The transverse-momentum differential radial flow observable $v_0\left(p_T\right)$, recently proposed and measured by the ATLAS and ALICE Collaborations, provides a novel tool to probe radial expansion dynamics in high-energy heavy-ion collisions. In this work, we conduct a detailed study of $v_0\left(p_T\right)$ using a blast-wave model that incorporates hydrodynamic-like expansion and thermal emission. We introduce event-by-event fluctuations in the transverse expansion velocity and kinetic freeze-out temperature using Gaussian probability distributions. Our results show that increasing the mean expansion velocity leads to a clear mass ordering in $v_0\left(p_T\right)$, while fluctuations in both expansion velocity and freeze-out temperature significantly enhance the magnitude of $v_0\left(p_T\right)$, particularly at higher $p_T$. We fit blast-wave model calculations for identified hadrons ($\pi , K$, and $p$) to recent ALICE data from Pb-Pb collisions at $\sqrt{s_{NN}}=5.02$ TeV using a Bayesian parameter estimation framework. The extracted mean transverse expansion velocity decreases, while the kinetic freeze-out temperature increases, from central to peripheral collisions. Additionally, the freeze-out temperatures inferred from $v_0\left(p_T\right)$ are systematically higher than those obtained from conventional $p_T$-spectra fits, likely due to the reduced sensitivity of $v_0\left(p_T\right)$ to resonance decay contributions.

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• Collective flow
• Particle correlations & fluctuations
• Quark-gluon plasma
• Relativistic heavy-ion collisions