Abstract In the realm of microfluidics, the dynamics of droplets have become a focal point of attention and research for potential applications in Lab-on-a-Chip devices or microanalysis systems. The behavior of droplets is contingent upon the characteristics of the flow, liquid properties, and geometric parameters. Droplet behaviors during passage through a T-junction involve breakup and non-breakup(NB) regime. In this study, the simultaneous influence of capillary number ( Ca ), viscosity ratio ( λ ), and length ratio ( l/w ) on the droplet behavior within the T-junction microchannel is investigated through three-dimensional numerical simulations. A novel model is proposed that incorporates the viscosity ratio in predicting the critical Ca ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mrow> <mml:msub> <mml:mi>a</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>cr</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) for the transition from NB to breakup regime, which was not considered in previous studies. The critical Ca is a function of the viscosity ratio and length ratio, determined and governed by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mrow> <mml:msub> <mml:mi>a</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>cr</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>&gt;</mml:mo> <mml:mrow> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mfrac> <mml:mi>w</mml:mi> <mml:mi>l</mml:mi> </mml:mfrac> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:mrow> </mml:msup> </mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>λ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . The reliability of the proposed model is validated through numerical simulations and earlier theoretical predictive models. Additionally, the study investigates the influence of the viscosity ratio on droplet behavior. A newly observed regime, called the Trap regime, is identified in microchannels with a rectangular cross-section, typically occurring at low Ca s. Furthermore, a comparative analysis is conducted to highlight the differences in droplet breakup behavior between square and rectangular microchannel cross-sections.

In this article, the behavior of Maxwell nanofluid flow over a stretchable cylinder is investigated. The nanofluid under study is synthesized by integrating single-walled carbon nanotubes and multi-walled carbon nanotubes into sodium alginate as the base fluid. The effects of thermal radiation, external magnetic field, and viscous dissipation on the fluid flow are considered to enhance the heat transfer efficiency. The governing set of partial differential equations is modeled and subsequently transformed into a set of ordinary differential equations using appropriate similarity transformations. The resulting equations are solved numerically using the Runge-Kutta-Fehlberg method in conjunction with the shooting procedure. Graphical simulations are utilized to illustrate the influence of various key parameters on the relevant physical quantities. The temperature profiles amplify with a rise in the Eckert number, curvature, and radiation parameters but decline with increasing nanoparticle concentration, while engineering metrics, including the skin friction coefficient and local Nusselt number, are analyzed and tabulated to evaluate the performance characteristics of the nanofluid system. The skin friction coefficient increases with higher curvature, magnetic field strength, Maxwell fluid parameters, and nanoparticle concentration, while the Nusselt number decreases with rising Eckert number, nanoparticle concentration, and Maxwell fluid parameters.

Under severe accident conditions of nuclear power plants, the lower head of a reactor pressure vessel can be at risk of creep deformation and potential failure. This study presents a computational model that can represent the creep deformation of the lower head through the application of shell theory. To account for the large deformation due to creep, kinematic equations are derived and implemented. Particularly, this study provides details of the mathematical formulation, which were lacking in previous studies. The analysis results using the developed model are compared with those of finite element analysis, considering deformation history, stress distribution, and deformed shape. A dimensionless time for the creep deformation is proposed based on the results, which can characterize the effective strain at failure. Finally, the developed model is applied to OECD lower head failure test for validation.

We present asymptotic and numerical solutions for the axisymmetric diverging radial flow of a viscoplastic Bingham fluid in narrow gaps of varying thickness. The asymptotic solution by Muravleva (2017) is used, which is compared with the finite element analysis result. The result clarifies the recent confusion discussed by Zou et al. (2021) and the articles referred to therein. The viscosity regularization error is also discussed briefly. The flow kinematics is investigated by using the non-persistence-of-straining tensor developed by Thompson and Souza Mendes (2005). It is noted that the local kinematics of the diverging radial flow can be significantly affected by the variable gap thickness, especially in the pseudo-plug region.