where V is the cumulative volume of filtrate water, A is the effective

area for filtration, Dp1 is the pressure difference across the algal cake-layer as shown in Fig。 2, l is viscosity of water, and R is the

hydraulic resistance of the cake-layer。 Algal  cake-layer resistance is assumed to be proportional to the cake-layer thickness, ‘,   by,

R ¼ bðralgae; eÞ· ‘ ð2Þ

where b is the specific resistance of the cake-layer, related to   ralgae

and porosity e of the algal cake-layer。

Cake-dewatering compartmentAlgae feed vessel

 Water pump

Fig。 1。 Flow-chart of algae-dewatering using a rotary drum vacuum filter with three distinctive zones for algae-filtering, algae-dewatering, and algae-discharging。

P。 Shao et al。 / Chemical Engineering Journal 268 (2015) 67–75 69

Fig。 2。  Algal cake-layer containing network pathways for water filtrate and the structure of the underneath filter medium。

According to Kozeny and Carman [24–26], the specific resis- tance is determined  by,

Inserting Eq。 (11) into Eq。  (7)    yields,

where K is a constant equal to 5 for spherical packing [24,25], and Sv is the surface area contained in a unit solid volume of the packing。 Thus,

Substituting Eq。 (12) to Eq。 (6)  yields

Eq。  (13)  is  the  fundamental  equation  governing  water trans-

Inserting  Eq。  (4)into  Eq。 (3)yields45ð1 — eÞ2

port through the network channel as  depicted  in  Fig。  2。  Dp1  is the   driving  force   for  water   transport  through   the  cake-layer,

and the denominator term represents  the  hydraulic  resistance for the  filtrate water, revealing that  a  larger filter  area, a    bigger

Inserting Eq。  (5) into Eqs。 (2) and (1)  gives Eq。    (6)

  algaeA · Dp1

algal size, a greater cake-layer porosity, and a lower algae concen- tration  all  contribute  to  smaller  hydraulic  resistance  for   water

6 transport。

dt ¼ 45ð1 — eÞ2 l · ‘ ð Þ

The thickness of algal cake-layer is determined by the volume of the algae accumulated on the surface of filter medium    by

ð1 — eÞA‘ ¼ V algae ð7Þ

The volume fraction of algae in the algae feed is dependent upon the algae concentration, which is defined in Eq。 (8)。 Note in wet algae, about 60% are dry algal biomass [17],

V algaeqalgae m 0:6

3。2。 Transport of filtrate water through the filter    medium

The filter medium either in cloth, polyester mesh or nylon- coated metal thread for the rotary drum vacuum filter is consid- ered to have uniform permeability over its entire surface。 To facilitate the treatment of mass transport through these usually non-cylindrical pore  structures,  they are modeled as  an array    of

uniform cylindrical pores of a hydraulic radius。 The equivalent pore

size of these media is determined by [27] Eq。   (14),

where V algae is the volume of the wet algae, and qalgae is the specific gravity of the wet algae。 According to Eq。 (8), the volume fraction of algae in the algae feed can be written   as: