Wireless mesh networks recently emerge as a flexible, low-cost and multipurpose networking platform with wired infrastructure connected to the Internet. A critical issue in mesh networks is to maintain network activities for a long lifetime with high energy efficiency. As more and more outdoor applications require long-lasting, high energy efficient and continuously-working mesh networks with batterypowered mesh routers, it is important to optimize the performance of mesh networks from a battery-aware point of view. Recent study in battery technology reveals that discharging of a battery is nonlinear. Batteries tend to discharge more power than needed, and reimburse the overdischarged power later if they have sufficiently long recovery time. Intuitively, to optimize network performance, a mesh router should recover its battery periodically to prolong the lifetime. In this paper, we introduce a mathematical model on battery discharging duration and lifetime for wireless mesh networ...