A reduced model for droplet dynamics with interfacial viscosity
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910010390347776 |
|---|---|
| author | Guglietta, Fabio Taglienti, Diego Sbragaglia, Mauro |
| author_facet | Guglietta, Fabio Taglienti, Diego Sbragaglia, Mauro |
| contents | We propose an extension of the phenomenological Maffettone-Minale (MM) model (P.L. Maffettone and M. Minale, J. Non-Newton. Fluid Mech. 78, 227-241 (1998)) to describe the time-dependent deformation of a droplet with interfacial viscosity in a shear flow. The droplet, characterised by surface tension $σ$, is spherical at rest with radius $R$ and deforms into an ellipsoidal shape under a shear flow of rate $G$, described by a symmetric second-order morphological tensor $\boldsymbol{S}$. In addition to surface tension, the extended MM (EMM) model incorporates interfacial shear and dilatational viscosities, $μ_s$ and $μ_d$, through the corresponding Boussinesq numbers $\mbox{Bq}_s=μ_s/μR$ and $\mbox{Bq}_d=μ_d/μR$, where $μ$ is the bulk viscosity. A central goal of this work is to quantify the parameter range over which the EMM model provides a realistic description of droplet deformation, as a function of the capillary number Ca$=μR G/σ$ and the Boussinesq numbers. To this end, model predictions are systematically compared with fully resolved numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15616 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A reduced model for droplet dynamics with interfacial viscosity Guglietta, Fabio Taglienti, Diego Sbragaglia, Mauro Fluid Dynamics Soft Condensed Matter We propose an extension of the phenomenological Maffettone-Minale (MM) model (P.L. Maffettone and M. Minale, J. Non-Newton. Fluid Mech. 78, 227-241 (1998)) to describe the time-dependent deformation of a droplet with interfacial viscosity in a shear flow. The droplet, characterised by surface tension $σ$, is spherical at rest with radius $R$ and deforms into an ellipsoidal shape under a shear flow of rate $G$, described by a symmetric second-order morphological tensor $\boldsymbol{S}$. In addition to surface tension, the extended MM (EMM) model incorporates interfacial shear and dilatational viscosities, $μ_s$ and $μ_d$, through the corresponding Boussinesq numbers $\mbox{Bq}_s=μ_s/μR$ and $\mbox{Bq}_d=μ_d/μR$, where $μ$ is the bulk viscosity. A central goal of this work is to quantify the parameter range over which the EMM model provides a realistic description of droplet deformation, as a function of the capillary number Ca$=μR G/σ$ and the Boussinesq numbers. To this end, model predictions are systematically compared with fully resolved numerical simulations. |
| title | A reduced model for droplet dynamics with interfacial viscosity |
| topic | Fluid Dynamics Soft Condensed Matter |
| url | https://arxiv.org/abs/2512.15616 |