Torsional fracture of viscoelastic liquid bridges

Abstract

Short liquid bridges are stable under the action of surface tension. In applications like electronic packaging, food engineering, and additive manufacturing, this poses challenges to the clean and fast dispensing of viscoelastic fluids. Here, we investigate how viscoelastic liquid bridges can be destabilized by torsion. By combining high-speed imaging and numerical simulation, we show that concave surfaces of liquid bridges can localize shear, in turn localizing normal stresses and making the surface more concave. Such positive feedback creates an indent, which propagates toward the center and leads to breakup of the liquid bridge. The indent formation mechanism closely resembles edge fracture, an often undesired viscoelastic flow instability characterized by the sudden indentation of the fluid’s free surface when the fluid is subjected to shear. By applying torsion, even short, capillary stable liquid bridges can be broken in the order of 1 s. This may lead to the development of dispensing protocols that reduce substrate contamination by the satellite droplets and long capillary tails formed by capillary retraction, which is the current mainstream industrial method for destabilizing viscoelastic liquid bridges.

Torsional instability of constant viscosity elastic liquid bridges

“…Edge fracture is a flow instability characterized by the sudden indentation of the fluid's free surface when a viscoelastic fluid is sheared at above a certain critical shear rate. 17–24 Historically, Tanner and Keentok 18 first realized that the second normal stress difference N 2 is important in driving edge fracture. By assuming a semicircular indent of radius a in a second-order fluid with surface tension σ , they derived a criterion of edge fracture which reads | N 2 | > 2 σ /3 a .…”

“…The second way is to define two additional dimensionless parameters, namely, the elastocapillary number Ec and the recently introduced Tanner number Tn. 17 The elastocapillary number Ec ≡ Wi/Ca = λσ / ηR characterizes the combined importance of elastic stress and capillary stress as compared to viscous stress. The Tanner number Tn ≡ WiCa = ληRΩ 2 / σ characterizes the relative importance of torsion-induced normal stress and capillary stress.…”

“…In this work, we take a step further and show that torsion can effectively destabilize liquid bridges made of constant viscosity elastic liquid (Boger fluid) as well. The Boger fluid we used has a relaxation time of λ ∈ O (1 s), which is 1000 times larger than that of the silicone oil used by Chan et al 17 Hence, elastocapillarity is expected to play a much more pivotal role in the liquid bridge deformation process. In fact, deformation of the liquid bridge under torsion depends on how the elastocapillary effect competes with the torsion-induced normal stress effect.…”

“…Recently, Chan et al 17 propose that the aforementioned two drawbacks of the elongation method can be overcome using torsion, i.e. , rotating one end of the viscoelastic liquid bridge while keeping the other end fixed.…”

“…Using a viscoelastic silicone oil with a characteristic relaxation time of λ ∈ O (1 ms) as the model fluid, they show that when the liquid bridge is subjected to torsion it undergoes edge fracture, a flow instability characterized by the sudden indentation of the fluid's free surface when a viscoelastic fluid is sheared at above a critical rate. 17–24 The indent caused by the viscoelastic stresses propagates towards the vertical centerline of the liquid bridge, which creates a horizontal cut and causes the bridge radius to undergo power-law decay, hence resulting in the clean and quick breakup of the liquid bridge.…”