Paper
Green Chemistry
removing a primary reactant, noting that this is consistent sufficient to overcome the capillary forces to break the fluid
with the high surface area of thin films present in the VFD.
Reagent delivery into a hydrophilic sample tube15 (Fig. 3A
and C) established the optimal rotational speed of 6950 rpm
for enhancement of the reaction. This is slightly different to
reagent delivery into a hydrophobic tube, with a shift in
optimal rotational speed to 7000 rpm (Fig. 3B and D). Given
that these rotational speeds are similar, but not exact, the
surface coating has a direct effect on the optimal rotational
speed. The rotational landscape is less erratic when reagent
delivery occurs on the wall of the sample tube (Fig. 3C and D).
This suggests that some phenomenon exists in the hemisphere
of the sample tube that contributes further to VFD-mediated
enhancement.
film. This occurs when the droplet radius reaches
ꢀ
ꢁ
1=3
3γrn
2ρg
a ¼
;
ð2Þ
where ρ is the density of the fluid, γ is the surface tension of
the fluid and a is the acceleration due to gravity. For Q =
0.50 mL min−1, this equation predicts around 30 drops per
minute. This prediction matched the experimental outcome
for methanol. Each drop falls vertically from the tip of the
needle and lands in the hemisphere end of the rotating
sample tube (Fig. 2). A viscous Stokes boundary layer of scale
thickness
ꢂ ꢃ
1=2
ν
The majority of VFD-mediated reactions use standard boro-
silicate sample tubes with reagents delivery occurring in the
hemisphere at the base of the tube. At the rotational speeds of
6000, 6400, 6650 and 6950 rpm there is VFD-mediated
δ ¼
;
ð3Þ
Ω
forms at the base of the droplet, with the fluid in it accelerat-
ing azimuthally to experience a centrifugal force throwing it
radially outward. Here, ν is the kinematic viscosity and Ω is the
angular velocity of the tube. This expulsion of fluid (now rotat-
ing) from beneath the drop brings new fluid (not yet rotating)
is in contact with the boundary in a manner similar to that
found in an Ekman layer.18 The fluid expelled from beneath
the droplet drains radially in a spiralling motion with viscous
stresses balancing the centrifugal force. The maximum shear
stress experienced during the initial acceleration, scaled as:
enhancement. This presumably arises from
a harmonic
vibration creating a Faraday wave within the sample tube. The
Faraday wave which results, is hypothesised to prolong high
shear stress on the reagents, increase micromixing and
shorten reaction paths, all contributing to the observed
increase in yield.
An emerging concept in VFD flow chemistry is the ability to
alter the fluids surface tension during processing. At the
microscale, high shear stress rates lead to changes in the
fluids surface tension. The changing surface tension could
facilitate the removal of water, thus enhancing the position of
1
2
3
σ ¼ ρðνΩ Þ ;
ð4Þ
equilibrium (vide supra). Indeed, we observe a condensate although high shear is sustained as the fluid drains radially
forming on the jet feeds and exit tubing during VFD proces- outwards and up the hemispherical end of the tube. The drain-
sing. The room temperature removal of the water by-product ing film eventually merges with the film of fluid coating the
may explain the VFD-based equilibrium enhancement com- inside of the inclined rotating tube. The time taken for the
pared to a non-VFD-mediated solution. This is a phenomenon fluid to drain out of the hemisphere plays a key role in setting
that we are currently exploring in detail.
the maximum flow rate. Through understanding how to maxi-
mize the shear stress on the reagents as they enter the VFD,
more efficient reaction design can be achieved, helping to
generate more efficient processing. The droplet itself is acceler-
Flow rate considerations
Understanding the effect of flow rate allows the design of more ated into the established thin film on a time scale
efficient continuous flow protocol. Typically, the flow rate
determines the residence time of reagents; however, through
this work we have discovered that flow rate plays an important
1
2
τ ¼ a=ðνΩÞ ;
ð5Þ
whereas the thickness of the remnant film decreases gradually
as:
role in micromixing and the level of shear stress generated. In
synthesizing di-esters, the flow rate, Q, was varied from
0.20 mL min−1 to 1.00 mL min−1 and the yield monitored
(Fig. 4) A range of di-acids (C5–C10) and alcohols (methanol,
ethanol, n-propanol and n-butanol) were chosen as reaction
partners. The results indicate that the flow rate is highly
important for reaction optimization. In maturing an under-
standing of this phenomenon, we now develop a model of the
fluid flow in the VFD.
ꢂ
ꢃ
1=2
ν
Ω2t
h ꢀ
;
ð6Þ
which emphasizes that it could take a long time for the thin
film to flow (drain) from the hemisphere and into the thin
film up the tube, leading to different shearing rates within the
rotating tube. Based purely on the acceleration phase, these
scaling arguments predict a reactant feed upper limit of
The feed stream containing the reactants is introduced at a
mean flow rate, Q, through a metal feed tube of radius rn
(internal diameter – 2.04 mm). Although Q is continuous,
1
2
2
Q ꢀ a ðνΩÞ ;
ð7Þ
surface tension promotes the formation of droplets at the tip which is around an order of magnitude greater than the optimal
of the needle. A droplet grows in size until its weight is conditions found here. This suggests that, as expected, many
Green Chem.
This journal is © The Royal Society of Chemistry 2015