Understanding how viscoelastic stresses couple with geometric changes and boundary compliance remains a central challenge in predicting flow behavior in complex fluids in microfluidic systems. In this talk, I will present our recent advances on steady and oscillatory flows of constant‑viscosity viscoelastic (Boger) fluids in compliant three‑dimensional microchannels. Our work combines comprehensive experiments with predictive theory to understand Boger‑fluid flows in deformable 3D PDMS-based microchannels under steady and oscillatory pressure‑driven conditions.
For steady, weakly viscoelastic flow (small Deborah number), flow‑induced deformation curves the streamlines, producing a reduction in pressure drop that is well captured by our theory based on the Oldroyd‑B model (J. Non‑Newton. Fluid Mech. 313, 104990, 2023; Phys. Rev. Applied 24, 034001, 2025). Our results demonstrate that even modest viscoelasticity, when coupled with wall compliance, can significantly alter the hydrodynamic resistance of a viscoelastic flow.
Next, I will turn to our development of a theory for elastoinertial flow rectification in oscillatory Boger‑fluid flow through deformable 3D microchannels, building on Zhang & Rallabandi (J. Fluid Mech. 996, A16, 2024) and Huang, Pande, Feng & Christov (J. Fluid Mech. 1022, A38, 2025). This flow exhibits three distinct nonlinearities: (i) advective inertia, (ii) the upper‑convected derivative in the constitutive law, and (iii) pressure‑driven deformation of the cross‑section. Together, these nonlinearities extract a nonzero mean flow under zero‑mean forcing, i.e., streaming. To disentangle their respective roles, we employ a double perturbation expansion, assuming weak viscoelasticity (a small Weissenberg number but arbitrary Deborah number) and weak wall compliance, which enables the exact determination of the primary oscillatory pressure field, whereas the cycle‑averaged streaming pressure is found by solving a linear boundary‑value problem.
A parameter‑space study reveals that the streaming response is highly tunable by the Deborah number, including cases where viscoelasticity substantially enhances elastoinertial rectification. These insights suggest new design principles for microfluidic systems that sort cells and particles in biological fluids for lab‑on‑a‑chip and organ‑on‑a‑chip technologies.
This talk will include results from productive joint work with E. Boyko, S. Pande, J. Feng, A. Huang, and S. G. Chun.
This work was supported, in part, by the U.S. National Science Foundation under grant no. CMMI-2245343.