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Normal and oblique drop impact of yield stress fluids with thixotropic effects

Published online by Cambridge University Press:  06 August 2019

Cassio M. Oishi Open the ORCID record for Cassio M. Oishi [Opens in a new window] ,
Roney L. Thompson Open the ORCID record for Roney L. Thompson [Opens in a new window]  and
Fernando P. Martins Open the ORCID record for Fernando P. Martins [Opens in a new window]
Cassio M. Oishi
Affiliation:
Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista ‘Júlio de Mesquita Filho’, 19060-900 Presidente Prudente, SP, Brazil
Roney L. Thompson*
Affiliation:
Department of Mechanical Engineering, COPPE, Universidade Federal do Rio de Janeiro, Centro de Técnologia, Ilha do Fundão, Rio de Janeiro, RJ 24210-240, Brazil
Fernando P. Martins
Affiliation:
Departamento de Matemática e Computação, Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista ‘Júlio de Mesquita Filho’, 19060-900 Presidente Prudente, SP, Brazil
*
†Email address for correspondence: [email protected]
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Abstract

Normal and oblique drop impact on a solid surface is numerically analysed for yield stress fluids. A rich diversity of results are generated as a consequence of the exploration of the inertial, elastic, plastic and thixotropic features of the process, as well as the inclination of the solid surface. We show that drops of more thixotropic fluids have a higher tendency to bounce in the normal impact, and to roll or to bounce in the case of an oblique drop impact. Concerning elasticity, we found a critical value for the elastic Ohnesorge number above which no bouncing takes place. Experimental findings such as the fact that the stored energy due to the elasticity of the fluid drop plays a role similar to the stored energy of an interfacial nature in inelastic fluid drops are corroborated in the present study.

JFM classification

Drops and Bubbles: Drops Non-Newtonian Flows: Non-Newtonian Flows Interfacial Flows (free surface): Interfacial Flows (free surface)
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 876 , 10 October 2019 , pp. 642 - 679
Copyright
© 2019 Cambridge University Press 

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Oishi et al. supplementary movie 1

Numerical prediction of the structure parameter $\lambda$ at different dimensionless times using $Re=2.05$, $\tau_y=0.7$. From (column) left to right: $t_{eq}=5, 20$, and from (row) top to bottom: $Wi=0.05, 2$. The reader will find, in the supplementary material, the file Movie1.mp4 with the movie of the evolution displayed in this figure.

Download Oishi et al. supplementary movie 1(Video)
Video 1.4 MB

Oishi et al. supplementary movie 2

Numerical predictions of the structural parameter $\lambda$ at different dimensionless times using $Re=13.49$, $\tau_y=0.7$ and $Wi=0.5$ or $2.0$. Columns from left to right: $t_{eq}=5, 20$. The reader will find in the supplementary material the movie with the complete evolution of the motions shown in this figure.

Download Oishi et al. supplementary movie 2(Video)
Video 1.5 MB

Oishi et al. supplementary movie 3

Drop interface profiles for a surface at an inclination of $\theta=30 \degree$. The fixed non-dimensional parameter for the EVPT material is $Wi=0.05$; The thixotropic times shown are $t_{eq}=1, 5, 20$

Download Oishi et al. supplementary movie 3(Video)
Video 6.3 MB

Oishi et al. supplementary movie 4

Drop interface profiles for a surface at an inclination of $\theta=30 \degree$. The fixed non-dimensional parameter for the EVPT material is $Wi=2$; The times shown are $t_{eq}=1, 5, 20$. The drop interface profiles considering an Oldroyd-B fluid with $Wi=2$ for different $Re$ are also included

Download Oishi et al. supplementary movie 4(Video)
Video 10 MB

Oishi et al. supplementary movie 5

Numerical prediction of the structural parameter $\lambda$ at different dimensionless times using $Re=13.49$, $\tau_y=0.7$, $t_{eq}=5,$ and $Wi=0.5$ for a surface at an inclination of $\theta=30 \degree$. The reader will find, in the supplementary material, the file Movie5.mp4 with the movie of the complete evolution of the case shown in this figure.

Download Oishi et al. supplementary movie 5(Video)
Video 975 KB

Oishi et al. supplementary movie 6

Numerical prediction of the structural parameter $\lambda$ at different dimensionless times using $Re=13.49$, $\tau_y=0.3$, $t_{eq}=20,$ and $Wi=0.5$ for a surface at an inclination of $\theta=30 \degree$. The reader will find, in the supplementary material, the file Movie6.mp4 with the movie of the complete evolution of the case shown in this figure.

Download Oishi et al. supplementary movie 6(Video)
Video 1.4 MB

Oishi et al. supplementary movie 7

Set of evolutions with plastic number and dimensionless thixotropic time fixed. In the left column, $\tau_y=0.1$ and $t_{eq}=5$. In the right column, $\tau_y=0.7$ and $t_{eq}=20$. Normal impact, Re=2.05, Wi=0.05.

Download Oishi et al. supplementary movie 7(Video)
Video 2 MB

Oishi et al. supplementary movie 8

Set of evolutions with plastic number and dimensionless thixotropic time fixed. In the left column, $\tau_y=0.1$ and $t_{eq}=5$. In the right column, $\tau_y=0.7$ and $t_{eq}=20$. Normal impact, Re=2.05, Wi=2.00.

Download Oishi et al. supplementary movie 8(Video)
Video 1.4 MB

Oishi et al. supplementary movie 9

Set of evolutions with plastic number and dimensionless thixotropic time fixed. In the left column, $\tau_y=0.1$ and $t_{eq}=5$. In the right column, $\tau_y=0.7$ and $t_{eq}=20$. Normal impact, Re=13.49, Wi=0.05.

Download Oishi et al. supplementary movie 9(Video)
Video 950.1 KB

Oishi et al. supplementary movie 10

Set of evolutions with plastic number and dimensionless thixotropic time fixed. In the left column, $\tau_y=0.1$ and $t_{eq}=5$. In the right column, $\tau_y=0.7$ and $t_{eq}=20$.Normal impact, Re=13.49, Wi=2.00.

Download Oishi et al. supplementary movie 10(Video)
Video 1.7 MB

Oishi et al. supplementary movie 11

Set of evolutions with plastic number and dimensionless thixotropic time fixed. In the left column, $\tau_y=0.1$ and $t_{eq}=5$. In the right column, $\tau_y=0.7$ and $t_{eq}=20$. Inclined plane, $30^0$, Re=2.05, Wi=0.05.

Download Oishi et al. supplementary movie 11(Video)
Video 1.2 MB

Oishi et al. supplementary movie 12

Set of evolutions with plastic number and dimensionless thixotropic time fixed. In the left column, $\tau_y=0.1$ and $t_{eq}=5$. In the right column, $\tau_y=0.7$ and $t_{eq}=20$. Inclined plane, $30^0$, Re=2.05, Wi=2.00.

Download Oishi et al. supplementary movie 12(Video)
Video 1.4 MB

Oishi et al. supplementary movie 13

Set of evolutions with plastic number and dimensionless thixotropic time fixed. In the left column, $\tau_y=0.1$ and $t_{eq}=5$. In the right column, $\tau_y=0.7$ and $t_{eq}=20$. Inclined plane, $30^0$, Re=13.49, Wi=0.05.

Download Oishi et al. supplementary movie 13(Video)
Video 746.1 KB

Oishi et al. supplementary movie 14

Set of evolutions with plastic number and dimensionless thixotropic time fixed. In the left column, $ au_y=0.1$ and $t_{eq}=5$. In the right column, $ au_y=0.7$ and $t_{eq}=20$. Inclined plane, $30^0$, Re=13.49, Wi=2.00.

Download Oishi et al. supplementary movie 14(Video)
Video 1.3 MB

Oishi et al. supplementary movie 15

Set of evolutions with Weissenberg and dimensionless thixotropic time fixed. In the top left position, $Wi=0.05$ and $t_{eq}=5$. In the top right position, $Wi=0.05$ and $t_{eq}=20$. In the bottom left position, $Wi=2.00$ and $t_{eq}=5$. In the top right position, $Wi=2.00$ and $t_{eq}=20$. Normal impact, Re=2.05, $\tau_y$=0.1.

Download Oishi et al. supplementary movie 15(Video)
Video 1.7 MB

Oishi et al. supplementary movie 16

Set of evolutions with Weissenberg and dimensionless thixotropic time fixed. In the top left position, $Wi=0.05$ and $t_{eq}=5$. In the top right position, $Wi=0.05$ and $t_{eq}=20$. In the bottom left position, $Wi=2.00$ and $t_{eq}=5$. In the top right position, $Wi=2.00$ and $t_{eq}=20$. Normal impact, Re=2.05, \tau_y=0.7.

Download Oishi et al. supplementary movie 16(Video)
Video 1.4 MB

Oishi et al. supplementary movie 17

Set of evolutions with Weissenberg and dimensionless thixotropic time fixed. In the top left position, $Wi=0.05$ and $t_{eq}=5$. In the top right position, $Wi=0.05$ and $t_{eq}=20$. In the bottom left position, $Wi=2.00$ and $t_{eq}=5$. In the top right position, $Wi=2.00$ and $t_{eq}=20$. Normal impact, Re=13.49, \tau_y=0.1.

Download Oishi et al. supplementary movie 17(Video)
Video 1.4 MB

Oishi et al. supplementary movie 18

Set of evolutions with Weissenberg and dimensionless thixotropic time fixed. In the top left position, $Wi=0.05$ and $t_{eq}=5$. In the top right position, $Wi=0.05$ and $t_{eq}=20$. In the bottom left position, $Wi=2.00$ and $t_{eq}=5$. In the top right position, $Wi=2.00$ and $t_{eq}=20$. Normal impact, Re=13.49, \tau_y=0.7.

Download Oishi et al. supplementary movie 18(Video)
Video 1.3 MB

Oishi et al. supplementary movie 19

Set of evolutions with Weissenberg and dimensionless thixotropic time fixed. In the top left position, $Wi=0.05$ and $t_{eq}=5$. In the top right position, $Wi=0.05$ and $t_{eq}=20$. In the bottom left position, $Wi=2.00$ and $t_{eq}=5$. In the top right position, $Wi=2.00$ and $t_{eq}=20$. Inclined plane, $30^0$, Re=2.05, \tau_y=0.1.

Download Oishi et al. supplementary movie 19(Video)
Video 1.5 MB

Oishi et al. supplementary movie 20

Set of evolutions with Weissenberg and dimensionless thixotropic time fixed. In the top left position, $Wi=0.05$ and $t_{eq}=5$. In the top right position, $Wi=0.05$ and $t_{eq}=20$. In the bottom left position, $Wi=2.00$ and $t_{eq}=5$. In the top right position, $Wi=2.00$ and $t_{eq}=20$. Inclined plane, $30^0$, Re=2.05, \tau_y=0.7.

Download Oishi et al. supplementary movie 20(Video)
Video 1.8 MB

Oishi et al. supplementary movie 21

Set of evolutions with Weissenberg and dimensionless thixotropic time fixed. In the top left position, $Wi=0.05$ and $t_{eq}=5$. In the top right position, $Wi=0.05$ and $t_{eq}=20$. In the bottom left position, $Wi=2.00$ and $t_{eq}=5$. In the top right position, $Wi=2.00$ and $t_{eq}=20$. Inclined plane, $30^0$, Re=13.49, \tau_y=0.1.

Download Oishi et al. supplementary movie 21(Video)
Video 867.6 KB

Oishi et al. supplementary movie 22

Set of evolutions with Weissenberg and dimensionless thixotropic time fixed. In the top left position, $Wi=0.05$ and $t_{eq}=5$. In the top right position, $Wi=0.05$ and $t_{eq}=20$. In the bottom left position, $Wi=2.00$ and $t_{eq}=5$. In the top right position, $Wi=2.00$ and $t_{eq}=20$. Inclined plane, $30^0$, Re=13.49, \tau_y=0.7.

Download Oishi et al. supplementary movie 22(Video)
Video 1.1 MB