Simplifying analysis of sorption of SVOCs to particles: Lumped parameter method and application condition

• Application condition of lumped parameter method (LPM) within finite duration.
• The critical Lt is higher than 0.1 and decreases as Fom increases.
• Formula to calculate critical Lt obtained to facilitate practical application.
• Particle-phase SVOC concentration accurately predicted by LPM.
• Greatly facilitate concentration prediction and exposure assessment.

Dynamic mass transfer between semi-volatile organic compounds (SVOCs) and particles needs accurate and simple description for exposure assessment. The lumped parameter method (LPM) is such a simplified approach. The classical condition under which LPM applies in mass transfer is that the Little number (Lt = vtL/D/K, dimensionless ratio of internal resistance to external one) is less than 0.1 when dimensionless excessive concentration is constrained to be less than 5%. It should be noted that the condition above justifies application of LPM from time = 0 to ∞. However, in indoor environments, lifetime of airborne particles tends to be finite, e.g., on the order of one hour. The application condition of LPM for such finite duration has not been clarified. Using dimensionless analysis, we derived a correlation to relates the critical Little number (Ltc) with Fom (Fom = Dt/r2, a dimensionless parameter for duration time). It shows that the applied condition of LPM for finite duration is less strict. For example, if Fom < 10−4, Ltc is smaller than 5.2. To illustrate application of the simplified approach and corresponding accuracy of the results, an example is presented for analyzing the transient mass transfer processes between SVOCs and airborne particles in practical residential buildings. The approach is also useful to address various transient mass transfer problems within finite time.