Steady-State and Dynamic Behavior of Geometry-Tunable Microfluidic Passive Flow Regulators

Passive flow regulators enable autonomous, stable flow control without external electronics or active feedback. However, their dynamic response remains insufficiently investigated, limiting their potential integration into time-dependent fluidic circuits. Here, we present a reduced-order analytical framework based on an electrical analogy, along with systematic experimental characterization of a passive microfluidic flow regulator inspired by a fluidic transistor architecture. Devices with channel widths ranging from 300 to 700 µm were fabricated using soft lithography to examine how geometry affects both the regulated flow rate and its transient response. Steady-state characterization revealed nonlinear flow-pressure relationships, with narrower channels exhibiting higher fluidic resistance and earlier onset of flow saturation. Dynamic characterization showed dominant first-order low-pass behavior governed by fluid-structure interactions within the elastofluidic network. The effective bandwidth decreases with increasing channel width, revealing a fundamental trade-off between throughput and transient response. Experimental data agreed well with the developed reduced-order fluidic resistance-capacitance model. Thus, geometry-dependent transient dynamics can be captured using compact, physically interpretable parameters without relying on a complex fluid-structure-interaction model. These findings establish quantitative geometry-dynamics relationships and provide practical design guides for integrating compliant flow-controlling elements into microfluidic circuits, lab-on-a-chip, and autonomous microfluidic systems with reliable and predictable dynamic performance.