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Moving contact line dynamics calculations include two models: precursor film models and slip models. The lubrication approximation method is used to establish a three-dimensional mathematical model to analyze the droplet thermocapillary migration behavior on a non-uniformly heated solid substrate with a wettability track. The contact line dynamics in the slip model and the disjoining pressure effect in the precursor model are proposed to regulate the substrate wettability. Both models are numerically implemented to investigate droplet spreading for three cases: free spreading on an isothermal substrate, thermocapillary migration on a uniform wettability substrate, and thermocapillary migration on a wettability-confined track. For the case of free spreading on an isothermal substrate, the three-dimensional results of the slip and precursor contact line models are essentially consistent with two-dimensional slip model results. For the case of thermocapillary migration on a uniform wettability substrate, the results of the two models essentially agree with the experimental results. Decreasing the thermal gradient reduces the discrepancies between the two models that result from the coordinate transformation method used in the slip model, which reduces the contact angles measured in the y-direction and enlarges the advancing contact angle in the migration direction. For the case of thermocapillary migration on a wettability-confined track, the slip model gradually shows a "dynamic-pinning" behavior with increasing equilibrium contact angle in the hydrophobic region. By contrast, the precursor film model maintains a stationary pinning behavior but separates a residual liquid outside the track. The precursor film model is preferred over the slip model in lubrication approximations for three-dimensional fluids when calculating complex moving contact dynamics caused by wettability differences. However, the precursor film model must be further optimized to prevent numerical instability. [ABSTRACT FROM AUTHOR]

This study investigates the crystallization of acetaminophen (ACET) in ultrapure water and a 10 wt.% aqueous polyacrylic acid (PAA) solution using non‐photochemical laser‐induced nucleation (NPLIN) for the first time. Using a 532 nm nanosecond laser, two distinct crystal morphologies—rhombic and tetragonal plate‐like—are formed in both solvents after adding impurities. Notably, the PAA solution showed a reduced number of crystals and slower growth rates compared to ultrapure water, suggesting that the acidic polymer modulates crystal growth. Interestingly, crystals are not induced by the laser without impurities. However, impurities like copper phthalocyanine (CuPc) or boron carbide (CB4) enabled successful NPLIN, with CB4 showing higher nucleation efficiency than CuPc. The study also explores how laser power affects nucleation probability and identifies potential laser energy thresholds. Experimental data on ACET crystal sizes over time are fitted to derived equations, which accurately represented trends and predicted results. The nanoparticle heating mechanism and the role of acidic polymers in affecting nucleation probability and growth rate are discussed, along with potential mechanisms for changes in crystal morphology. [ABSTRACT FROM AUTHOR]

This paper provides a novel approach to determining optimal sampling locations for chlorine decay model calibration. Three questions are investigated: (1) What is the minimum number of chlorine sample locations needed? (2) How many combinations of sampling locations are available? (3) What is the optimal location combination? To answer the first two questions, the mathematical expressions of the chlorine concentrations between any two sampling locations are developed and sampling point relationship matrices are generated, then a mixed integer programming (MIP) algorithm is developed. Once obtained, the solutions to the first two questions are used to calculate the chlorine decay wall reaction coefficients and sensitivity matrix of chlorine concentration to wall reaction coefficients; then, sampling location combinations achieved in the second question are sorted using a D-optimality algorithm. The model frame is demonstrated in a case study. [ABSTRACT FROM AUTHOR]