## 2 Characteristics of Biofilm Growth in Porous Media
### Nuclear Magnetic Resonance Measurement  
Nuclear magnetic resonance (NMR) T\({}_{2}\) imaging of biofilms in porous media is a direct measurement of the number and state of \({}^{1}\)H nuclei in the biofilm matrix and pore space. After being excited by a radio frequency (RF) pulse, the nuclei relax to their initial equilibrium. The spin-lattice relaxation time T\({}_{1}\) and spin-spin relaxation time T\({}_{2}\) can be used to characterize such relaxation progress. They are both affected by the physical and chemical environment (e.g., pore size and paramagnetic ions). The amplitude of the obtained NMR relaxation signal is directly proportional to the amount of water molecules that are contained in biofilms and pore space. The phase shift of the measured signal can be used to determine the displacement that arises from the fluid flow, which is the basis for NMR velocity imaging. More details about NMR imaging can be find in many articles [68, 69, 70]. There are many studies involving NMR measurement of biofilms such as those investigating hydrodynamic dispersion, mass transfer, and transport processes in porous biosystems as well as the structure of biofilms in a porous bioreactor. The growth of biofilm in fluids and the flow anomalies associated with this process have been measured by NMR imaging. In an NMR T\({}_{2}\) image (Figure 4a), the light area with high T\({}_{2}\) values represents the bulk water, while the darker area with low T\({}_{2}\) values represents the biofilm [43]. Contrast agents without any effects on the growth of the biofilms were added to the feed to decrease the experiment time or to enhance the boundary between the biofilm and the bulk water. \begin{table}
\begin{tabular}{c c} \hline \hline
**Contrast Agent** & **Disadvantages** \\ \hline Hollow silver-coated microspheres [54] & Toxic \\  & Limited surface attachment \\ \hline Mixture of barium sulfate and potassium & Toxic \\  & Fast sedimentation \\  & Heterogeneous distribution \\ \hline
1-Chloronaphtalene [20] & Toxic \\  & Immiscible with water \\ \hline  & Less soluble \\  & Form colloids \\ \hline  & Toxic \\  & Fast sedimentation \\  & Heterogeneous distribution \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The disadvantages of contrast agents used in this review. Through NMR T\({}_{2}\) imaging, the non-uniform structure of biofilms growing with time can be monitored nondestructively [43; 45; 46]. The internal structure of biofilm matrix, such as holes, can also be detected [45; 46]. NMR velocity measurement is different from PTV measurement mentioned in X-ray method. PTV measurement is a detection for track of flowing tracer particles [57], whereas NMR velocity measurement is a measurement for residual phase shift of nuclear spins varying with time [46]. Through NMR velocity imaging, fluid velocity redistribution induced by the growth of biofilm development can be obtained as well as the local shear stress [43; 45; 46]. The change of velocity field leads to the change of mass concentration field, which affects the mass transport from bulk to biofilm [71; 72]. Therefore, the measurement of velocity field is crucial to the analysis of mass transport between biofilm and fluid. When the NMR technique is used to map the growth of biofilm in porous media, the problem becomes complicated. The spatial resolution restricts the NMR instrument's capacity to structure images of biofilms in pore space. [PERSON] et al. [58] performed biofilm growth experiments in a transparent parallel plate reactor and a bioreactor with glass beads in it, and employed the nuclear magnetic resonance imaging technique to identify and image biofilm growth. The diameter of the glass beads used to model the porous media were between 1 and 1.5 mm. As a result, the distance between particles (glass beads) was large (if the beads are packed tightly, the distance can reach a maximum value of 1000 \(\upmu\)m, while the thickness of the biofilm is about 300 \(\upmu\)m at most) [4; 73; 74; 75], leading to the early success in imaging.