time_gap = 4;
no_of_iterations = t_max/time_gap + 1;
hold on 
for i = 1:(no_of_iterations-0)
    %solution = A(:,1+time_gap*(i-1)/delta_t)+Ab(:,1+time_gap*(i-1)/delta_t);
    solution = ex(:,1+time_gap*(i-1)/delta_t);
    set(gca,'FontSize',20)
    plot(0:delta_z:H+vb,solution,'LineWidth', 2)
    %semilogy(0:delta_z:H+vb, solution, 'LineWidth', 2)
    xlabel('z')
    ylabel({'live cell fraction: \epsilon_x(z,t)'})
    %ylabel({'antimicrobial ion concentration: A(z,t)'})
    ylabel({'antimicrobial ion concentration:'; 'A(z,t) + A_b(z,t)'});
    ylim([0,inf])
    xlim([0,inf])
    %set(gca, 'YScale', 'log');
    annotation('arrow',[0.4,0.4],[.15,.35])
    %annotation('arrow',[.8,.8],[.4,.9])
end 
hold off