Използвайте LIKE/regex с променлива в mongoid

searchterm = (params[:searchlogparams][:searchterm])
@tweets = Tweet.any_of({ :text => Regexp.new ("/.*"+searchterm+".*/") })

или

searchterm = (params[:searchlogparams][:searchterm])
@tweets = Tweet.any_of({ :text => /.*#{searchterm}.*/ })