# Finite element simulations of viscoelastic flow of blade coating using the log-conformation tensor

## Abstract

Previous studies have demonstrated the benefits of the log-conformation formulation to model viscoelastic fluids; it increases stability at high Weissenberg numbers and ensures that the conformation tensor remains positive-definite. Many studies have applied the log-conformation tensor formulation to benchmark cases; however, relatively few studies investigate using the formulation on more complex flows. In this paper, we extend the log-conformation formulation to the manufacturing-relevant flow of blade coating. We first verify the log-conformation formulation on the benchmark problem of flow past a cylinder using the finite element method, and then apply it to the blade-coating process, in which a viscoelastic fluid entrained by a moving substrate passes under a blade at a constant web speed. We investigate various rheological effects and the resulting film thickness for the blade-coating problem, and compare the results from the log-conformation formulation to those of the original stress formulation. To this end, we show that the log-conformation formulation agrees well with other established methods, and also increases the maximum achievable web speed in the blade-coating problem.

- Authors:

- Univ. of New Mexico, Albuquerque, NM (United States).
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1498769

- Report Number(s):
- SAND2018-4957J

Journal ID: ISSN 0045-7930; 662963

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Computers and Fluids

- Additional Journal Information:
- Journal Volume: 180; Journal Issue: C; Journal ID: ISSN 0045-7930

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; 42 ENGINEERING; Viscoelastic fluids; Log-conformation formulation; Coating flows; Finite element method

### Citation Formats

```
Martin, Richard, Tjiptowidjojo, Kristianto, Ortiz, Weston, and Rao, Rekha. Finite element simulations of viscoelastic flow of blade coating using the log-conformation tensor. United States: N. p., 2018.
Web. doi:10.1016/j.compfluid.2018.12.001.
```

```
Martin, Richard, Tjiptowidjojo, Kristianto, Ortiz, Weston, & Rao, Rekha. Finite element simulations of viscoelastic flow of blade coating using the log-conformation tensor. United States. doi:10.1016/j.compfluid.2018.12.001.
```

```
Martin, Richard, Tjiptowidjojo, Kristianto, Ortiz, Weston, and Rao, Rekha. Mon .
"Finite element simulations of viscoelastic flow of blade coating using the log-conformation tensor". United States. doi:10.1016/j.compfluid.2018.12.001. https://www.osti.gov/servlets/purl/1498769.
```

```
@article{osti_1498769,
```

title = {Finite element simulations of viscoelastic flow of blade coating using the log-conformation tensor},

author = {Martin, Richard and Tjiptowidjojo, Kristianto and Ortiz, Weston and Rao, Rekha},

abstractNote = {Previous studies have demonstrated the benefits of the log-conformation formulation to model viscoelastic fluids; it increases stability at high Weissenberg numbers and ensures that the conformation tensor remains positive-definite. Many studies have applied the log-conformation tensor formulation to benchmark cases; however, relatively few studies investigate using the formulation on more complex flows. In this paper, we extend the log-conformation formulation to the manufacturing-relevant flow of blade coating. We first verify the log-conformation formulation on the benchmark problem of flow past a cylinder using the finite element method, and then apply it to the blade-coating process, in which a viscoelastic fluid entrained by a moving substrate passes under a blade at a constant web speed. We investigate various rheological effects and the resulting film thickness for the blade-coating problem, and compare the results from the log-conformation formulation to those of the original stress formulation. To this end, we show that the log-conformation formulation agrees well with other established methods, and also increases the maximum achievable web speed in the blade-coating problem.},

doi = {10.1016/j.compfluid.2018.12.001},

journal = {Computers and Fluids},

number = C,

volume = 180,

place = {United States},

year = {2018},

month = {12}

}