# Microrheometric study of damage and rupture of capsules in simple shear flow

Chaymae El Mertahi, Nicolas Grandmaison, Claire Dupont, Rachid Jellali, Anne-Virginie Salsac, Delphine Brancherie

<figure><img src="image_1.png" /></figure>

## To cite this version:

Chaymae El Mertahi, Nicolas Grandmaison, Claire Dupont, Rachid Jellali, Anne-Virginie Salsac, et al.. Microrheometric study of damage and rupture of capsules in simple shear flow. Multidisciplinary Biomechanics Journal, 2025, 49th congress of the Société de Biomécanique, 10.46298/mbj.14496. hal-04737973v2

HAL Id: hal-04737973

https://hal.science/hal-04737973v2

Submitted on 31 Jan 2025

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

<figure><img src="image_2.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
# Microrheometric study of damage and rupture of capsules in simple shear flow

Chaymae El Mertahiª, Nicolas Grandmaisonª, Claire Dupontª, Rachid Jellaliª, Anne-Virginie Salsacª*, Delphine Brancherieᵇ

a Université de Technologie de Compiègne, CNRS, Biomechanics and Bioengineering, 60203 Compiègne, France

b Université de Technologie de Compiègne, Roberval, 60203 Compiègne, France

* Corresponding author: anne-virginie.salsac@utc.fr

Received date: 05/04/2024

Accepted date: 28/06/2024

Publication date: 31/01/2025

**Keywords:** microcapsules, microrheometry, damage, rupture

© 2025 The Authors

Licence CC-BY 4.0

Published by Société de Biomécanique

## 1. Introduction

Microcapsules are fluid droplets surrounded by a thin elastic membrane, used in industry to protect and transport active substances, aromas, cells.... When subjected to an external flow, they undergo strong deformations, which can potentially lead to their breakup. Depending on the application, the rupture is to be avoided to preserve the internal content or promoted to allow the release of the internal substance. To control this release, it is crucial to understand the mechanisms of damage and rupture.

Since the 1990's, capsule membrane properties have been studied until breakup, subjecting the particles to various flow conditions: simple shear flow (Chang and Olbricht 1993), hyperbolic flow (Xie et al. 2017), spinning flow (Husmann et al. 2005), tube flow (Wang et al. 2021)..... However, few studies have provided a comprehensive set of experimental data on rupture or has investigated the underlying damage phenomena leading to breakup. To overcome the lack of experimental data in the literature, we have conducted a microrheometric study of microcapsules, subjecting them to simple shear flow conditions leading to their damage and rupture.

## 2. Methods

### 2.1 Suspension preparation for microrheometric tests

2% (w/v) ovalbumin capsules are prepared using an interfacial cross-linking technique (Edwards-Lévy et al. 1993).

This method yields spherical, deformable capsules with radii spanning from a few microns to a few hundreds of microns. To prevent osmotic stress due to concentration differences between internal and external fluids, capsules are suspended in a glycerol solution that contains 3% (w/v) ovalbumin.

### 2.2 Microrheometry

Our study of capsule motion is conducted in a Couette flow, produced within a counter-rotating micro-rheometer (Wang et al. 2021). A volume of 10 ml of capsule-in-glycerol suspension is introduced into the 1 mm-gap between the cylinders and sheared varying two parameters: the shear rate $\dot{\gamma}$ and the exposure time $t_E$ during which capsules are subjected to shear. The profile of deformed capsules is captured from below using a 45° mirror placed under the inter-cylinder gap. The characteristic lengths are then determined by fitting the profiles to an ellipse with ImageJ, giving the semi-major axis $L_1$ and the semi-minor axis $L_2$ of the capsule.

### 2.3 Identification of the membrane elasticity and its evolution

To determine the elastic properties of the capsule membrane, we use the numerical results from Wang et al. (2021), linking the capsule deformation in the shear plane ($D_{12} = \frac{L_1 - L_2}{L_1 + L_2}$) to the elastic capillary number $Ca$ (ratio of the viscous to elastic forces) and to $L_3$ (the semi-axis length of the capsule in the direction perpendicular to the shear plane, normalized by the initial radius of the capsule $a$). From the numerical curves obtained
with the neo-Hookean law, we determine the values
of *Ca* and *L*₃. We can then deduce the values of the
initial capsule radius *a* = √*L*₁*L*₂*L*₃ from volume conser-
vation and of the surface shear modulus *G*�s = *μ*γ*a*/*Ca* from
the capillary number definition, where *μ* is the average
viscosity observed during the experiment, derived from
rheometer measurements taken at each time point. The
viscosity varies across experiments due to its sensitivity
to temperature changes.

## 2.4 Experimental characterization of capsule rupture

In this study, we assume that the distribution of capsules
in glycerol is homogeneous and that the occurrence of
rupture directly impacts the number of capsules present
in the solution. To characterize the capsule rupture, we
thus observe 10 µl of the capsule-in-glycerol suspension
under an optical microscope before exposure to shear
and we manually count the number and measure the
size of capsules present in the sample. The same pro-
cedure is applied on 10-µl-samples taken after exposure
to shear. We vary the values of shear rate and expo-
sure time to shear tE, and determine the percentage of
ruptured capsules by comparing the capsule number
before (Nbefore) and after (Nafter) shearing.

**3. Results and discussion**

**3.1 Capsule damage**

We explore damage by examining the time evolution
of capsule surface shear modulus *G*<sub>s</sub> in flow. Our study
demonstrates that when *t*<sub>E</sub> exceeds 2 minutes, a nota-
ble decrease in surface shear modulus occurs. This
underlines the significant role of hydrodynamic forces
in causing capsule damage.

**3.2 Capsule rupture**

In this study, we investigate the influence of various
parameters on rupture dynamics, particularly focusing
on capsule size and capillary number. We find a clear
correlation between capsule size and rupture kinetics,
noting that larger capsules tend to rupture more rapidly.
Additionally, our analysis shows that as the capillary
number increases, the percentage of ruptured capsules
(ΔN = (Nbefore - Nafter) / Nbefore) also rises. This observation can be
attributed to the dominance of viscous forces over the
capsule's elastic resistance at higher capillary numbers,
increasing the probability of rupture.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Evolution of the percentage of ruptured capsules as a function of the capillary number and exposure time to shear.</figcaption></figure>

Furthermore, we examine how exposure time *t*<sub>E</sub> affects rupture behavior. Our analysis shows that as exposure time increases, the capillary number needed for rupture decreases (Figure 1). This phenomenon is attributed to the progressive accumulation of residual stresses within the capsule over time due to prolonged exposure to shear forces. These accumulated stresses weaken the capsule's membrane, reducing the limit stress required for rupture.

**4. Conclusions**

During our study on capsule damage and rupture under
shear flow, we have made several significant obser-
vations. Firstly, we have noted a gradual decrease in
surface shear modulus over time, indicating decreased
mechanical integrity with prolonged shear exposure.
This underscores the importance of understanding
the evolving material properties under shear stress.
Moreover, we have found that rupture resistance is
influenced not only by the capillary number but also by
factors such as exposure time, shear rate, and capsule
size. Higher capillary numbers and shear rates have
resulted in faster rupture, while larger capsules have
tended to rupture earlier.

**Funding**

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. ERC-2017-COG - MultiphysMicroCaps).
**Conflict of Interest Statement**

The authors report no conflict of interest.

**References**

Chang, K-S., & Olbricht, W-L. (1993). Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow. *J. Fluid Mech.* 250, 609-633.

Xie, K., De Loubens, C., Dubreuil, F., Gunes, D-Z., Jaeger, M., & Leonetti, M. (2017). Interfacial rheological properties of self-assembling biopolymer microcapsules. *Soft Matter* 13, 6208-6217.

Husmann, M., Rehage, H., & Dhenin, E. (2005). Deformation and bursting of nonspherical polysiloxane microcapsules in a spinning-drop apparatus. *J. Colloid Interf. Sci.* 282, 109-119.

Wang, X-Y., Merlo, A., Dupont, C., Salsac, A-V., & Barthès-Biesel, D. (2021). A microfluidic methodology to identify the mechanical properties of capsules: comparison with a microrheometric approach. *Flow* 1, E8.

Edwards-Lévy, F., Andry, M-C., & Lévy, M-C. (1993). Determination of free amino group content of serum albumin microcapsules using trinitrobenzenesulfonic acid: effect of variations in polycondensation pH. *International Journal of Pharmaceutics*. 96, 85-90.