Floc size distributions of suspended kaolinite in an advection transport dominated tank: measurements and modeling

Abstract

In estuaries and coastal waters, floc size and its statistical distributions of cohesive sediments are of primary importance, due to their effects on the settling velocity and thus deposition rates of cohesive aggregates. The development of a robust flocculation model that includes the predictions of floc size distributions (FSDs), however, is still in a research stage. In this study, a one-dimensional longitudinal (1-DL) flocculation model along a streamtube is developed. This model is based on solving the population balance equation to find the FSDs by using the quadrature method of moments. To validate this model, a laboratory experiment is carried out to produce an advection transport-dominant environment in a cylindrical tank. The flow field is generated by a marine pump mounted at the bottom center, with its outlet facing upward. This setup generates an axially symmetric flow which is measured by an acoustic Doppler velocimeter (ADV). The measurement results provide the hydrodynamic input data required for this 1-DL model. The other measurement results, the FSDs, are acquired by using an automatic underwater camera system and the resulting images are analyzed to validate the predicted FSDs. This study shows that the FSDs as well as their representative sizes can be efficiently and reasonably simulated by this 1-DL model.

Appendix A Details of the underwater camera system

This system was developed to measure the FSDs of kaolinite suspensions. This camera system is improved based on that given by Shen and Maa (2016a). It includes a Sony Alpha NEX-5R camera body with 4912 × 3264 pixels for images, a NEX E mount to Nikon F mount adaptor, three Kenko extension tubes (36 + 20 + 12 mm), a Nikon Macro Nikor 55 mm lens, and a +10 close-up lens that mounted sequentially (Fig. 14). These settings magnify the subject, from a subject size of 10.7 × 7.2 mm to an image size of 23.5 × 15.6 mm, i.e., a subject-to-image ratio (SIR) of 1: 2.2, and thus, changes the resolution from 4.8 μm per pixel to 2.2 μm per pixel. Using at least 2 × 2 pixels to identify a floc, the minimum sphere equivalent floc size that can be identified by this camera system is around 5 μm, which is roughly consistent with the primary particle median size of cohesive sediment minerals in the natural environment. The shutter speed is set to 1/1000 s to catch the fast moving particles, the aperture is set at the maximum, f/2.8, to receive more lights and to limit the focus depth to about 2 mm. The ISO is set to 100 to minimize noise which may be considered as primary particles or small flocs. The trigger to take pictures is controlled by a commercially available remote control unit which is powered and controlled via a four-pin connector, J2, on the control board.

The major improvement on the current system is to replace the original LED light source by a 150 mW green laser module with a concave lens to spread the laser light. This laser module is mounted on the same side of the camera lens (i.e., front illumination) and points to the center of the image window. It is connected and controlled by the control board via a three-pin connector, J1. The above components are assembled and protected in a PVC tube with one cover made by PVC plate, and the other made by a 23-mm-thick plexiglass plate to allow pictures to be taken. Through air dielectric, the distance between the subject and lens (DSL) is slightly larger than 23 mm, but it increases to 29 mm when the plexiglass cover is placed between the lens and the subject. This gives around 5 mm distance between the cover and the front of the camera lens to take pictures for any subject that is within 1 mm of the other side of the plexiglass cover. The power for this camera system is provided by a set of four 18,650 lithium rechargeable batteries (i.e., 16VDC) inside the PVC tube via the connector, J3. This power is converted to 3.7 V to provide power for the laser source, converted to 5 V for the microcontroller, and converted to 3 V for the camera remote control. A magnetic switch which is attached on the PVC cover can be turned on if a magnetic bar is placed on the other side of the PVC cover. Once the switch is closed, the microcontroller begins to work following the instruction of the control program. This program generates periodic pulses which are fed into the gate of two field effect transistors (FETs), (i.e., 2N7000 and RFP2N08L, respectively) which behave as two electronic switches, K1 and K2. The timing of these two pulses match so that when the camera is taking images, the laser light is on. The program is set to take pictures every 2 s until the battery for the camera is exhausted. Nevertheless, this system operates for about 3 h before the batteries need to be changed. This working duration is sufficient for the current application, and much longer than the previous system (Shen and Maa 2016a) that uses LED light source. For field measurements in a typical tidal estuary, more improvements can be arranged to extend the operation duration. Finally, the acquired floc images are processed using the MATLAB Image Processing toolbox to statistically find the FSDs (Shen and Maa 2016a).

Fig. 14

Schematic diagram of the controlling system for acquiring images