We investigate the dynamics of a swimming microorganism inside a surfactant-laden drop for axisymmetric configurations under the assumptions of small Reynolds number and small surface Péclet number $(Pe_{s})$. Expanding the variables in $Pe_{s}$, we solve the Stokes equations for the concentric configuration using Lamb’s general solution, while the dynamic equation for the stream function is solved in the bipolar coordinates for the eccentric configurations. For a two-mode squirmer inside a drop, the surfactant redistribution can either increase or decrease the magnitude of swimmer and drop velocities, depending on the value of the eccentricity. This was explained by analysing the influence of surfactant redistribution on the thrust and drag forces acting on the swimmer and the drop. The far-field representation of a surfactant-covered drop enclosing a pusher swimmer at its centre is a puller; the strength of this far field is reduced due to the surfactant redistribution. The advection of surfactant on the drop surface leads to a time-averaged propulsion of the drop and the time-reversible swimmer that it engulfs, thereby causing them to escape from the constraints of the scallop theorem. We quantified the range of parameters for which an eccentrically stable configuration can be achieved for a two-mode squirmer inside a clean drop. The surfactant redistribution shifts this eccentrically stable position towards the top surface of the drop, although this shift is small.

Live-cell imaging reveals the phenotypes and mechanisms of cellular function and their dysfunction that underscore cell physiology, development, and pathology. Here, we report a 3D super-resolution live-cell microscopy method by integrating radiality analysis and Fourier light-field microscopy (rad-FLFM). We demonstrated the method using various live-cell specimens, including actins in Hela cells, microtubules in mammary organoid cells, and peroxisomes in COS-7 cells. Compared with conventional wide-field microscopy, rad-FLFM realizes scanning-free, volumetric 3D live-cell imaging with sub-diffraction-limited resolution of ∼150 nm (x-y) and 300 nm (z), milliseconds volume acquisition time, six-fold extended depth of focus of ∼6 µm, and low photodamage. The method provides a promising avenue to explore spatiotemporal-challenging subcellular processes in a wide range of cell biological research.

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