# Impact Dynamics and Freezing Performance of Porcine Bile Droplets on Horizontal Cold Substrates: Towards Advanced and Sustainable Food Processing

## TL;DR

This study explores how porcine bile droplets behave and freeze on cold surfaces, offering insights for better food processing techniques.

## Contribution

The paper introduces porcine bile's thermophysical properties into droplet impact dynamics on cryogenic surfaces for the first time.

## Key findings

- Lower substrate temperatures significantly reduce freezing time by up to 45% for smaller droplets.
- High Weber number droplets form flattened ice layers, while low Weber number droplets form smooth hemispherical ice caps.
- The study reveals multiscale freezing mechanisms of biological fluids at low temperatures.

## Abstract

With the development of the agro-processing industry, the efficient cryogenic treatment and resource utilization of porcine bile—a high-value byproduct—has received increasing attention. This study investigates the dynamic behaviour and freezing characteristics of porcine bile droplets upon impact on cold substrates under varying conditions of surface temperature (−10 °C to −20 °C) and impact velocity (0.18–0.59 m/s). The effects of droplet size, dimensionless numbers (Weber, Reynolds, Bond, Ohnesorge, and Prandtl), and thermal gradients were systematically analyzed. A thermoelectric cooling substrate combined with high-speed imaging was used to quantitatively characterize the spreading ratio, retraction ratio, and freezing time of droplets. The results show that the maximum spreading ratio increases with higher impact velocity but decreases with lower substrate temperature. Lower substrate temperatures significantly shorten the freezing time, with a maximum reduction of up to 45%, particularly for smaller droplets. Droplets with high Weber numbers (We > 3) form flattened ice layers with preserved retraction patterns, while those with low Weber numbers (We < 1) generate smooth, hemispherical ice caps. For the first time, the thermophysical properties of porcine bile were incorporated into the framework of droplet impact dynamics on cryogenic surfaces. The findings reveal multiscale freezing mechanisms of biological fluids at low temperatures and provide a theoretical basis for optimizing processes such as freeze-drying and cryogenic sterilization in agro-product processing.