Typical capillary number-based flow map with flow patterns: (a) threading (●), (b) jetting (▶), (c) dripping (◼), (d) tubing (◆), (e) viscous displacement (+). fluid pair: .
Stable capillary thread diameter vs flow rate ratio . Inset: experimental micrograph with arrow showing contact line between and and glass wall. Fluid pairs: (●), (◼), (⊠), (○), (◻), and (▷).
Jetting regime. Thread breakup location occurs near fluid junction and is adjusted with flow rates in : (a) , ; (b) , ; (c) , ; (d) , (fluid pair: ).
Normalized jetting droplet diameter vs the flow rate ratio . Solid line: . Inset: ratio vs . Solid line: . Fluid pairs: (◆), (⊠), (◻) (◇), (▷), (△).
Experimental critical thread length before jetting droplets compared to the prediction of Eq. (3) (solid line). Fluid pairs: (◆), (▲), (⊗), (⊠), (◻), (◇), and (△).
Examples of microchannel confinement of varicose deformations (flow rates in ): (a) Bead-on-a-string structure: , ; (b) , ; (c) , .
Dynamics of dripping: (a) Time series of a cycle of viscous droplet formation: (i)–(ii) cap displacement, (ii)–(iii) cap squeezing, (iii)–(iv) pinching, (v) tail stretching, and (vi)–(vii) complete breakup. (b) Time-space diagram of (a) with corresponding events taken along the centerline of the channel. (c) Front velocity of a small droplet, , during breakup (flow rates in ): , (fluids pair: ). (d) Front velocity of a large droplet, , during breakup: , (fluids pair: ). The arrow indicates the end of the pinching stage.
Normalized droplet length vs . Line (i): , line (ii): . Fluids pairs: (●), (◆), (▲), (▶), (⊗), (⊠), (○), (○), (◇), (▷), and (△). Inset: effect of for fixed volume fraction: (flow rates in ) (a) , ; (b) , ; (c) (fluid pair: G3E).
Critical tail length at breakup, , of a viscous droplet vs Eq. (5). Fluids: (●), (◆), (▲), (▶), (⊗), (⊠), (⊠), (▷), and (△). Inset: Example of cometlike droplets with long tails (flow rates in ): [(a) and (b)] , ; (c) (fluids pair: ).
Examples of flow regimes limiting the steady formation of threads and droplets: (a) Hysteresis between tubing and threading regimes (flow rates in ): (i) , and , (ii) , and (fluid pair: ). (b) Viscous displacement regime (finger of at counterflow with ): (i) , , (ii) , , (iii) , , (iv) and, . (c) Typical wetting behaviors: (i) sticking droplet, , ; stratification: (ii), , (iii) , .
Physicochemical properties of pairs of liquids ( and ): and are corresponding viscosities, is the viscosity ratio, and is the interfacial tension. For marked by (∗), the volume percentage of glycerol in the mixture is given. All properties are measured at room temperature.
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