# Mathematical modelling of contact lens moulding

Ellen A. Murphy, William Lee

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

Compression moulded contact lenses are produced by placing fluid between two moulds and squeezing the fluid outwards to form the shape of the lens. A common problem seen in this process is that at times the fluid moves outwards asymmetrically, resulting in partially formed lenses. In this article, the system is modelled using the thin film equations and the results are analysed to find the optimal operating setup to reduce asymmetrical flow. A simple model with one curved surface and one flat surface is considered first. This assumption is verified by a more realistic model that investigates the effects of curvature on the dynamics of the fluid. The simple model is modified to include the effect of surface tension. The results of this model show that surface tension plays no role in the fluid dynamics for this particular fluid. A second modified model allows for lateral movement of the lower mould. The model shows that allowing the lower mould to slide hinders the symmetrical flow of the fluid.
Original language English 473-495 23 IMA Journal of Applied Mathematics 82 3 28 Mar 2017 https://doi.org/10.1093/imamat/hxw060 Published - 1 Jun 2017 Yes

### Fingerprint

Contact lenses
Molding
Mathematical Modeling
Lens
Contact
Fluid
Fluids
Surface Tension
Surface tension
Lenses
Model
Thin Film Equation
Curved Surface
Squeezing
Fluid Dynamics
Fluid dynamics
Lateral
Compaction
Compression
Curvature

### Cite this

title = "Mathematical modelling of contact lens moulding",
abstract = "Compression moulded contact lenses are produced by placing fluid between two moulds and squeezing the fluid outwards to form the shape of the lens. A common problem seen in this process is that at times the fluid moves outwards asymmetrically, resulting in partially formed lenses. In this article, the system is modelled using the thin film equations and the results are analysed to find the optimal operating setup to reduce asymmetrical flow. A simple model with one curved surface and one flat surface is considered first. This assumption is verified by a more realistic model that investigates the effects of curvature on the dynamics of the fluid. The simple model is modified to include the effect of surface tension. The results of this model show that surface tension plays no role in the fluid dynamics for this particular fluid. A second modified model allows for lateral movement of the lower mould. The model shows that allowing the lower mould to slide hinders the symmetrical flow of the fluid.",
author = "Murphy, {Ellen A.} and William Lee",
note = "This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record Murphy, Ellen A. and Lee, William (2017) Mathematical modelling of contact lens moulding. IMA Journal of Applied Mathematics, 82 (3). pp. 473-495, is available online at: https://doi.org/10.1093/imamat/hxw060.",
year = "2017",
month = "6",
day = "1",
doi = "10.1093/imamat/hxw060",
language = "English",
volume = "82",
pages = "473--495",
journal = "IMA Journal of Applied Mathematics",
issn = "0272-4960",
publisher = "Oxford University Press",
number = "3",

}

Mathematical modelling of contact lens moulding. / Murphy, Ellen A.; Lee, William.

In: IMA Journal of Applied Mathematics, Vol. 82, No. 3, 01.06.2017, p. 473-495.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Mathematical modelling of contact lens moulding

AU - Murphy, Ellen A.

AU - Lee, William

N1 - This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record Murphy, Ellen A. and Lee, William (2017) Mathematical modelling of contact lens moulding. IMA Journal of Applied Mathematics, 82 (3). pp. 473-495, is available online at: https://doi.org/10.1093/imamat/hxw060.

PY - 2017/6/1

Y1 - 2017/6/1

N2 - Compression moulded contact lenses are produced by placing fluid between two moulds and squeezing the fluid outwards to form the shape of the lens. A common problem seen in this process is that at times the fluid moves outwards asymmetrically, resulting in partially formed lenses. In this article, the system is modelled using the thin film equations and the results are analysed to find the optimal operating setup to reduce asymmetrical flow. A simple model with one curved surface and one flat surface is considered first. This assumption is verified by a more realistic model that investigates the effects of curvature on the dynamics of the fluid. The simple model is modified to include the effect of surface tension. The results of this model show that surface tension plays no role in the fluid dynamics for this particular fluid. A second modified model allows for lateral movement of the lower mould. The model shows that allowing the lower mould to slide hinders the symmetrical flow of the fluid.

AB - Compression moulded contact lenses are produced by placing fluid between two moulds and squeezing the fluid outwards to form the shape of the lens. A common problem seen in this process is that at times the fluid moves outwards asymmetrically, resulting in partially formed lenses. In this article, the system is modelled using the thin film equations and the results are analysed to find the optimal operating setup to reduce asymmetrical flow. A simple model with one curved surface and one flat surface is considered first. This assumption is verified by a more realistic model that investigates the effects of curvature on the dynamics of the fluid. The simple model is modified to include the effect of surface tension. The results of this model show that surface tension plays no role in the fluid dynamics for this particular fluid. A second modified model allows for lateral movement of the lower mould. The model shows that allowing the lower mould to slide hinders the symmetrical flow of the fluid.

U2 - 10.1093/imamat/hxw060

DO - 10.1093/imamat/hxw060

M3 - Article

VL - 82

SP - 473

EP - 495

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

SN - 0272-4960

IS - 3

ER -