In wireless sensor networks (WSNs), a space filling curve (SFC) refers to a path passing through all nodes in the network, with each node visited at least once. By enforcing a linear order of the sensor nodes through an SFC, many applications in WSNs concerning serial operations on both sensor nodes and sensor data can be performed, with examples including serial data fusion and path planning of mobile nodes. Although a few studies have made efforts to find such SFCs in WSNs, they primarily target 2D planar or 3D surface settings and cannot be directly applied to 3D volumetric WSNs due to considerably more complex geometric features and topology shapes that the 3D volumetric settings introduce. This article presents BLOW-UP, a distributed, scalable, and connectivity-based algorithm to construct an SFC for a 3D volumetric WSN (or alternatively to linearize the 3D volumetric network). The main idea of BLOW-UP is to decompose the given 3D volumetric network into a series of connected and closed layers, and the nodes are traversed layer by layer, incrementally from the innermost to the outermost, yielding an SFC covering the entire network, provably at least once and at most a constant number of times. To the best of our knowledge, BLOW-UP is the first algorithm that realizes linearization in 3D volumetric WSNs. It does not require advance knowledge of location or distance information. It is also scalable with a nearly constant per-node storage cost and message cost. Extensive simulations under various networks demonstrate its effectiveness on nodes’ covered times, coverage rate, and covering speed.