To address this gap in our understanding, we comprehensively explore flow and clogging in a common biopolymer. We investigate a dilute polymer system with an added crosslinker: crosslinking drives a transition from a fluid to a gelled state. Simultaneously, we observe transitions in the dynamic behavior. The transition from flow to clogging includes a region where the dynamics are intermittent, due to deposition and ablation of the gel from the channel walls. While phase diagrams or processing maps refer to states of matter at thermodynamic equilibrium, we present our results in the form of a "dynamic" or "flow phase diagram" acknowledging that the material phase largely determines flow dynamics. Alginate is a biopolymer commonly used in food, cosmetics, and medicine, including about ¼ of the published research in 3D bioprinting. We mix alginate and its crosslinking agent, calcium, in a microfluidic device in which two inlet streams meet at a Y-shaped junction. Upon examining a broad range of conditions, we find, for the first time, a surprising deposition/ablation pattern seen when alginate is crosslinked with calcium in flow through a microfluidic device. We have not seen descriptions or reproductions of any similar intermittent flow. When mixed with calcium, low concentrations of alginate quickly form a gel which deposits on the channel wall. As the gel grows and obstructs the flow, maintaining a constant flow rate in the channel requires an increase in driving pressure. This pressure increase, in turn, increases both the linear velocity of the fluid and the viscous shear stress felt at the wall. At a certain driving pressure however, the gel ablates from the wall and is washed out of the device, returning the driving pressure to baseline. Despite the simplicity of the chemical composition, the system exhibits rich dynamics. Remarkably, as long as flow is maintained, the gel continually grows and ablates at regular driving pressures and time intervals. Exploration of the flow phase diagram indicates that composition and flow rate control both the degree of deposition and the frequency of ablation.