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Microfluidic large-scale integration (mLSI) is a promising platform for high-throughput biological applications. Design automation for mLSI has made much progress in recent years. Columba and its succeeding work Columba 2.0 proposed a mathematical modeling method that enables automatic design of manufacturing-ready chips within minutes. However, current approaches suffer from a huge computation load when the designs become larger. Thus, in this work, we propose Columba S with a focus on scalability. Columba S applies a new architectural framework and a straight channel routing discipline, and synthesizes multiplexers for efficient and reconfigurable valve control. Experiments show that Columba S is able to generate mLSI designs with more than 200 functional units within three minutes, which enables the design of a platform for large and complex applications. [ABSTRACT FROM AUTHOR]