Methodology for Online Estimation of Rheological Parameters in Polymer Melts Using Deep Learning and Microfluidics

TL;DR

This work addresses online estimation of rheological parameters for polymer melts in microfluidic circuits by combining a 1D hydraulic RC model with synthetic data generation and a bidirectional GRU to map pressure-drop and flow-rate signals to parameters $eta_0$, $n$, and $lambda$. The methodology generates a large synthetic dataset of 5500 experiments, trains a neural network to infer viscosity model parameters from four signals, and verifies identifiability via cross-validation and curve-consistency checks. Key findings show that the behavior index $n$ is the most detectable parameter under the chosen setup, with the bidirectional GRU providing stable online estimates and enabling potential inline rheology monitoring and iterative device design. The approach offers a pathway to reduce physical prototyping and accelerate microfluidic device development for real-time polymer melt rheology applications, with scope to extend to more complex fluids and validation against physical prototypes.

Abstract

Microfluidic devices are increasingly used in biological and chemical experiments due to their cost-effectiveness for rheological estimation in fluids. However, these devices often face challenges in terms of accuracy, size, and cost. This study presents a methodology, integrating deep learning, modeling and simulation to enhance the design of microfluidic systems, used to develop an innovative approach for viscosity measurement of polymer melts. We use synthetic data generated from the simulations to train a deep learning model, which then identifies rheological parameters of polymer melts from pressure drop and flow rate measurements in a microfluidic circuit, enabling online estimation of fluid properties. By improving the accuracy and flexibility of microfluidic rheological estimation, our methodology accelerates the design and testing of microfluidic devices, reducing reliance on physical prototypes, and offering significant contributions to the field.

Figures (6)

• Figure 1: Methodology diagram. The elements in blue, a), b) and d), operate together with the simulator to generate a dataset, X, Y, with which the deep learning model is trained at block e). The simulator uses the predictions of the deep learning model to run simulations, producing an estimation dataset, $\hat{X}, \hat{Y}$, which is compared at f) with the original dataset to verify the methodology.
• Figure 2: Simulated microfluidic circuit. a) shows the fluidic system diagram composed by one input hydraulic resistance, $R_1$, one capacitance characterized by its volume, $V$, and one output hydraulic resistance, $R_2$. b) shows the analogous electrical circuit.
• Figure 3: Diagram showing the simulation flow. a) generates set of parameters for which block b) creates a random input pressure signal. In the simulation loop, c) calculates all the algebraic expressions and d) resolves the variation of volume in the capacitance, integrated by e). If the conditions of f) don't match, a new signal is generated and the loop is run again. Otherwise, a new set of parameters is created and the process starts again.
• Figure 4: Designed artificial neural network. It receives four inputs signals: $\Delta P_1$, $\Delta P_2$, $Q_1$, $Q_2$, and outputs three viscosity parameters: $\eta_0$, $n$ and $\lambda$. The bidirectional GRU layers provides the model with memory capability to deal with temporal signals. The fully connected layers enhance its capacity to model complex functions. The dropout layer helps to regularize the model.
• Figure 5: Two simulations performed over 100s with the same random pressure input signal. The parameters correspond to shear-thickening fluid ($n=1.1$) with, first, $\lambda = 1.0e-4$ (left), and second, $\lambda = 1.0e-5$ (right). In the rightmost simulation it can be observed that the fluid doesn't go into non-Newtonian regime ($\alpha \ll 1.0$), thus the viscosity remains low, producing higher-values of flow-rate.