| Summary: | Changes of shape are important in many situations of interest in biology at different typical length scales. Approaches for modelling the behaviour of droplets in suspension and thermallydriven motion of the molecular chains in enzymes are presented. Both models use orthogonal basis functions to describe the spatial dependences in a spherical geometry. Both models also describe the effect of time-dependent boundary data on the shape of the bodies involved, a stochastic response for the enzyme model (dimensions of the order 10−9 m) and smooth response for the colloidal model (dimensions of the order 10−6 m). The first model presented considers the behaviour of a droplet of fluid surrounded by a thin film of host fluid, both fluids being Newtonian and immiscible, with a well-defined continuous and smooth interface between these regions. The flows for the droplet and host fluid are assumed axisymmetric with small Reynold numbers. An extension of traditional lubrication theory is used to model the flow for the host fluid and a multi-modal Stokes flow is used to derive the flow within the droplet, subject to continuity conditions at the interface between the droplet and host fluid. The interface is free to move in response to the flows, under the effects of interfacial tension. Asymptotic expansions for the flow variables and interface are used to find the simplest behaviour of the system beyond the leading order. The second unique modelling approach used is the method of Zernike moments. Zernike moments are an extension of spherical harmonics to include more general radial dependence and the ability to model holes, folded layers etc. within and on the unit sphere. The method has traditionally been used to describe the shape of enzymes in a static time-independent manner. This approach is extended to give results based on the thermally-driven motion of atoms in molecules about their equilibrium positions. The displacements are assumed to be fitted by Normal probability distributions. The precision and accuracy of this model are considered and compared to similar models. Results are plotted and discussed for both regimes and further extensions, improvements and basis for further work are discussed for both approaches.
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