Since its emergence from the communication engineering community around one and a half decades ago, the field of Synthetic Molecular Communication (SMC) has experienced continued growth, both in the number of technical contributions from a vibrant community and in terms of research funding. Throughout this process, the vision of SMC as a novel, revolutionary communication paradigm has constantly evolved, driven by feedback from theoretical and experimental studies, respectively. It is believed that especially the latter ones will be crucial for the transition of SMC towards a higher technology readiness level in the near future. In this spirit, we present here a comprehensive survey of experimental research in SMC. In particular, this survey focuses on highlighting the major drivers behind different lines of experimental research in terms of the respective envisioned applications. This approach allows us to categorize existing works and identify current research gaps that still hinder the development of practical SMC-based applications. Our survey consists of two parts; this paper and a companion paper. While the companion paper focuses on SMC with relatively long communication ranges, this paper covers SMC over short distances of typically not more than a few millimeters.