Computationally Informed Design of a Multi-Axial Actuated Microfluidic Chip Device

Abstract

This paper describes the computationally informed design and experimental validation of a microfluidic chip device with multi-axial stretching capabilities. The device, based on PDMS soft-lithography, consisted of a thin porous membrane, mounted between two fluidic compartments, and tensioned via a set of vacuum-driven actuators. A finite element analysis solver implementing a set of different nonlinear elastic and hyperelastic material models was used to drive the design and optimization of chip geometry and to investigate the resulting deformation patterns under multi-axial loading. Computational results were cross-validated by experimental testing of prototypal devices featuring the in silico optimized geometry. The proposed methodology represents a suite of computationally handy simulation tools that might find application in the design and in silico mechanical characterization of a wide range of stretchable microfluidic devices.

Figure 1

Key structural elements of the MCD. (a) Planar view of three different shape configurations for the vacuum actuators (in blue). (b,c) Planar view (b) and three-dimensional sketch (c) of the MCD structure. From left to right, the porous membrane (PM), the vacuum chambers (VC), and the perfusion channels (PC) are highlighted in blue colour. Length scale in [μm].

Figure 2

Computational model. (a–c) Mesh element quality distribution over the entire MCD (a) and two progressive zoomed views of the culture chamber (b,c). Colour code refers to tetrahedral mesh quality (1 represents the highest quality). (d,e) Mesh distribution (d) and arrow plot of the displacement field (e) along the mid-planar section for the entire device. (f) Zoomed view on the displacement field on the PM (the equibiaxial loading case is highlighted by pressure arrows).

Figure 3

Results of numerical analysis. (a) Displacement field induced on the PM under uniaxial (left), equibiaxial (center) and biaxial 3:5 (right) loading patterns for a maximum pressure p = −500 mbar. White arrows indicate the local horizontal and vertical components of the displacement field. (b) Color map and isolevel contours of the first invariant of deformation for the corresponding loading patterns. A limited range of strain values is displayed for the three cases, i.e. [0.04 ÷ 0.1]. (c) Color map of the von Mises stress distribution for the three loading patterns. A limited range of stress levels ([0.5 ÷ 1] · 10⁵ Pa) is displayed.

Figure 4

MCD actuation. (a,b) Optical macrographs of the MCD prototype (a) and of the actuation setup (b). (c) 1:1 comparison between simulated (left half) and experimental (right half) displacement fields for the porous membrane (PM) under actuation at a vacuum level of – 500 mbar (scale bar: 200 μm). Arrows in color highlight displacement vectors for a set of markers at different distances (250, 500, 750 μm) from the center of the membrane.

Figure 5

Model validation under equibiaxial loading (negative pressure). (a–c) Displacement field components (horizontal and vertical, u, v, respectively) taken at r = 500 μm from the center of the PM for three representative points. ‘Exp’ refers to measured data as the mean of three independent experiments on different devices; NLE, MR and OGD refer to nonlinear elastic (7), Moonery-Rivlin (8) and Ogden (9) material models, respectively. The insets indicate the position of the points with coordinates (origin is set in the center of the membrane): (a) (0, 500), (b) (353, 353), (c) (500, 0). The table reports the average percentage error of the displacement for the three selected points for the peak pressure (500 mbar) vs. the three material models.

Figure 6

Tuning of material models. Fitting of experimental stress vs. stretch ratio curves for 10:1 v/v (empty circles) and 15:1 v/v (filled circles) PDMS using different material models: (a) nonlinear elastic (Eq.(7)); (b) hyperelastic Mooney-Rivlin (Eq. (8)); (c) hyperelastic Ogden (Eq. (9)). Tensile and compressive tracts are shown up to 100% and 25% strain, respectively.

Figure 7

MCD microfabrication. Schematic representation of the membrane fabrication steps (a,b) and of the multi-step bonding process: upper half with the PM (c,d) and final alignment of the two halves (e). 3D schematic view of the assembled MCD (f): upper (green) and lower (red) culture chambers with the interposed PM (gray).