Abstract. An analytical approach is presented to obtain the sloshing natural frequencies and modes of ideal liquid in a rigid cylindrical container with a rigid annular baffle. The free surface waves of the liquid are considered in the analysis. The artificial interfaces are introduced to divide the complicated liquid domain into several simple sub-domains. The exact analytical solutions of velocity potential of liquid corresponding to every sub-domain are obtained by using the method of separation of variables and the superposition principle. The Eigen-frequency equation is precisely derived by using the Fourier-Bessel expansion on the free surface and the artificial interfaces of the liquid. The convergence study shows high accuracy and fast convergence of the present approach. The comparative studies with those available from literature are made, excellent agreements have been achieved. Numerical results showing the variations of natural frequencies and modes versus position and inner diameter of the annular baffle are provided.

Surfactin is one of the most widely studied biosurfactants due to its many potential applications in different fields. In the present study, Bacillus velezensis BS‐37, initially identified as a strain of Bacillus subtilis, was used to efficiently produce surfactin with the addition of glycerol, an inexpensive by‐product of biodiesel production. After 36 hr of growth in glycerol medium, the total surfactin concentration reached more than 1,000 mg/L, which was two times higher than that in sucrose medium. Moreover, the addition of l‐ and d‐Leu to the culture medium had opposite effects on surfactin production by BS‐37. While surfactin production increased significantly to nearly 2,000 mg/L with the addition of 10 mM l‐Leu, it was dramatically reduced to about 250 mg/L with the addition of 10 mM d‐Leu. To systemically elucidate the mechanisms influencing the efficiency of this biosynthesis process, we sequenced the genome of BS‐37 and analyzed changes of the transcriptome in glycerol medium in response to d‐/l‐leucine. The RPKM analysis of the transcriptome of BS‐37 showed that the transcription levels of genes encoding modular surfactin synthase, the glycerol utilization pathway, and branched‐chain amino acid (BCAA) synthesis pathways were all at a relatively high level, which may offered an explanation why this strain can efficiently use glycerol to produce surfactin with a high yield. Neither l‐Leu nor d‐Leu had a significant effect on the expression of genes in these pathways, indicating that l‐Leu plays an important role as a precursor or substrate involved in surfactin production, while d‐Leu appears to act as a competitive inhibitor. The results of the present study provide new insights into the synthesis of surfactin and ways of its regulation, and enrich the genomic and transcriptomic resources available for the construction of high‐producing strains.