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Continuous-flow microfluidic large-scale integration (mLSI) shows increasing importance in biological/chemical fields, thanks to its advantages in miniaturization and high throughput. Current mLSI is designed manually, which is time-consuming and error-prone. In recent years, design automation research for mLSI has evolved rapidly, aiming to replace manual labor by computers. However, previous design automation approaches used to design each microfluidic layer separately and over-simplify the layer interactions to various degrees, which resulted in a gap between realistic requirements and automatically generated designs. In this paper, we propose a module model library to accurately model microfluidic components involving layer interactions; and we propose a co-layout synthesis tool, Columba, which generates AutoCAD-compatible designs that fulfill all designs rules and can be directly used for mask fabrication. Columba takes plain-text netlist descriptions as inputs, and performs simultaneous placement and routing for multiple layers while ensuring the planarity of each layer. We validate Columba by fabricating two of its output designs. Columba is the first design automation tool that can seamlessly synchronize with the manufacturing flow. [ABSTRACT FROM AUTHOR]