ELSEVIER Understanding Adhesion: A Means for Preventing Fouling R. Oliveira • Adhesion of particulate materials is an important step in the formation Engenharia Biol6gica, of fouling. Because the size of such materials is generally less than 1 tzm, Unicersidade do Minho, the phenomenon can be described in terms of colloid chemistry. Accord- Braga, Portugal ingly, the net force of interaction between foulants and the surface has been described in terms of DLVO theory (van der Waals attraction and electrostatic double-layer repulsion). However, those forces are sometimes not sufficient to describe the formation of fouling. Recent works have made it possible to calculate the effect of hydrophobic interactions and steric forces, which can also be taken into account. In aqueous media, the various types of interactions can be strongly affected by the pH, the ionic strength, the type of ions, and the presence of polymeric molecules. The objective of this work is to give a general overview of the basic physicochemical factors playing a role in fouling and to outline some practical aspects related to the theoretical reasoning to help prevent or at leasl[ mitigate fouling. © Elsevier Science Inc., 1997 Keywords: adhesion, DLVO theory, surface free energy, hydrophobic interactions, steric forces, ionic strength, ion bridging INTRODUCTION tant roles. In bifouling, the adhesion of microorganisms can be strongly dependent on their external appendages. The accumulation of inorganic particles, microorganisms, The net effect is a balance between all possible interac- macromolecules, and corrosion products on heat ex- tions. A knowledge of the roles of the main variables changer surfaces gives rise to the so-called fouling phe- affecting the interactions outlined above is of great impor- nomenon. The development of fouling is perceived as a tance, because their correct manipulation can help to multistage process, of which adhesion of the fouling agents prevent or at least mitigate fouling. to surfaces is an essential step. Fouling occurs when gravitational forces are negligible; DLVO FORCES this means that only particulate materials of colloidal size (with dimensions < 1 /zm) will adsorb onto solid surfaces Van der Waals Forces immersed in flowing fluids. Larger particles are not able to adhere, because gravitational and hydrodynamic forces Van der Waals forces are dependent on the geometry and are strong enough to remove them. on the physical and chemical properties of the interacting The principal attractive forces between colloidal parti- bodies. The most common interacting geometries can be cles are due to van der Waals interactions. However, when very often approximated to a sphere-plate type or to a the particles are immersed in liquid medium, as it is very plate-plate type (two parallel semi-infinite plates), al- often the case in heat exchangers, electrostatic double- though other geometries also can be considered [3]. It is layer forces can develop; these forces are generally repul- customary to calculate energies rather than forces, which sive. Consequently, the adhesion step in a fouling process are easily interconverted, taking into account that force is has been described in the literature in terms of the theory the derivative of energy with respect to distance. The used to explain the stability of lyophobic colloids-- correspondent energy is given, for sphere-plate and two- the DLVO theory, named after B. V. Derjaguin, L. D. plate geometries, respectively, by Landau, E. J. W. Verwey, and J. Th. G. Overbeek [1, 2]. AR In addition to DLVO forces (van der Waals and elec- Vw~ 6H ' (1) trostatic), other types of interactions--such as hydropho- A bic interactions in polar media, ion bridging, and steric interactions in the presence of polymers--can play impor- Vw~" 12IrH2, (2) Address correspondence to Dr. R. Oliveira, Engenharia Biol6gica, Universidade do Minho, 4709 Braga Codex, Portugal. Experimental Thermal and Fluid Science 1997; 14:316-322 © Elsevier Science Inc., 1997 0894-1777/97/$17.00 655 Avenue of the Americas, New York, NY 10010 PII S0894-1777(96)00134-3 Understanding Adhesion 317 where R is the radius of the spherical particle, H is the The potential energy arising from the interpenetration distance of separation, and A is the Hamaker constant. of electrical double layers depends on the geometry of the This constant, which accounts for the molecular nature of interacting bodies and on the electrical behavior during the interacting entities, is named after H. C. Harnaker [4], the interaction. Generally, it is assumed that the interac- who extended F. London's theory [5] to the interaction tions may occur either at constant surface potential or at between solid bodies, assuming the additivity of molecular constant surface charge. interactions. The Hamaker constant for the interaction in An estimate of the energy of interaction for the vacuum of two solid bodies of the same material (i) can be sphere-plate type geometry is given by Eq. (6) when the calculated from the molecular properties of the material interaction takes place at constant surface potential [9] by the relation and by Eq. (7) when the surface charge is kept constant Aii = 3/4qrZNi2ot2hvo, (3) [101. where N/ is the number of atoms per unit volume, a is I"(DOLsp~--- ~'rrR{(~01 + ~/02 )2 In[1 + exp(-KH)] the static polarizability of the atom i, h is Planck's con- stant, and v 0 is the frequency of the electron in the +(¢Ol -- ¢o2) 2 ln[1 - exp(--KH)]}, (6) ground state [6]. For the interaction of two different bodies (1 and 2) in vacuum, the resulting Hamaker con- V~)Ls p ~ -- 8"ffR{(~o 1 - if/02 )2 ln[1 + exp( - KH)] stant is the geometric mean of the individual constants. If the two different materials 1 and 2 are immersed in a medium 3, the overall Hamaker constant is given by +(q'0l + ¢02 )2 In[1 -- exp(-KH)]}, (7) A132 = ( A¢ S. - (4) where VD~L and VI~ L are the potential energies of interac- tion at constant potential and at constant charge, respec- The additivity principle is not strictly valid for con- tively; ~b01 and ~b02 are the electrical surface potentials of densed media interactions. In 1972, Visser [6] presented the flat surface and spherical particle at infinite separa- an excellent review of all the available methods for the tion; R is the sphere radius; e is the electrical permittivity calculation of Hamaker constants. Thenceforward, it is of the medium; and K is the reciprocal double-layer worth noting the work of Israelachvili [7], assuming some thickness, or Debye-Hiickel parameter, given in SI units by simplifications to calculate the Hamaker constants from optical data in the ultraviolet region, and the approach 1000e2NA 2 proposed by van Oss and collaborators [8], based on K 2 ~ ~ziMi, (S) surface free energy calculations. According to the approach based on the surface free energy, the Hamaker constant is calculated by where e is the electron charge, N A is Avogadro's number, K B is Boltzmann's constant, T is the absolute tempera- Zig = yiLWo.24~H2, (5) ture, z i is the counter-ion valence, and M i is the counter- where y LW is the Lifshitz-van der Waals (apolar) compo- ion molarity. 1/K has the dimensions of length, and this is nent of the surface free energy and H 0 is the equilibrium why it is called the double-layer thickness, being always separation between the interacting bodies (see the section related to the ionic strength of the medium. This relation on hydrophobic interactions), determined by the balance arises from the definition of ionic strength (I), which for a between Born repulsion and van der Waals attractive symmetric electrolyte is given by forces. The approach of van Oss et al. [8] is a very simple method, when compared with the tiresome calculations 1 2 I = "~ziM i. (9) based on the optical properties proposed by Israelachvili [7]. Moreover, despite the improvements in the obtention of electromagnetic data, it is still very difficult to have Equations (6) and (7) are valid only for surface poten- enough data for a great number of materials. tials < 25 mV, although they can be used without signifi- cant errors for potentials of as much as 60 mV, when Electrostatic Double-Layer Forces KH > 10 [11]. The condition of constant surface potential is consid- When solid bodies are immersed in a liquid medium, ered to exist if the surface charge is determined by the especially in water, they show a generalized tendency to adsorption of ions, whereas the situation of constant sur- acquire an electrical surface charge, owing to preferential face charge is generally assumed when isomorphic substi- adsorption of ions, by dissociation of surface groups or by tutions take place [11]. The most common case in biologi- isomorphic substitutions in the lattice (e.g., clay minerals). cal systems is an intermediate situation where the surface At neutral pH, most of the solid bodies, including mi- charge is acquired by ionization or dissociation of surface croorganisms, possess a net negative charge. groups. Several models are found in the literature [12-15] The charge acquisition by a surface immersed in an to deal with such complex situations. aqueous medium promotes a redistribution of the ions in There is still a practical impossibility in determining the solution. The ions of opposite charge (counter-ions) will surface potentials; thus, in all the calculations, they are be attracted to the surface, whereas the ions of same sign replaced by zeta potential values [16]. Zeta potential (co-ions) will be repelled. This effect creates an electrical values of small particles are easily obtained by micro- double layer at the proximity of the surface. When two electrophoresis. The same technique can be used for sur- charged solid bodies of like sign approach each other, the faces of macroscopic bodies after grinding; otherwise interpenetration of the two double layers will lead to streaming-potential measurements can be utilized for such repulsion.