INSIGHT - Comments
Vol. 2 No. 2 - What I Wish I Knew About Lyophilization
After reading your last issue, Its a good opportunity to ask for the topic of lyophilization where someone doesn’t know enough. In my case, the heat transfer is my weakest point, I wish I knew more about that. Also, how does the pressure inside the freeze-dryer chamber influence on the mechanisms of heat transfer?
Thanks in advance for your help and assistance
Ing. Orlando Martinez Garcia March 1999
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Instituto FINLAY Apartado 11600
Grupo Nacional de Validacion
Ave 27 No. 19805, La Lisa, Ciudad La Habana
Telefono (53) 7 21 79 11
Fax (53) 7 33 67 54
(53) 7 33 60 75
e-Mail orlando@gnv.finlay.edu.cu
gnv@ceniai.inf.cu
Cuba
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Response by Dr. Jennings
In answer to the first part of your question you should be aware that energy is the main driving force for the lyophilization process. Energy must be removed in order to freeze the product and added to conduct the primary and secondary drying processes. The rate for each step of the process will depend on the heat transfer rate. In its simplest form the heat transfer rate (q) of a system can be expressed as
q = (KA/d) [T(1) - T(2)] cal/sec (1)
where K is the thermal conductivity of the system, A is area, d the thickness and (in the case of lyophilization) T(1) could represent the shelf temperature while T(2) is the product temperature. It is assumed that the heat transfer associated with gas thermal conductivity and radiant energy are insignificant.
In the case of the primary drying process, q will be directly proportional to (T(1) - T(2)). If T(2) were to remain constant, then the rate of sublimation will directly related to q.
Now the second part of your question assumes that you have a firm understanding of the phase diagrams and in particular for that of water. For example, it should be understood that at pressures lower than 4.58 Torr there will only be two phases present at the ice-gas interface (vapor and ice) and the temperature of the ice surface will be determined by the vapor pressure of water vapor at the ice surface.
Now in the above example, we increase the pressure in the system such that the heat transfer rate (qg) resulting from the thermal conductivity of the gases in the chamber become significant. In general, this would require pressures ³ 100 mTorr. With T(1) constant, T(2) will increase along with an increase in the temperature of the ice at the interface (T(1)). If the temperature differential across the frozen matrix (T(2) - T(i)) is increased, then there will be an increase in the sublimation rate. However, if the pressure in the system were increased to where it would equal the vapor pressure of ice at T(1), then T(1) = T(2) and q will approach zero. If q approached 0 then the sublimation rate, for all practical purposes will also approach zero and drying is done by diffusion rather then by the flow of gases from the container. The lesson here is that one should not indiscriminately increase the chamber pressure without knowing the effect that it will have on the heat transfer rate. Second, if the increase in T(2) exceeds the collapse temperature then one may find themselves vacuum drying rather than lyophilizing and find that the final cake exhibits collapse or meltback (see the Figure associated with the seminar notes on the web site).
Response by Ing. Orlando Martinez Garcia
First, I will talk about my weakest point. I understood what you have explained but I really want to know about the other mechanisms (radiation and convection). I read somewhere I don't remember now that there was a relationship between pressure and these transfer mechanisms. For example, when the pressure is too low, the heat transfer by convection is no significant because of the absence of gas molecules able to transfer the heat, then the transfer mechanism by conduction prevails above the convection one . I am no sure if it's right or wrong. This subject comes to my mind because I remembered your INSIGHT issue Vol.1 No.8 "Getting A Handle on the Freeze-Dryer Door" when you talked about the transfer heat through the door of the freeze-dryer. When you said: " It is assumed that the heat transfer associated with gas thermal conductivity and
radiant energy are insignificant ". This what I want to know, that is to say, the theory about the different mechanisms of heat transfer, what happens when the pressure increase or decrease and how this could affect the heat transfer and why. I hope you could understand what I try to say.
Ing. Orlando Martinez Garcia March 1999
===============================================
Instituto FINLAY Apartado 11600
Grupo Nacional de Validacion
Ave 27 No. 19805, La Lisa, Ciudad La Habana
Telefono (53) 7 21 79 11
Fax (53) 7 33 67 54
(53) 7 33 60 75
e-Mail orlando@gnv.finlay.edu.cu
gnv@ceniai.inf.cu
Cuba
===============================================
Response by Dr. Jennings
First of all you are quite correct that convection does not play a part when the drying chamber is under vacuum. It can be, however, a factor during the freezing process. For freezing performed on the shelves of the dryer, convection will be a factor in the heat transfer of energy from the walls of the chamber and the door. A poorly thermally insulated drying chamber can impose a limit to the minimum shelf temperature. Should this limit prevent the formation of a frozen matrix, then one experience “puffing” .
For your second point, it should be understood that the statement “It is assumed that the heat transfer associated with gas thermal conductivity and radiant energy are insignificant” appears in my first response to your question and not in Vol. 1 No. 8 - Getting A Handle on the Freeze-Dryer Door. I made the above assumption to simplify the discussion so that equation 1 would be the main source of energy during the drying process.
Now let us take the discussion one step further and assume that the pressure is still low so that gas thermal conductivity is not a factor but the shelf temperature is 25 oC and the product temperature is -50 oC. With such a large temperature differential radiant heat transfer (qr) now becomes a contributing factor to the energy transferred from the shelf to the product. Such a heat transfer rate qr can be expressed by Stefan’s Law, i.e.,
qr = 5.67 x 10-12 [e(1)T(1)4 - e(2)T(2)4]
where the temperature T is expressed in K (degrees Kelvin) and the term “e” is the emissivity of the respective surfaces.
Now when we increase the pressure (e.g., >100 mTorr) then the contribution from the thermal conductivity of the gases in the chamber becomes a contributing factor to total energy transfer and qg can be expressed as
qg = A’ 4/3 La Pu [273.1/T(2)]1/2 [T(1) - T(2)] watts (3)
where A’ is the area, La is the thermal conductivity of the gas and Pu is chamber pressure in mTorr. Please note that A’ in equation 3 differs from that in equation 1. In equation 1, A will represent only 2% to 5% of the cross sectional area of the vial, whereas, A’ will approach the total cross sectional area.
Once again, I must caution that an increase in the energy heat transfer may not lead to an increase in the sublimation rate of ice at the gas-ice interface.
