Dynamic　behaviors　of　double　emulsion　droplets　flowing　through　the　Y-shaped　bifurcation　are　experimentally　studied　and　the　influences　of　droplet　length,　droplet　velocity,　and　liquid　viscosity　are　particularly　discussed.　The　flow　patterns　of　double　emulsion　droplets　are　categorized　by　typical　features　in　motion,　namely　the　number　of　interfacial　breakups　and　the　coupling　effect　between　interfaces.　Critical　conditions　for　the　existence　of　the　coupling　effect　are　determined　by　the　relative　difference　between　the　residence　time　of　inner　and　outer　droplets.　Influences　of　the　droplet　length　and　velocity　on　the　transition　laws　of　flow　patterns　are　summarized,　and　the　corresponding　dynamic　mechanisms　are　discussed　through　characteristics　of　the　interfacial　deformations.　Breakup　conditions　of　inner　and　outer　droplets　are　individually　identified　and　their　variations　in　liquid　systems　with　different　viscosity　ratios　are　analyzed　with　the　aid　of　the　built　theory　of　single　emulsion　droplets.　Universal　phase　diagrams　of　the　flow　patterns　are　established　by　taking　into　account　the　physical　parameters　of　both　inner　and　outer　droplets,　which　characterize　all　working　forces　including　the　viscous　force,　the　squeezing　force,　the　interfacial　tension,　and　the　coupling　force　that　is　the　unique　feature　during　the　breakup　of　multiple　interfaces.　©　2022　Elsevier　B.V.