ABSTRACT
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683
II. Fixed Charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686
A. Dissociation of Functional Groups or Proton Absorption . . . . . . . . . . . . . . . . 686
B. Successive Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 687
C. Absorption or Chelation of Metallic Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688
D. Nonuniform Distribution of Functional Groups . . . . . . . . . . . . . . . . . . . . . . . 689
1. Planar Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689
2. Curvilinear Membrane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690
III. Electrostatic Potential Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691
A. Poisson-Boltzmann Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691
B. Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693
C. Several Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694
1. Low Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694
2. Negatively Charged Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699
3. Positively Charged Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701
4. Numerical Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702
5. Other Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703
IV. Phenomena Related to Biological Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703
A. Cellular Movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703
B. Electrophoresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704
C. Stability of Cell Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705
1. Stability Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705
2. Critical Coagulation Concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705
D. Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706
Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711
Over the past century, the interdisciplinary knowledge about colloids and interfacial phenomena
has gradually developed into a prosperous field in science and engineering. Both theoretical
development and experimental study on macroscopic and microscopic systems have become a
great significance [1]. Recently, the issues related to biological cells have attracted much attention
for fundamental research and application. For the interaction between biological cells and bio-
interfaces or among cells, deposition, adsorption, and flocculation are the most important
phenomena. The knowledge about deposition of cells onto various bio-surfaces is crucial to
understand numerous physiological disorders commonly encountered in practice, for example,
the secondary tumor growth. Cancer cells are transported by blood circulation from the position
of primary tumor to the vascular endothelium of other body tissues during the spread of malignant
tumor. For the deposition of biological cells, two stages are in series, migration to the vicinity of a
solid interface by external field followed by adhesion, are the widely adopted mechanisms [2].
Also, investigations on bio-adsorption behavior and flocculation among biological cells in an
electrolyte solution are essential in understanding the biomedical performance of cells. Obser-
vations for bio-adsorption phenomena include adherence of platelets on a blood-vessel lumen
to generate embolisms [3], adhesion of bacteria on a tooth wall to erode dental enamels [4],
and adsorption of various proteins on an air-water interface to form bubbles [5]. In industrial
process, immobilization technique of microbes on microcarriers in a bioreactor plays an important
role. In addition, typical examples for bio-flocculation are: abnormal aggregation of dysfunctional
platelets inside pathological blood-vessel, yielding fatal consequences like thrombogenesis or cor-
onary thrombus formation and bleeding, and collagen self-assembly under physiological condition
in connective tissue.
