Species – Concentration set to 0 at electrode – Bulk concentration towards bulk electrolyte

• Momemtum transfer

– Laminar flow – Specified bulk velocity

Current Distribution Results

Extension to 3D • Add a Deforming 3D Geometry

• Add Potential Equation in Electrolyte

• Use Potential and Concentration

Dependent Electrode Kinetics

• Switch to a Time-dependent Solver