The gravity-driven flow of Herschel-Bulkley fluids in a syringe and the transition to dripping
Abstract
Many food, cosmetic, and pharmaceutical products exhibit yield stress, which conditions their flow. In this study, experiments and simulations were combined to provide a quantitative understanding of the effect of the rheological properties of Herschel-Bulkley fluids on the gravity-driven flow in a syringe. Such a flow is key for drip feeding and intravenous drug administration. It is also used worldwide to assess the "consistency" of drinks and their safety for people with swallowing disorders, according to IDDSI (International Dysphagia Diet Standardisation Initiative). The transition between jetting and dripping regimes is discussed, and an expression is proposed for the critical Weber number below which dripping occurs, considering its dependence on the Bond, Ohnesorge numbers and on the flow index. Rheological maps are proposed to quantitatively describe the interplay between rheological properties on the flow and the volume left after 10s, which conditions the IDDSI consistency classification. The analysis shows the dominant role of viscous dissipation for fluids classified as IDDSI levels 2 and 3, in contrast to the more pronounced influence of the Herschel-Bulkley yield stress on the flow for less viscous fluids (level 1 consistency). Finally, a dimensionless Hydrostatic-Yield time (HY) is proposed, which allows explaining all experimental and simulation flow results using a single master curve. These findings provide new insights into gravity-driven flow in a syringe, and into the jetting-to-dripping transition. They could contribute to improving the formulation and safety of beverages for people with swallowing disorders, as well as improving popular protorheology methods, such as the syringe flow test.
Related
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BibTeX
@misc{lecanu2026gravitydriven,
title = {{The gravity-driven flow of Herschel-Bulkley fluids in a syringe and the transition to dripping}},
author = {Rémi Lecanu and Kaixin Xu and Guy Della Valle and Cassandre Leverrier and Adrien Izzet and Marco Ramaioli},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.inrae.fr/hal-05753500v1},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The gravity-driven flow of Herschel-Bulkley fluids in a syringe and the transition to dripping
AU - Rémi Lecanu
AU - Kaixin Xu
AU - Guy Della Valle
AU - Cassandre Leverrier
AU - Adrien Izzet
AU - Marco Ramaioli
PY - 2026
DA - 2026/09/17
PB - HAL
UR - https://hal.inrae.fr/hal-05753500v1
AB - Many food, cosmetic, and pharmaceutical products exhibit yield stress, which conditions their flow. In this study, experiments and simulations were combined to provide a quantitative understanding of the effect of the rheological properties of Herschel-Bulkley fluids on the gravity-driven flow in a syringe. Such a flow is key for drip feeding and intravenous drug administration. It is also used worldwide to assess the "consistency" of drinks and their safety for people with swallowing disorders, according to IDDSI (International Dysphagia Diet Standardisation Initiative). The transition between jetting and dripping regimes is discussed, and an expression is proposed for the critical Weber number below which dripping occurs, considering its dependence on the Bond, Ohnesorge numbers and on the flow index. Rheological maps are proposed to quantitatively describe the interplay between rheological properties on the flow and the volume left after 10s, which conditions the IDDSI consistency classification. The analysis shows the dominant role of viscous dissipation for fluids classified as IDDSI levels 2 and 3, in contrast to the more pronounced influence of the Herschel-Bulkley yield stress on the flow for less viscous fluids (level 1 consistency). Finally, a dimensionless Hydrostatic-Yield time (HY) is proposed, which allows explaining all experimental and simulation flow results using a single master curve. These findings provide new insights into gravity-driven flow in a syringe, and into the jetting-to-dripping transition. They could contribute to improving the formulation and safety of beverages for people with swallowing disorders, as well as improving popular protorheology methods, such as the syringe flow test.
ER -