Adsorption of Viruses on Activated Carbon Adsorption of Escherichia coli Bacteriophage T4 on Activated Carbon as a Diffusion-Limited Process John T. Cookson, Jr.’ California Institute of Technology, Pasadena, Calif. Theory
Adsorption of Escherichia coli bacteriophage T ? on activated carbon was interpreted as a diffusion-limited process. A diffusion-limited model was developed by solving the diffusion equation with a Langmuir adsorption boundary condition. Data obtained for optimum adsorption conditions were applied to the theory yielding an experimental diffusion cofficient range of 5.6 X to 16.6 X 1 0 P sq. cm. per sec. for bacteriophage T1. This diffusion coefficient is in excellent agreement with the accepted range of 4 X to 8 X 10W sq. cm. per sec. A diffusion-limited theory may also represent adsorption at conditions other than the maximal ; however, under these conditions a clear conclusion on the limiting process cannot be made.
As indicated for adsorption on host cells, virus adsorption by activated carbon may be diffusion limited. Although agitation was provided, concentration gradients were present in the neighborhood of the carbon particles. This condition would manifest itself as a resistance to mass transfer near the carbon’s surface, where adsorption rate is limited by the diffusivity of the virus. The amount of virus n, carried to area A of the carbon can be expressed by Fick’s first law. Adsorption is limited by diffusion in the liquid phase of small virus particles toward large, essentially stationary carbon particles. Microscopic observation of carbon particles indicated that they are approximately spherical in shape. dn, dt
=
- D A N - dn dr
where
T
he need of processes for the removal or inactivation of water-borne viruses has been demonstrated beyond question by their transmission in polluted streams and drinking water. Supposedly purified drinking water has been found to carry animal viruses (D’Silva, 1957; Kabler et al., 1961). Adsorption appears to play a major role in virus removal. Virus adsorption occurs in the activated sludge, flocculation, and filtration processes. The author has previously reported on equilibria and kinetics of Escherichia coli bacteriophage Tq adsorption on activated carbon (Cookson and North, 1967). The present report is concerned with the development of a diffusion-limited model for adsorption based on the von Smoluchowski equation and Langmuir isotherm. Previously presented data (Cookson and North, 1967) for bacteriophage T4 adsorption on activated carbon are analyzed by the diffusionlimited model. Adsorption of Escherichia coli bacteriophage T4 o n activated carbon has been shown to be reversible, to obey the Langmuir isotherm, and conform to reversible second-order kinetics (Cookson and North, 1967). Under optimum adsorption conditions, however, a plausible interpretation may be provided by a diffusion-limited model. Adsorption of bacteriophage to host cells has been analyzed in terms of the von Smoluchowski theory of diffusion-limited processes. Under optimum conditions, adsorption rate is equivalent to the diffusion rate (Puck et al., 1951 ; Delbruck, 1940; Delbruck er al., 1950). The success in attachment to host cells is almost loo%, each collision resulting in adsorption. Host cell adsorption capacity is that of a close-packed, single layer of viruses (Garen, 1954). Present address, Department of Civil Engineering, University of Maryland, College Park, Md.
n,
=
n = D = A =
N = t = r =
the concentration of adsorbed virus, virus particles/ cu. cm. the concentration of virus in solution, virus particles/ cu. cm. virus diffusivity, sq. cm./sec. the surface area of a spherical carbon particle of radius a, sq. cm. the concentration of carbon particles with radius a, number of particles/cu. cm. time, sec. distance from the carbon particle, cm.
The concentration gradient is expressed by dnldr. Substituting 4 w 2 for A and integrating the right side of Equation 1 between limits of a to 03 and n, to n, for r and n, respectively, yields :
* dt
=
-47raDN(n, - n,)
where a is the radius of the carbon particle, and n, and n, are the virus concentrations in solution at the carbon surface and in the bulk of the solution. The rate of adsorption would be expressed by the constant k = 4 r a D N . Adsorption equilibrium will exist at the carbon-solution interface. Hence, a virus back pressure is exerted at the surface, which is proportional to the fraction of utilized sites. The back pressure can be incorporated into the diffusion equation with the aid of the Langmuir isotherm. The Langmuir equation can be expressed as follows : (3)
where q is the number of virus particles adsorbed per milligram of carbon, K is the equilibrium constant, ce is the virus Volume 1, Number 2, February 1967 157
concentration in solution at equilibrium, and Z is the number of sites per milligram of carbon. At equilibrium, ce is equivalent to n,. If C, is the concentration of carbon (milligram per milliliter), then the surface concentration of adsorbed virus particles, n,, can be expressed as n, = qC,. The initial site concentration, likewise, is cs = ZC,. Substituting into Equation 3 and solving for n, yield : (4) The virus concentration in the bulk of the solution, n,, plus the concentration of adsorbed viruses, nu, must equal the virus concentration at zero time in the bulk solution:
n,
+ n, = n,,
(5)
Substituting Expressions 4 and 5 into Equation 2 gives the rate Of virus adsorption to N carbon particles of radius a as the net result of a driving force and back pressure: dna -dt
=
K(cs
-
Ha)
Integrating with the boundary conditions that at t one obtains:
'/z (Kc, - n,,K '12
In
- 1) __ P
