Diffuse approximation for identification of the mechanical properties of microcapsules

Abstract

A novel data-driven real-time procedure based on diffuse approximation is proposed to characterize the mechanical behavior of liquid-core microcapsules from their deformed shape and identify the mechanical properties of the submicron-thick membrane that protects the inner core through inverse analysis. The method first involves experimentally acquiring the deformed shape that a given microcapsule takes at steady state when it flows through a microfluidic microchannel of comparable cross-sectional size. From the mid-plane capsule profile, we deduce two characteristic geometric quantities that uniquely characterize the shape taken by the microcapsule under external hydrodynamic stresses. To identify the values of the unknown rigidity of the membrane and of the size of the capsule, we compare the geometric quantities with the values predicted numerically using a fluid-structure-interaction model by solving the three-dimensional capsule-flow interactions. The complete numerical data set is obtained off-line by systematically varying the governing parameters of the problem, i.e. the capsule-to-tube confinement ratio, and the capillary number, which is the ratio of the viscous to elastic forces. We show that diffuse approximation efficiently estimates the unknown mechanical resistance of the capsule membrane. We validate the data-driven procedure by applying it to the geometric and mechanical characterization of ovalbumin microcapsules (diameter of the order of a few tens of microns). As soon as the capsule is sufficiently deformed to exhibit a parachute shape at the rear, the capsule size and surface shear modulus are determined with an accuracy of 0.2% and 2.7%, respectively, as compared with 2–3% and 25% without it, in the best cases (Hu et al. Characterizing the membrane properties of capsules flowing in a square-section microfluidic channel: Effects of the membrane constitutive law. Phys Rev E 2013; 87(6): 063008). Diffuse approximation thus allows the capsule size and membrane elastic resistance to be provided quasi-instantly with very high precision. This opens interesting perspectives for industrial applications that require tight control of the capsule mechanical properties in order to secure their behavior when they transport active material.

Mechanical characterization of core-shell microcapsules

“…The mechanical properties of the microcapsule are obtained by using an inverse analysis method, a technique developed by the BMBI group [63,91,92]. The basic idea is to compare the profiles of deformed capsules from the numerical model and the experimental measurement.…”

A microfluidic methodology to identify the mechanical properties of capsules: comparison with a microrheometric approach

“…The inverse analysis strategy consists of identifying the mechanical properties from the experimental deformed profiles using the data-driven automatic procedure of Quesada et al (2020). The databases contain the predicted steady-state values of 𝐿 𝑧 and 𝐿 𝑝 as functions of parameters 𝐶𝑎 𝑠 and 𝑎/𝑙 for the different constitutive laws (NH, GH 𝜈 𝑠 = 0.5, 0.2, 0) corresponding to figures 3 and 5.…”

“…The velocity and deformed profile of each capsule are then compared with the corresponding quantities computed by a full numerical model of the capsule in flow: this inverse analysis yields a value of the shear elastic modulus of the enclosing wall (Chu et al, 2011;Gubspun et al, 2016;Hu, Sévénié, Salsac, Leclerc, & Barthès-Biesel, 2013;Lefebvre, Leclerc, Barthès-Biesel, Walter, & Edwards-Lévy, 2008). The advantage of the technique is that it is straightforward, can be automated (Quesada, Dupont, Villon, & Salsac, 2020) and may thus yield statistical results for a population. However, up to now, the modulus values thus obtained have mostly been used in a relative sense to analyse the effect of a specific parameter (membrane polymerization conditions, capsules size) on the mechanical properties of a given capsule population.…”

A Data-Driven Space-Time-Parameter Reduced-Order Model with Manifold Learning for Coupled Problems: Application to Deformable Capsules Flowing in Microchannels

“…Unfortunately, Lagrange polynomial interpolation is not suitable for parameter spaces of arbitrary dimension because of the curse of dimensionality and because it may suffer from instability issues (Runge phenomenon). Rather than using polynomial interpolation, we propose to use a Diffuse Approximation (DA) technique [ 18 , 29 ] which is an approximation method based on local low-order polynomial reconstruction (of order one or two) using a compactly-supported kernel function and weighted least squares. The DA method is known to be a robust and reliable approach which is less sensitive to the location of the sampling points.…”

“…They are composed of an elastic membrane protecting a liquid inner core and are used in suspension in another liquid. Testing them in microfluidic environments offers great potential to determine the capsule behavior and characterize the mechanical properties of the membrane [ 23 , 24 , 25 , 26 , 27 , 28 , 29 ], but also for sorting or enrichment of capsule suspensions [ 30 , 31 , 32 , 33 , 34 ]. We presently focus on the flow of a dilute suspension of initially spherical micrometric capsules in a microfluidic channel, which is a complex three-dimensional inertialess fluid-structure interaction problem that interestingly depends on only two independent design variables: the capillary number of the capsule , which is a non-dimensional number that estimates the order of magnitude of the viscous forces acting on the capsule with respect to the elastic forces that build up in the membrane, and the confinement ratio that provides a comparison between the initial capsule diameter and the channel width.…”