Adhesive injection into thin bond-lines was studied to establish a computationally efficient prediction tool for flow-front evolution, internal velocities and injection pressures. A reduced-order gap-flow approach based on the Partially Filled Gap Model (PFGM) was extended from squeeze-flow to injection by introducing localised inlets, explicit outlets and gravitational body-force contributions for inclined gaps, and was verified against reference problems for source-flow kinematics, conservation of injected volume and gravity-driven redistribution. Experimental validation was performed in a quasi-two-dimensional glass-plate flow cell using a Newtonian silicone-oil model fluid. Several inlet–outlet arrangements and inclinations were investigated, and flow fronts, in-plane velocity fields (Particle Image Velocimetry) and inlet-pressure histories were measured. The simulations reproduced the observed front shapes and filling sequence, with Dice–Sørensen coefficients of 0.95–0.99 for the flow-front comparisons, captured the main features of the velocity profiles away from inlet and outlet regions, with average deviations on the order of 10%, and recovered the characteristic multi-stage pressure evolution; pressure changes relative to the initial offset agreed with the simulation within about 1 mbar at characteristic times. Systematic offsets in absolute pressure level were attributed to additional hydraulic losses in the upstream supply system not represented in the cavity-scale model. The validated model was then applied to a sensitivity analysis and to a frame-like cavity representative of panel-to-frame bonding, demonstrating strong dependences of pressure and injection-induced forces on viscosity, gap height and in-plane dimensions, including an approximately h − 3 dependence of pressure and force levels on gap height and an approximately L x 2 dependence of the maximum plate force on lateral size, and illustrating how gravity and boundary layout influence asymmetric filling. Extensions to adhesive-specific rheology, curing, wetting and discrete gas bubbles remain topics for future work.
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Flaig et al. (2026) studied this question.
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