Plot 3D implicit function

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Dear all,

I want to plot the following function C(x,y,z,t) with C and t being fixed, so we can get the implicit function of z in terms of x and y.

The plot should look like with C and t are known. x, y in the interval of [0 15].

I write a code like this, but it gives an empty figure, no geometry is shown in the figure. Could anyone help me identify the error or give me some other solutions to produce such plots

 u0=0.5;   v0=u0;  w0= -1; 
x0=5; y0=x0; z0=x0; % initial injection position
D0=0.1;
U=sqrt(u0^2+v0^2+w0^2);
lim=10; 
N=200;
c0=0.01;
t=0.1;
f=@(x,y,z) 1./(8*abs(u0*v0*w0).*sqrt((pi*D0*t).^3.*x.*y.*z.*x0.*y0.*z0)).*(x./x0).^(-2*D0*u0).*(y./y0).^(-2*D0*v0).*(z./z0).^(-2*D0*w0)...
    .*exp(4.*D0.*t./((1/u0^2.*(log(x./x0)).^2+1/v0^2.*(log(y./y0)).^2+1/w0^2.*(log(z./z0)).^2)+(3+D0.^2.*U.^2).*t.^2))-c0;
interval = [0 10 0 10 0 10];
fimplicit3(f);