Surfing of drops on moving liquid–liquid interfaces

Spontaneous Transfer of Droplets across a Microfluidic Liquid–Liquid Interface

“…The hydrodynamic pressure Δ P hydro in the liquid film could be expressed by eq : ∂ ∂ x ( h 3 12 μ ∂ p ∂ x ) = ∂ ∂ x ( h false( u d + u b false) 2 ) + ( w normald − w normalb ) − u d .25em ∂ h ∂ x where h is the thickness of the liquid film, μ is the viscosity of the liquid in the film, x is the axial coordinate, p is the pressure in the liquid film, u d is the tangential velocity of the droplet surface, u b is the tangential velocity of the liquid–liquid interface, and w d and w b indicate the velocities at which the droplet and interface approach each other. Figure shows a local diagram of the liquid film and its related parameters.…”

“…The liquid film resistance is composed of the Laplace pressure Δ P Laplace caused by the curvature of the interface and the hydrodynamic pressure Δ P hydro inside the liquid film. , Because all events of liquid film rupture in this experiment occur at the droplet head, the curvature at the droplet head should be used when Δ P Laplace is calculated by Young–Laplace equations. The curvature of the droplet head is positively correlated to the droplet size and increases with the flow rate of TSC, as shown in Figure .…”

“…31 However, the nonzero velocity of the interface would minimize the pressure at the outlet of the liquid film (the droplet head), which has been proved in the literature. 29 The hydrodynamic pressure ΔP hydro in the liquid film could be expressed by eq 5: 29…”

Migration and Spreading of Droplets across a Fluid–Fluid Interface in Microfluidic Coflow

“…A mismatch in the interfacial tension (IFT) values of a drop and an interface gives rise to the Marangoni effect which promotes partial coalescence . A few droplet coalescence studies involving the coflow of bulk fluids indicate a longer coalescence time compared to the corresponding stagnant fluids due to a higher lubrication pressure in the film separating the droplet and fluid–fluid interface . The spreading of drops over liquid–liquid/air–liquid interfaces is an outcome of the interplay between gravity, inertia, viscosity, and surface/IFT forces, wherein the spreading length ( l ) scales with time ( t ) as l ∼ t b , and a wide range of exponents ( b ) has been reported in the literature. − Although most of such studies are conducted for air–liquid interfaces, only a few experimental investigations deal with spreading of a droplet at a liquid–liquid interface. , In such studies, spreading was studied in stagnant fluids in macroscale setups, which limits its applicability in a microfluidic co-flowing system as a strong confinement effect, fluid inertia, and negligible gravity would greatly alter the phenomena.…”

“…2 A few droplet coalescence studies involving the coflow of bulk fluids indicate a longer coalescence time compared to the corresponding stagnant fluids due to a higher lubrication pressure in the film separating the droplet and fluid−fluid interface. 7 The spreading of drops over liquid−liquid/air−liquid interfaces is an outcome of the interplay between gravity, inertia, viscosity, and surface/IFT forces, wherein the spreading length (l) scales with time (t) as l ∼ t b , and a wide range of exponents (b) has been reported in the literature. 8−15 Although most of such studies are conducted for air−liquid interfaces, only a few experimental investigations deal with spreading of a droplet at a liquid−liquid interface.…”