Inverse integral transformation method to derive local viscosity distribution measured by optical tweezers.

Complex fluids have a non-uniform local inner structure; this is enhanced under deformation, inducing a characteristic flow, such as an abrupt increase in extensional viscosity and drag reduction. However, it is challenging to derive and quantify the non-uniform local structure of a low-concentration solution. In this study, we attempted to characterize the non-uniformity of dilute and semi-dilute polymer and worm-like micellar solutions using the local viscosity at the micro scale. The power spectrum density (PSD) of the particle displacement, measured using optical tweezers, was analyzed to calculate the local viscosity, and two methods were compared. One is based on the PSD roll-off method, which yields a single representative viscosity of the solution. The other is based on our proposed method, called the inverse integral transformation method (IITM), for deriving the local viscosity distribution. The distribution obtained through the IITM reflects the non-uniformity of the solutions at the micro scale, i.e., the distribution widens above the entanglement concentrations of the polymer or viscoelastic worm-like micellar solutions.

Contraction behaviors of Vorticella sp. stalk investigated using high-speed video camera. I: Nucleation and growth model.

The contraction process of living Vorticella sp. has been investigated by image processing using a high-speed video camera. In order to express the temporal change in the stalk length resulting from the contraction, a damped spring model and a nucleation and growth model are applied. A double exponential is deduced from a conventional damped spring model, while a stretched exponential is newly proposed from a nucleation and growth model. The stretched exponential function is more suitable for the curve fitting and suggests a more particular contraction mechanism in which the contraction of the stalk begins near the cell body and spreads downwards along the stalk. The index value of the stretched exponential is evaluated in the range from 1 to 2 in accordance with the model in which the contraction undergoes through nucleation and growth in a one-dimensional space.

Contraction behaviors of Vorticella sp. stalk investigated using high-speed video camera. II: Viscosity effect of several types of polymer additives.

The contraction process of living Vorticella sp. in polymer solutions with various viscosities has been investigated by image processing using a high-speed video camera. The viscosity of the external fluid ranges from 1 to 5mPa·s for different polymer additives such as hydroxypropyl cellulose, polyethylene oxide, and Ficoll. The temporal change in the contraction length of Vorticella sp. in various macromolecular solutions is fitted well by a stretched exponential function based on the nucleation and growth model. The maximum speed of the contractile process monotonically decreases with an increase in the external viscosity, in accordance with power law behavior. The index values approximate to 0.5 and this suggests that the viscous energy dissipated by the contraction of Vorticella sp. is constant in a macromolecular environment.