Effect of confinement on the deformation of microfluidic drops

Abstract

We study the deformation of drops squeezed between the floor and ceiling of a microchannel and subjected to a hyperbolic flow. We observe that the maximum deformation of drops depends on both the drop size and the rate of strain of the external flow and can be described with power laws with exponents 2.59 ± 0.28 and 0.91 ± 0.05 respectively. We develop a theoretical model to describe the deformation of squeezed drops based on the Darcy approximation for shallow geometries and the use of complex potentials. The model describes the steady-state deformation of the drops as a function of a non-dimensional parameter Ca δ 2 , where Ca is the capillary number (proportional to the strain rate and the drop size) and δ is a confinement parameter equal to the drop size divided by the channel height. For small deformations, the theoretical model predicts a linear relationship between the deformation of drops and this parameter, in good agreement with the experimental observations.

Droplet relaxation in Hele-Shaw geometry: Application to the measurement of the nematic-isotropic surface tension

“…where α is a number (of the order of 0.36) that depends very little on both the confinement ratio k = R/ h and the viscosity ratio r = μ 1 /(μ 1 + μ 2 ) (in the limit 4 k 10 and 0 r 10/11) [1]. These predictions have not yet been checked in microfluidic devices and the reason certainly arises from the difficulty in preparing ellipsoidal droplets of different sizes in a fluid at rest at infinity (although this could be done by submitting for a short time the droplet to a hyperbolic flow [2]). For this reason, we performed this experiment in a different way by observing the coalescence and the relaxation of droplets of isotropic liquid in a homeotropic sample of nematic liquid crystal.…”

Assessment of a miniature four-roll mill and a cross-slot microchannel for high-strain-rate stagnation point flows

“…where Q is in (µL/hr) and γ is in (s -1 ). The strain rate in the cross junction can be crudely estimated using [16]:…”

“…The flow generated at the intersection of the cross-slot is similar to that of the Taylor's four-roll mill [3] with hyperbolic streamlines and the velocity field given by equation 1. Similar to four-roll mills, cross-slot microfluidic devices have been used for the characterisation and observation of deformation and breakup of bubbles and droplets [16]. However, they have also been used for confining micron-size beads [4,[17][18][19], trapping a motile bacterium [20], stretching a DNA polymer strain [4,[21][22][23] and for phenotyp-ing of cancerous cells [24,25] under pure straining flows.…”

Stagnation point flows in analytical chemistry and life sciences

“…Following these groundbreaking investigations, the crossslot generated ow was also adapted for techniques in investigating cell deformability, 204,205 polymersome dynamics, 206 break up of CNT bundles, 207 stretch-coil instabilities, 208 solution dynamics, 110,118,209 extensional viscosity, 120 DNA stretching/ compaction, 210,211 and polymer rheology. 123,[212][213][214][215][216] Using this device, cell deformability measurements were achieved by harnessing cell concentrations by viscoelastic micro ows of polymer solution, 204 CNT breakup was attained by simply increasing ow rates, 207 drop deformation was examined as a function of connement, 209 and DNA compaction was triggered by introducing Na + and polyethylene glycol (PEG) to the DNA molecules held at the stagnation point. 210 Of the aforementioned applications, one particularly interesting use of the cross-slot generated stagnation is for the precise control of droplet coalescence, 217 while generating multiple emulsions; a concept that hold a lot of promise in pharmaceutics.…”