How do users on social platforms consume content shared by their friends? Is this consumption socially motivated, and can we predict it? Considerable prior work has focused on inferring and learning user preferences with respect to broadcasted, or open-network content in public spheres like webpages or public videos. However, user engagement with narrowcasted, closed-network content shared by their friends is considerably under-explored, despite being a commonplace activity. Here we bridge this gap by focusing on consumption of visual media content in closed-network settings, using data from Snapchat, a large multimedia-driven social sharing service with over 200M daily active users. Broadly, we answer questions around content consumption patterns, social factors that are associated with such consumption habits, and predictability of consumption time. We propose models for patterns in users' time-spending behaviors across friends, and observe that viewers preferentially and consistently spend more time on content from certain friends, even without considering any explicit notion of intrinsic content value. We also find that consumption time is highly correlated with several engagement-based social factors, suggesting a large social role in closed-network content consumption. Finally, we propose a novel approach of modeling future consumption time as a learning-to-rank task over users? friends. Our results demonstrate significant predictive value (0.815 P@1, 0.650 nDCG@10) using only social factors. We expect our work to motivate additional research in modeling consumption and ranking of online closed-network content.