<?php


$array[] = array(
   'name'=>'name1',
   'email'=>'email1',
   'empty'=>''
);
$array[] = array(
   'name'=>'name2',
   'email'=>'email2',
   'empty'=>''
);
$array[] = array(
   'name'=>'',
   'email'=>'',
   'empty'=>''
);


$array = array_map('array_filter', $array);

print_r($array);

Array
(
    [0] => Array
        (
            [name] => name1
            [email] => email1
        )

    [1] => Array
        (
            [name] => name2
            [email] => email2
        )

    [2] => Array
        (
        )

)