The transient rotational relaxation of a rigid spherical particle subjected to a suddenly applied constant torque is investigated in an incompressible micropolar fluid. The analysis is performed within the framework of Eringen’s micropolar continuum theory under creeping-flow conditions. Velocity-slip and spin-slip boundary conditions are incorporated to account for interfacial effects. The governing equations are solved analytically in the Laplace transform domain. The transient particle angular velocity is then recovered by numerical inversion of the transformed solution. An exact analytical solution is also obtained in the Newtonian limit and is used to validate the general formulation. The results show that the angular velocity increases monotonically toward its steady-state value, whereas the angular acceleration decays continuously with time. Increasing the particle-to-fluid density ratio delays the rotational response because of enhanced particle inertia. Stronger micropolar coupling introduces additional hydrodynamic resistance and prolongs the relaxation process. In contrast, increasing the spin parameter accelerates the transient response by reducing the resistance to microrotation at the particle surface. The slip parameter exhibits a non-monotonic influence. Moderate slip enhances the rotational response, whereas excessive slip weakens the hydrodynamic coupling between the particle and the surrounding fluid. Overall, the results demonstrate that fluid microstructure and interfacial slip jointly govern the transient transfer of angular momentum. The proposed formulation provides new physical insight into torque-driven particle motion in complex fluids and is relevant to microfluidic systems, suspension rheology, targeted drug delivery, and other microscale applications.
Objectives This study examined how holistic nursing competence is shaped in digitally mediated oncology practice by investigating the direct effect of quality climate, the mediating role of digital empathy, and the moderating role of nurses’ attitudes toward artificial intelligence (AI). Methods A cross-sectional study was conducted among 432 oncology nurses working in oncology departments of six hospitals in Egypt with fully implemented digital health systems. Nurses completed validated measures assessing quality climate, digital empathy, holistic nursing competence, and attitudes toward AI. A moderated mediation model was tested using PROCESS macro (Model 14) to examine direct, indirect, and conditional effects. Results Quality climate was positively associated with both digital empathy and holistic nursing competence. Digital empathy showed a strong positive relationship with holistic nursing competence and mediated the association between quality climate and holistic competence. Nurses’ attitudes toward AI moderated the relationship between digital empathy and holistic nursing competence, such that the association was stronger among nurses with more positive AI attitudes. The indirect effect of quality climate on holistic nursing competence through digital empathy was significantly amplified at higher levels of AI attitude, confirming a moderated mediation effect. Conclusion Holistic oncology nursing competence in the digital era is a sociotechnical outcome shaped by organizational culture, empathic capacity, and nurses’ orientations toward AI. Supportive quality climates foster digital empathy, while positive AI attitudes strengthen the translation of empathic engagement into holistic care. Implications for Nursing Practice Oncology nurse leaders should intentionally cultivate quality climates that prioritize psychological safety, integrate digital empathy into clinical education, and support ethically grounded AI adoption to preserve holistic, person-centered oncology nursing in technology-driven care environments.
