During Phase Transition
3.2 Flow and Aggregation Characteristics of Thermo-responsive Spheres During
3.2.3 Flow Characteristics of PNIPAM Hydrogel Spheres During the Phase Transition in a Transparent Glass Pipe
The inner wall of the transparent Pyrex glass pipe is pretreated to be hydrophilic [3].
In the measuring section between point A and point B (Fig.3.1b), the temperature range is designed to include the LCST of PNIPAM. The interior diameter of the pipe is 6.4 mm, and the length of section AB is 400 mm. Digital pickup camera is used to record flow behaviors of PNIPAM spheres inside the pipe during the phase transition. Because the operating temperature of the rotameter flowmeter should be the room temperature (about 20 ºC), much lower than outlet temperature (about 43 ºC), a cooling bottle is used. Before the experiment of measuring the flow characteristics of the spheres, the following considerations should be confirmed.
First, it is necessary to confirm that the range of Reynolds number falls in laminar flow, since the character of blood flow is viscous laminar flow in micro-blood circulation system. The pressure drops are measured at different flow rates; the results show that the Reynolds number for laminar flow should be lower than 547.
Therefore, the flow rates in the subsequent experiments are selected from 20 to
0 1 2 3 4 5 6 7
a 8
b
Temperature [°C]
Volume change ratio [ -]
0 10 20 30 40 50
0
0 10 20 30 40 50 60
10 20
30 40
Position [cm]
Position B Position A
LCST
T [°C]
Fig. 3.1 Thermo-responsive volume-phase transition characteristics of PNIPAM hydrogel spheres (a) and temperature distribution along the glass tube (b) (Reproduced with permission from Ref. [3], Copyright (2006), Elsevier)
60 ml/min. At each flow rate, PNIPAM hydrogel spheres with the same diameter are put into the pipe and the motions are recorded. Second, the temperature distribution along the testing tube should be confirmed. Considering the classical principle of convection heat transfer in the counterflow heat exchanger, the boundary conditions of constant thermal flow density is used to indicate that average temperature of liquid varies linearly along the testing tube from inlet. Figure 3.1b shows the temperature distribution along the testing tube, in which “position” is the position fixed on the tube section AB, “0 cm” stands for the inlet point B, and “40 cm”
meant the outlet point A. The average velocities of PNIPAM spheres in the pipe are calculated through the distance and time interval. A series of corresponding figures are snatched by media software from the videos of flow behaviors of the spheres when they are replayed.
3.2 Flow and Aggregation Characteristics of Thermo-responsive Spheres. . . 63
0 0.2 0.4 0.6 0.8 1 1.2
7~4 10~7 13~10 16~13 19~16 22~19 25~22 28~25 31~28 34~31 37~34
Position [cm]
Average velocity [cm/s]
flow
Fig. 3.2 Process of phase transition of a PNIPAM hydrogel sphere (a) and velocity variation of the PNIPAM hydrogel sphere during the process of phase transition in glass pipe (b). The fluid flow rate is 20 ml/min, and the unit for the position scale in (a) is cm (Reproduced with permission from Ref. [3], Copyright (2006), Elsevier)
Many interesting phenomena about the flow behaviors of PNIPAM hydrogel spheres are found during the phase transition. For one PNIPAM sphere (see Fig.3.2a), the process of phase transition is obvious along the pipe when the water temperature is increased across the LCST of PNIPAM. From the position scale of 10 cm (TD28ıC) to 19 cm (TD32.5ıC), the diameter of the sphere decreased rapidly while the velocity of it slowed down sharply (see Fig.3.2b). On the other hand, before and after this section, the diameter of the sphere had little change as well as the velocity. Because the smaller the sphere became, the closer it came to the bottom of laminar flow, the slower the average velocity of fluid became, and then the less the impetus force on the sphere became (see Fig.3.3a, b). The forces acted on the sphere are illustrated in Fig.3.3a, b. The drag force (F) and lift force
Fig. 3.3 (a, b) Forces acted on a PNIPAM hydrogel sphere in horizontal pipe before the phase transition (T<LCST) (a) and after the phase transition (T>LCST) (b). u0is the average velocity of fluid. (c) Forces and moments acted on two PNIPAM hydrogel spheres (with no initial distance) just after the phase transition in horizontal pipe and (d) flow and volume-change behavior of two PNIPAM hydrogel spheres (with a initial distance) during the process of phase transition in horizontal pipe (Reproduced with permission from Ref. [3], Copyright (2006), Elsevier)
3.2 Flow and Aggregation Characteristics of Thermo-responsive Spheres. . . 65
(T) are the result of pressure and shear stress that can be obtained by the integration of pressure and shear stress across the surface of the sphere [6]. Fbis the buoyancy force, N is the supporting force from the pipe wall, and f is the friction force that can be calculated as
f DN D .GFbT / (3.1)
whereis the coefficient of friction.
From Fig. 3.3a, b and Eq.3.1, it can be concluded that when the gravity of agglomerate of PNIPAM spheres (after aggregation) is so large that the friction force became bigger than the drag force (f>F), they would stop moving.
For two PNIPAM spheres, three conditions are introduced as follows: There is no initial distance between them at the entrance of pipe section AB, and the initial distances are 5.5 and 8.5 mm, respectively. Under the first condition, two spheres with no initial distance move forward steadily side by side; however, when they come to the position scale of about 15 cm, at which the temperature is 30.5ıC, their diameters decreased dramatically and the velocity slows down. When they come to the position scale of 18 cm, something interesting happens, i.e., the two spheres start to overturn and subsequently roll forward with the two spheres aggregating together. At high temperature (T>LCST), the hydrophobic effect of the PNIPAM hydrogel sphere surface makes them aggregate together. Because the velocity of fluid upside the sphere is bigger than that downside, as well as the existence of friction of pipe wall, when the friction force is larger than drag force (f>F) and the sum of moments MF,MFb, and MT is also larger than moment MG
(MFCMFbCMT>MG), an anticlockwise resultant moment occurred and made the two spheres overturn (see Fig.3.3c).
When the initial distance between the spheres is 5.5 mm at the entrance of pipe section AB (as shown in Fig.3.4a), the two spheres move forward with the distance keeping 5.5 mm at first. However, as phase transition goes on, the distance between them becomes closer and closer, especially from the position scale of 10 cm (TD28ıC) to 14 cm (TD30ıC). At the same time, the velocity of the two spheres decreases sharply in this section, while the difference between the two velocities is bigger than anytime else (see Fig.3.4b). From the position scale of 7 to 14 cm, the average velocities of sphere 2 are always larger than that of sphere 1; therefore, the distance between them becomes closer and closer. Finally they aggregate together after the phase transition due to the hydrophobic effect of the PNIPAM hydrogel spheres. Like the condition mentioned above, the two spheres roll forward subsequently. Before the phase transition, the velocity of fluid is almost the same as the velocity of the sphere; so at that time, there is little wake flow.
With the temperature increasing, since the velocity of sphere decreases, the velocity of fluid is larger than the velocity of the sphere, the fluid would flow around the sphere, and wake flow of sphere 2 enhances and makes the sphere 1 slow down.
0 0.2 0.4 0.6 0.8 1 1.2
7~4 10~7
13~10 14~13
17~14 20~17
Position [cm]
Average velocity [cm/s]
sphere2
sphere1 flow
b a
Fig. 3.4 Flow and aggregation characteristics (a) and velocity variation (b) of two PNIPAM hydrogel spheres (with initial distance of 5.5 mm) during the process of phase transition in horizontal pipe. The fluid flow rate is 20 ml/min, and the unit for the position scale in (a) is cm (Reproduced with permission from Ref. [3], Copyright (2006), Elsevier)
On the other hand, sphere 1 is in front of sphere 2, so the phase transition of sphere 1 as well as the decrease of velocity would be earlier than sphere 2. Because of the two effects, the two spheres come together, while the latter plays a more important role (see Fig.3.3d).
When the initial distance between the spheres at the entrance of pipe section AB (as shown in Fig.3.5a) comes to 8.5 mm, with the temperature increasing, the distance becomes close at first and then becomes far after the phase transition, and the two spheres do not aggregate together during the phase transition. The analysis of the average velocity of two spheres is shown in Fig.3.5b. It indicates that the average velocity of sphere 1 slows gently, whereas the average velocity of sphere 2 slows dramatically from the position scale of 13 cm (TD29.5 ıC) to 19 cm (TD32.5ıC). It is also found that the two PNIPAM spheres would never aggregate together during the phase transition when the initial distance between them at the entrance is larger than 8.5 mm.
If PNIPAM spheres aggregate together during the phase transition, different aggregation configurations for different numbers of spheres would be formed and then roll forward. For three PNIPAM spheres, if they aggregate together during the phase transition, they would form a regular triangle and then roll forward. A regular
3.2 Flow and Aggregation Characteristics of Thermo-responsive Spheres. . . 67
0 0.2 0.4 0.6 0.8 1 1.2
a
b
7~4 10~7 13~10 16~13 19~16 22~19 25~22 28~25 31~28
Position [cm]
Average velocity [cm/s]
sphere2
sphere1 flow
Fig. 3.5 Flow characteristics (a) and velocity variation (b) of two PNIPAM hydrogel spheres (with initial distance of 8.5 mm) during the process of phase transition in horizontal pipe. The fluid flow rate is 20 ml/min, and the unit for the position scale in (a) is cm (Reproduced with permission from Ref. [3], Copyright (2006), Elsevier)
tetrahedron would be formed for four PNIPAM spheres, a regular hexahedron would be formed with five spheres, and a regular octahedron would be formed with six spheres. At flow rate of 20 ml/min, a series of regular aggregation configurations of PNIPAM spheres during the phase transition are found. Because the fluid impetus on the spheres decreases as the phase transition goes on, when the impetus decreases to equal the friction of inner wall of the pipe, the spheres themselves would aggregate together owing to the impetus and then roll forward as rolling friction is smaller than breakaway friction. Furthermore, because the spherical particles with the same diameter gather together according to the best thick fill, i.e., the least interstice ratio,
Fig. 3.6 Flow and aggregation characteristics of ten PNIPAM hydrogel spheres (with initial distances less than 5.0 mm) during the process of phase transition in horizontal pipe. The fluid flow rate is 20 ml/min, and the unit for the position scale is cm (Reproduced with permission from Ref. [3], Copyright (2006), Elsevier)
these arrays are the most stable among all cases. When the number comes to ten, different phenomena occurred (see Fig.3.6). Since the agglomerate of PNIPAM spheres becomes too big, according to Eq.3.1, friction between pipe wall and the agglomerate is much bigger than fluid impetus on the agglomerate (f>F), and because the size of the agglomerate of the spheres is too big to roll inside the pipe or the sum of moments MF,MFb, and MT is smaller than moment MG(MFC MFbCMT<MG), the whole agglomerate stops at the position scale of 19 cm where the temperature is about 32.5 ºC after the phase transition. The above-mentioned phenomenon indicates that local heating on pathological part could be used to make thermo-responsive drug carriers slow down and even stop and release drugs there to achieve site-specific targeting therapeutic effects.