Negative mold fabrication
The negative mold was fabricated using an ELEGOO Saturn mono-stereolithography (MSLA) 3-D printer with Accura 25 resin (Fig. 1a-i). Due to the high hydrophobicity, the Accura 25 resin allows for demolding of cured PDMS without salinization. High aspect features such as large length versus small width/height and large height versus void geometry were achieved at a resolution of 50 µm. The complete mold was constructed out of 3-D printed sidewalls with grooves to hold 4 typical glasses delisco. wall structure can be freely placed on the negative mold with a loose tolerance. Use of a sealing membrane such as aluminum foil secured by tape avoids PDMS leaking during mold casting and curing. The mold and wall structure are reusable provided cleaning between each casting. In This work, we tested the samples with an aspect ratio (height/thickness) ranging from 1.5:1, 2:1, and 3:1.
(a) The fabrication process of the ADMC: (ai) SLA 3-D printed negative mold. (a-ii) PDMS casting on the SLA mold. (a-iii) Inlets and outlet of the channels are punched. The chip is bonded with PDMS to a 1 mm thick spin coated PDMS layer. (a-iv) The central channel has a glass capillary inserted as a sight glass. After filling the central channel with distilled water, the inlet is plugged. (bi) Photograph of the ADMC with orange fluorescent dye to distinguish between the liquid and air channels. (b-ii) and (b-iii) Before and after application of pressure to outside channels with green fluorescent dye. The thin wall between deflects and displaces fluid. (b-iv) Cross-section of the ADMC with a 500 µm sidewall. (c) The experimental setup—goniometer fitted with a 5X-120X magnification c-mount lens. The pressure is supplied using an ElvFlow controller. The camera and the flow controller are controlled using a LABVIEW program developed to collect images. in synchrony with read pressure (d) Schematics of the theoretical model. (Figure a(s) were drawn by SOLIDWORKS 2021: https://www.solidworks.com/media/solidworks-2021-pdm).
Microfluidic chip fabrication
PDMS base to crosslinker with a ratio of 10:1 was used based on the instruction from the manufacturer. We casted 10 mL of PDMS into the negative mold and a standard 25 psi vacuum desiccator was used to remove air bubbles from the uncured PDMS, paying special attention to removing air bubbles in void gaps (Fig. 1a-ii). The casted PDMS and mold were placed in a free convection oven at 45 °C for at least 4 h. Low temperature is required to avoid entering glass transition and deformation of the negative mold. After demolding, a biopsy punch (diameter: 1.5 mm) was used to form inlets and outlets in the desired channels (Fig. 1a-iii). For chip completion, we used a spin coated PDMS layer of approximately 1 mm in thickness as a bottom layer of the chip. To achieve this 1 mm layer, we spin coated four layers of PDMS at 350 RPM for 1 min per layer, curing in between each layer to achieve a layer of PDMS with an approximate thickness of 1 mm. Then, a very thin film of PDMS was spin coated on the cured 1 mm layer at 1000 RPM for 1 min as an adhesive layer between the spin coated PDMS and the casted PDMS chip. Finally, a glass capillary and an inlet plug were inserted into the ADMC chip (Fig. 1a-iv). A photograph of the dye filled ADMC sample is shown in Fig. 1b-i. As shown in Fig. 1b-ii and b-iii, after applying air pressure to the air chambers, the PDMS thin walls are deformed and squeezing the fluorescence dye. The The cross-section of the chip is shown in Fig. 1b-iv, clearly showing the stacked PDMS layers at the bottom.
Measurements of applied pressure and fluid displacement
The experimental setup is shown in Fig. 1c. Reservoir pressure was supplied to the system using lab air connected through a Drierite gas purifier (desiccator) inline to an Elve Flow flow controller (OB1 MK3+ to keep the air supply dry and clean. The flow controller operates between 0 and 2000 mbar and delivers reservoir pressure with a resolution of 100 µbar to the gas channels on the ADMC through rigid pneumatic tubing. The flow controller was outfitted with pressure transducers to measure applied pressure. tube was measured using a 5X–120X microscope lens attached to a 100 FPS goniometer camera. The acquisition sampling time was set to 60–75 Hz. A LabVIEW program was designed to synchronize the frame collection with the pressure measurements. Before, the experiments The flow controller and the goniometer were calibrated.
Detecting fluid displacement by image processing
An interactive routine was created to streamline and control processing of the image frames and pressure data. MATLAB was used to track the position of the liquid meniscus by means of image processing (the MATLAB code available in GITHUB). Each image was converted into an edge image using a Canny edge detection function, where the contrasting edges were converted to white lines on a black background. A sensitivity threshold was set between 0.2 and 0.6 and tuned depending on light intensity. To convert the image to engineering units, we performed calculation to determine the displacement of the meniscus of that frame relative to the first. A pixel conversion factor was calculated for each dataset based on the known thickness of the glass capillary in observation. Each glass capillary has an outside diameter of 2 mm ± 0.1 mm Compiling each of the frame data points together yielded the fluid dynamic response of our chip.
Theoretical models
A theoretical model was developed to understand the dynamics of fluid–structure interaction and to verify the experimental results. The model (Fig. 1d-I,d-ii) generally includes two sections—the pressurized channel and the vertical tube at the end of applying the unsteady Bernoulli equation to the device,
$$ mathop smallint nolimits_{I}^{T} rho frac{partial u}{{partial t}}ds + left( {P + frac{1}{2}rho u ^{2} + rho gz} right)_{T} – left( {P + frac{1}{2}rho u^{2} + rho gz} right)_{I} + rho gh_{L} = 0 $$
(1)
where P is the pressure, ρ is the fluid density, µ is the velocity, t is time, z is the height of the fluid (zI= 0 and zT is the height of the free surface in the vertical tube), and hL is the head loss in the flow, which generally takes account of the major and minor losses in the device. The subscription T and I denote the variables in the vertical tube and the horizontal pressurized channel. The total fluid in the device is conserved, therefore,
$$ u_{I} A_{I} = u_{T} A_{T} $$
(2)
where AI and AT are the cross-sectional areas of the pressurized channel and the vertical tube. To describe the tube deformation under the transmural pressure, the tube law is appliedtwenty threeie,
$$ P_{E} – P_{I} = P_{C} left[ {left( {frac{{A_{I} }}{{A_{0} }}} right)^{alpha } – 1} right] $$
(3)
where Ao is the initial cross-sectional area, PE. and PI are the pressure outside and inside the channel, PC is a deformation coefficient, and alpha is the exponent depending on the shape and materials of the channel. Various tube laws are proposed in the literature and the equation above is from the most popular one used in flexible tubes. Assuming the velocity in the pressurized channel is uniform and inserting the laminar Darcy -Weisbach equation with general loss coefficients, KI and KTie,
$$ h_{L} = K_{I} frac{mu L}{{rho gA_{I} }}u_{I} + K_{T} frac{mu z}{{rho gA_{ T} }}u_{T} = left( {frac{{K_{I} L}}{{A_{I} }} + frac{Kz}{{A_{T} }}frac{{ A_{I} }}{{A_{T} }}} right)frac{{mu u_{I} }}{rho g}. $$
(4)
we obtain,
$$ rho frac{{partial u_{I} }}{partial t}L + rho frac{{partial u_{T} }}{partial t}z + left( {frac {1}{2}rho u_{T}^{2} + rho gz} right) – left( {frac{1}{2}rho u_{I}^{2} + P_{ I} } right) + left( {frac{{K_{I} L}}{{A_{I} }} + frac{{K_{T} z}}{{A_{T} }} frac{{A_{I} }}{{A_{T} }}} right)mu u_{I} = 0, $$
(5)
where (mu) is the dynamic viscosity of the fluid.
Normalizing the equations yields,
$$ U_{I} A = frac{{A_{T} }}{{A_{0} }}U_{T} , $$
(6)
$$ frac{{partial U_{I} }}{partial T} + frac{{partial U_{T} }}{partial T}Z + frac{1}{2}U_{T }^{2} + Z – left( {Delta + beta A^{alpha } } right) – frac{1}{2}U_{I}^{2} + Kleft( { frac{1}{A} + frac{ZA}{{left( {frac{{A_{T} }}{{A_{0} }}} right)^{2} }}} right)gamma U_{I} = 0, $$
(7)
$$ U_{T} = frac{partial Z}{{partial T}}, $$
(8)
$$ frac{partial A}{{partial T}} = – AU_{I} , $$
(9)
where (U_{I} = frac{{u_{I} }}{{sqrt {gL} }}), (A = frac{{A_{I} }}{{A_{0} }}), (T = sqrt{frac{g}{L}} t), (Z = frac{z}{L}), (Delta = frac{{P_{C} + P_{E} }}{rho gL}), ( beta = frac{{P_{C} }}{rho gL}), (gamma = frac{{nu L^{frac{1}{2}} }}{{g^{frac{1}{2}} A_{0} }})and assume (K = K_{I} = K_{T}). This system of equations was solved using the ode15i function in MATLAB. The initial velocity was assumed zero and no deformation was assumed at t= 0.
