# A Machine Learning Approach to Predict Fluid Viscosity Based on Droplet Dynamics Features
## 1 Introduction
It has been shown that the three physical parameters that play a major role in the PD drop pattern of Newtonian fluids are viscosity \(\eta\), surface tension \(\sigma\), and inertia. The dimensionless numbers used to quantify the process are the Ohnesorge number (\(Oh=\mu/(\rho R\sigma)^{1/2}\)), Bond number (\(Bo=(\rho gR^{2})/\sigma\)), and Weber number (\(We=\rho U^{2}R/\sigma\)). Of these, surface tension is responsible for minimising the surface area of the fluid, giving it a spherical shape while viscous forces impede and slow down the flow of the fluid. Three theories have been developed to describe the kinetic behaviour of liquid neck contraction during capillary drop [16; 17; 18; 19; 20; 21; 22]. When the viscosity of the fluid is negligible, the liquid neck thickness changes exponentially concerning time \(h_{min}/R\sim\tau^{2/3}\), and inertia plays a major role in the contraction (I--inertia regime). \(\tau\) is the remaining time before pinch-off dimensionless. R denotes the outer radius of the needle, and the \(h_{min}\) denotes half of the fluid neck thickness dimension. When the inertia of the fluid is negligible, the contraction of the neck thickness follows the following scalar law \(h_{min}/R=(0.0709/Oh)\tau\). When the Reynolds number of the fluid is very small, viscosity plays a major role, showing the characteristics of Stokes flow (V--viscous regime). When both viscosity and inertia are not negligible, the change in the thickness of the liquid neck follows the following scalar law \(h_{min}/R=(0.0304/Oh)\tau\) or \(h_{min}\sim\tau^{1/2}\), viscosity, and inertia in the process of joint action of the liquid filament contraction fracture (IV--inertial viscous regime). The neck contraction process showed consistency under other complex influencing factors, which suggests that the results of neck contraction can be generalised to similar flow situations. [PERSON] et al. [21] investigated in detail the neck stretching and fracture process of droplets separated by collision. The results of this study showed that the neck contraction and fracture process of droplets bouncing and separating after the collision is consistent with the scalar law of the drop as it falls. [PERSON] et al. [23] investigated the neck shrinkage kinetics of paramagnetic solutions in a magnetic field environment. [PERSON] et al. [24] and [PERSON] et al. [25] investigated the droplet dropping and liquid bridge stretching in an electric field environment, respectively. [PERSON] et al. [26] investigated the generation process of micro-droplets in a double-layer pipeline. [PERSON] et al. [27] investigated the neck shrinkage kinetics of the droplet dropping on the surface of a horizontal pipeline. All these studies have shown that the necking contraction process that occurs during droplet formation, despite the presence of other influencing factors, is usually affected by the changes in the surface tension, viscosity, and inertia due to the influence of the three, thus altering the competing relationship between these three factors. Previously, the effect of low viscosity (\(Oh\) < 0.001), medium viscosity (\(1>Oh>0.001\)), and high viscosity (\(Oh>1\)) on the contraction of the liquid neck has been elucidated. [PERSON] et al. [22] studied the effect of viscosity ratio on fluid flow and found that at relatively high viscosities (\(6.3\times 10^{3}\) and \(3.3\times 10^{3}\)), the contraction region in the neck of the fluid shows an I-V-IV transition. Whereas, an I-V shift in the contraction region was observed for droplets with lower viscosities (\(6.4\times 10^{2}\)). [PERSON] et al. judged the contraction regime based on the exponential size of the contraction curve, with an exponent of 2/3 being the inertial regime (I), and an exponent of 1 being the viscous regime (V) as well as the viscous-inertial regime (IV). Similar to the way other researchers judge changes in contraction regions [23; 28; 29; 30; 31], their judgments of V and IV tenses are based on two non-overlapping, exponentially 1 contractions.