Production of monodisperse microbubbles avoiding microfluidics

Abstract

Here we report the production of monodisperse microbubbles by taking advantage of the large values of both the pressure gradients and of the local velocities existing at the leading edge of airfoils in relative motion with a liquid. It is shown here that the scaling laws for the bubbling frequencies and the bubble diameters are identical to those found in microfluidics. Therefore, the metre-sized geometry presented here is a feasible candidate to circumvent the inherent problems of using micron-sized geometries in real applications – namely, wettability, the low productivity and the clogging of the microchannels by particles or other impurities.

Method of mass production of monodisperse microbubbles aided by intense pressure gradients

“…Indeed, we showed in Reference 27 that the values of K f 1 and K b 1 in Equations ) for the aerator depicted in Figure 1c are the same as in the case of the bubble maker depicted in Figure 1b. Consequently, the results in Reference 27 support the validity of Equations ) in general types of flows whenever the pressure gradient is favorable, viscous stresses are negligible—this is usually verified for low viscosity liquids such as water—and when Bo ≳ O (1)—see Equation ), a condition which can be alternatively written as …”

“…Then, in order to reduce the diameters of the bubbles produced, we take advantage of the fact that Equations ) express that the bubbling frequency increases and the bubble diameter decreases when |∇ p | increases. Therefore, the strategy we proposed in References 26,27 to produce micron‐sized bubbles at high rates was to inject the gas in a region of the flow where |∇ p |/( ρ g ) ≫ 1. In Reference 26, the gas is injected at the entrance region of a tube, where the flow accelerates from rest up to a velocity U ∼ 1 ms −1 in a characteristic length L = 10 −3 m—see Figure 1b, so in this case |∇ p |/( ρ g ) ∼ U 2 /( g L ) ∼ O (10 2 ).…”

“…In Reference 26, the gas is injected at the entrance region of a tube, where the flow accelerates from rest up to a velocity U ∼ 1 ms −1 in a characteristic length L = 10 −3 m—see Figure 1b, so in this case |∇ p |/( ρ g ) ∼ U 2 /( g L ) ∼ O (10 2 ). In Reference 27, the gas is injected at the leading edge of an airfoil at an angle of attack α with respect to the incoming free stream of velocity U ∞ , see Figures 1c and 2. In this case, there also exists a very strong favorable pressure gradient at the point where bubbles are generated because the pressure changes from the maximum value at the stagnation point, , to the minimum value at the suction peak, in a distance which is much smaller than the chord c (see Figures 1c and 2).…”

“…Then, defining the pressure coefficient as the pressure gradient at x / c = 0, namely, at the leading edge of the airfoil—see Figures 1c and 2—can be expressed as with the positive value of the (favorable) dimensionless pressure gradient and indicating the arclength along the airfoil surface (see Figures 1c and 2). The numerical values of β , calculated in References 27,28 solving the Laplace equation subjected to the impenetrability condition at the airfoil surface, reveals that β ( α ) ≳ O (10 2 ). Consequently, the value of the pressure gradient is, in this case, comparable with that created using microfluidic geometries 26 because , with U ∞ ~ U and c ≫ L , with L the indicating the constant length, L = 10 −3 m (see Figure 1b,c).…”

“…For the case considered in Reference 27, bubbling frequencies and bubble diameters can be predicted once Equations ) are substituted into Equations ): with L = 10 −3 m and with K f 1 = 1.8 and K b 1 = 1.11 constants which do not depend on the geometry. Indeed, we showed in Reference 27 that the values of K f 1 and K b 1 in Equations ) for the aerator depicted in Figure 1c are the same as in the case of the bubble maker depicted in Figure 1b. Consequently, the results in Reference 27 support the validity of Equations ) in general types of flows whenever the pressure gradient is favorable, viscous stresses are negligible—this is usually verified for low viscosity liquids such as water—and when Bo ≳ O (1)—see Equation ), a condition which can be alternatively written as …”